Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of...

51
b c τ b c τ CP

Transcript of Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of...

Page 1: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

Averages of b-hadron c-hadron and τ -lepton properties

as of summer 2016

Heavy Flavor Averaging Group (HFAG)

N Body1

1Authors will be dened later

May 22 2017

Abstract

This article reports world averages of measurements of b-hadron c-hadron and τ -leptonproperties obtained by the Heavy Flavor Averaging Group (HFAG) using results availablethrough summer 2016 For the averaging common input parameters used in the variousanalyses are adjusted (rescaled) to common values and known correlations are takeninto account The averages include branching fractions lifetimes neutral meson mixingparameters CP violation parameters parameters of semileptonic decays and CKM matrixelements

1

Contents

1 Introduction 3

2 D decays 521 Interplay of direct and indirect CP violation 622 Semileptonic decays 9

221 Introduction 9222 DrarrP`ν` decays 9223 Form factor parameterizations 9224 Simple pole 10225 z expansion 10226 Three-pole formalism 11227 Experimental techniques and results 12228 Combined results for the D rarr K`ν` channel 14229 Combined results for the D rarr π`ν` channel 162210 Vcs and Vcd determination 162211 DrarrV `ν` decays 202212 Form factor measurements 21

23 Excited D(s) mesons 2524 Rare and forbidden decays 35

References 44

2

1 Introduction

Flavor dynamics is an important element in understanding the nature of particle physics Theaccurate knowledge of properties of heavy avor hadrons especially b hadrons plays an essentialrole for determining the elements of the Cabibbo-Kobayashi-Maskawa (CKM) weak-mixingmatrix [12] The operation of the Belle and BABAR e+eminus B factory experiments led to a largeincrease in the size of available B-meson D-hadron and τ -lepton samples enabling dramaticimprovement in the accuracies of related measurements The CDF and D0 experiments at theFermilab Tevatron have also provided important results in heavy avour physics most notablyin the B0

s sector In the D-meson sector the dedicated e+eminus charm factory experiments CLEOc

and BESIII have made signicant contributions Run I of the CERN Large Hadron Colliderdelivered high luminosity enabling the collection of even higher statistics samples of b andc hadrons and thus a further leap in precision in many areas at the ATLAS CMS and(especially) LHCb experiments With the LHC Run II ongoing further improvements arekeenly anticipated

The Heavy Flavor Averaging Group (HFAG) was formed in 2002 to continue the activities ofthe LEP Heavy Flavor Steering group [3] This group was responsible for calculating averages ofmeasurements of b-avor related quantities HFAG has evolved since its inception and currentlyconsists of seven subgroups

bull the B Lifetime and Oscillations subgroup provides averages for b-hadron lifetimes b-hadron fractions in Υ (4S) decay and pp or pp collisions and various parameters governingB0-B0 and BsB

0s mixing

bull the Unitarity Triangle Parameters subgroup provides averages for time-dependent CPasymmetry parameters and studies of B rarr DK decays and resulting determinations ofthe angles of the CKM unitarity triangle

bull the Semileptonic B Decays subgroup provides averages for inclusive and exclusive B-decay branching fractions and subsequent determinations of the CKM matrix elements|Vcb| and |Vub|

bull the B to Charm Decays subgroup provides averages of branching fractions for B decaysto nal states involving open charm or charmonium mesons

bull the Rare Decays subgroup provides averages of branching fractions and CP asymmetriesfor charmless radiative leptonic and baryonic B-meson and b-baryon decays

bull the Charm Physics subgroup provides averages of numerous quantities in the charmsector including branching fractions properties of charm baryons and of excited Dlowastlowast andDsJ mesons averages of D0-D0 mixing and CP and T violation parameters and anaverage value for the Ds decay constant fDs

bull the Tau Physics subgroup provides documentation and averages for a selection of τlepton quantities that most prot from the adoption of the HFAG prescriptions Inparticular the τ lepton branching fractions uncertainties and correlations are obtainedfrom a global t of the experimental results and this information is further elaboratedto compute several lepton universality tests and the CKM matrix element |Vus| The

3

τ lepton-avor-violating decays are documented and combinations of upper limits arecomputed

The Lifetime and Oscillations and Semileptonic subgroups were formed from the mergerof four LEP working groups The Unitary Triangle B to Charm Decays and Rare De-cays subgroups were formed to provide averages for new results obtained from the B factoryexperiments (and now also from the Fermilab Tevatron and CERN LHC experiments) TheCharm and Tau subgroups were formed more recently in response to the wealth of new dataconcerning D and τ physics Subgroups typically include representatives from Belle BABARand LHCb plus when relevant CLEO CDF and D0

This article is an update of the last HFAG preprint which used results available at leastthrough early 2012 [4] Here we report world averages using results available at least throughsummer 2014 In some cases results made available in the latter part of 2014 have been in-cluded1 In general we use all publicly available results that have written documentationThese include preliminary results presented at conferences or workshops However we do notuse preliminary results that remain unpublished for an extended period of time or for whichno publication is planned Close contacts have been established between representatives fromthe experiments and members of subgroups that perform averaging to ensure that the data areprepared in a form suitable for combinations

In the case of obtaining a world average for which χ2dof gt 1 where dof is the numberof degrees of freedom in the average calculation we do not usually scale the resulting erroras is presently done by the Particle Data Group [5] Rather we examine the systematics ofeach measurement to better understand them Unless we nd possible systematic discrepanciesbetween the measurements we do not apply any additional correction to the calculated errorWe provide the condence level of the t as an indicator for the consistency of the measurementsincluded in the average In case some special treatment was necessary to calculate an averageor if an approximation used in an average calculation might not be suciently accurate (egassuming Gaussian errors when the likelihood function indicates non-Gaussian behavior) weinclude a warning message

Chapter describes the methodology used for calculating averages In the averagingprocedure common input parameters used in the various analyses are adjusted (rescaled) tocommon values and where possible known correlations are taken into account Chapters present world average values from each of the subgroups listed above A brief summary ofthe averages presented is given in Chapter A complete listing of the averages and plotsincluding updates since this document was prepared are also available on the HFAG web site

httpwwwslacstanfordeduxorghfag

1 Particularly important new results have been included whenever possible The precise cut-o date forincluding results in the averages varies between subgroups

4

2 D decays

5

21 Interplay of direct and indirect CP violation

In decays of D0 mesons CP asymmetry measurements have contributions from both directand indirect CP violation as discussed in Sec The contribution from indirect CP viola-tion depends on the decay-time distribution of the data sample [6] This section describes acombination of measurements that allows the extraction of the individual contributions of thetwo types of CP violation At the same time the level of agreement for a no-CP -violationhypothesis is tested The observables are

AΓ equivτ(D 0rarrh+hminus)minus τ(D0rarrh+hminus)

τ(D 0rarrh+hminus) + τ(D0rarrh+hminus) (1)

where h+hminus can be K+Kminus or π+πminus and

∆ACP equiv ACP(K+Kminus)minus ACP(π+πminus) (2)

where ACP are time-integrated CP asymmetries The underlying theoretical parameters are

adirCP equiv

|AD0rarrf |2 minus |AD 0rarrf |2

|AD0rarrf |2 + |AD 0rarrf |2

aindCP equiv 1

2

[(∣∣∣∣qp∣∣∣∣+

∣∣∣∣pq∣∣∣∣)x sinφminus

(∣∣∣∣qp∣∣∣∣minus ∣∣∣∣pq

∣∣∣∣) y cosφ

] (3)

where ADrarrf is the amplitude for D rarr f [7] We use the following relations between theobservables and the underlying parameters [8]

AΓ = minusaindCP minus adir

CPyCP

∆ACP = ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

+ adirCPyCP

∆〈t〉τ

(4)

asymp ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

(5)

The rst relation constrains mostly indirect CP violation and the direct CP violation contri-bution can dier for dierent nal states In the second relation 〈t〉τ denotes the mean decaytime in units of the D0 lifetime ∆X denotes the dierence in quantity X between K+Kminus andπ+πminus nal states and X denotes the average for quantity X We neglect the last term in thisrelation as all three factors are O(10minus2) or smaller and thus this term is negligible with respectto the other two terms Note that ∆〈t〉τ 〈t〉τ and it is expected that |adir

CP| lt |∆adirCP|

because adirCP(K+Kminus) and adir

CP(π+πminus) are expected to have opposite signs [7]A χ2 t is performed in the plane ∆adir

CP vs aindCP For the BABAR result the dierence of

the quoted values for ACP(K+Kminus) and ACP(π+πminus) is calculated adding all uncertainties inquadrature This may overestimate the systematic uncertainty for the dierence as it neglectscorrelated errors however the result is conservative and the eect is small as all measurementsare statistically limited For all measurements statistical and systematic uncertainties areadded in quadrature when calculating the χ2 We use the current world average value yCP =(0866plusmn 0155) (see Sec ) and the measurements listed in Table 1

6

Table 1 Inputs to the t for direct and indirect CP violation The rst uncertainty listed isstatistical and the second is systematic

Year Experiment Results ∆〈t〉τ 〈t〉τ Reference2012 BABAR AΓ = (009plusmn 026plusmn 006) - - [9]2013 LHCb prompt AΓ(KK) = (minus0035plusmn 0062plusmn 0012) - - [10]

AΓ(ππ) = (0033plusmn 0106plusmn 0014) - -2014 CDF AΓ = (minus012plusmn 012) - - [11]2015 LHCb SL AΓ = (minus0125plusmn 0073) - - [12]2015 Belle AΓ = (minus003plusmn 020plusmn 007) - - [13]2008 BABAR ACP(KK) = (000plusmn 034plusmn 013)

ACP(ππ) = (minus024plusmn 052plusmn 022) 000 100 [14]2012 Belle prel ∆ACP = (minus087plusmn 041plusmn 006) 000 100 [15]2012 CDF ∆ACP = (minus062plusmn 021plusmn 010) 025 258 [16]2014 LHCb SL ∆ACP = (014plusmn 016plusmn 008) 001 107 [17]2016 LHCb prompt ∆ACP = (minus010plusmn 008plusmn 003) 012 210 [18]

In this t AΓ(KK) and AΓ(ππ) are assumed to be identical This assumption is sup-ported by all measurements to date A signicant relative shift due to nal-state dependentAΓ values between ∆ACP measurements with dierent mean decay times is excluded by thesemeasurements

The combination plot (see Fig 1) shows the measurements listed in Table 1 for ∆ACP andAΓ where the bands represent plusmn1σ intervals The point of no CP violation (00) is shownas a lled circle and two-dimensional 68 CL 95 CL and 997 CL regions are plotted asellipses The best t value is indicated by a cross showing the one-dimensional errors

From the t the change in χ2 from the minimum value for the no-CPV point (00) is55 which corresponds to a CL of 65 times 10minus2 for two degrees of freedom Thus the data areconsistent with the no-CP -violation hypothesis at 65 CL This p-value corresponds to 18σThe central values and plusmn1σ uncertainties for the individual parameters are

aindCP = (0056plusmn 0040)

∆adirCP = (minus0137plusmn 0070) (6)

Compared to the previous average the tension in the dierence between direct CP violationin the two nal states reduced while the common indirect CP violation moved away from theno CP violation point by about one standard deviation

7

0015 0010 0005 0000 0005 0010

aindCP

0015

0010

0005

0000

0005

0010

0015

∆adirCP

Contours contain 68 95 99 CL

CD

F

LHC

b S

L

LHC

b p

rom

pt

BaBarBelleCDF KK+ππLHCb SL KK+ππ

LHCb prompt KKLHCb prompt ππ

HFAG-charmWinter 16

no CPV

BaBar

Belle

CDF

LHCb

Figure 1 Plot of all data and the t result Individual measurements are plotted as bandsshowing their plusmn1σ range The no-CPV point (00) is shown as a lled circle and the best tvalue is indicated by a cross showing the one-dimensional uncertainties Two-dimensional 68CL 95 CL and 997 CL regions are plotted as ellipses

8

22 Semileptonic decays

221 Introduction

Semileptonic decays of D mesons involve the interaction of a leptonic current with a hadroniccurrent The latter is nonperturbative and cannot be calculated from rst principles thus it isusually parameterized in terms of form factors The transition matrix element is written

M = minusi GFradic2Vcq L

microHmicro (7)

where GF is the Fermi constant and Vcq is a CKM matrix element The leptonic current Lmicro isevaluated directly from the lepton spinors and has a simple structure this allows one to extractinformation about the form factors (in Hmicro) from data on semileptonic decays [19] Converselybecause there are no strong nal-state interactions between the leptonic and hadronic systemssemileptonic decays for which the form factors can be calculated allow one to determine Vcq [2]

222 DrarrP`ν` decays

When the nal state hadron is a pseudoscalar the hadronic current is given by

Hmicro = 〈P (p)|qγmicroc|D(pprime)〉 = f+(q2)

[(pprime + p)micro minus

m2D minusm2

P

q2qmicro

]+ f0(q2)

m2D minusm2

P

q2qmicro (8)

where mD and pprime are the mass and four momentum of the parent D meson mP and p are thoseof the daughter meson f+(q2) and f0(q2) are form factors and q = pprime minus p Kinematics requirethat f+(0) = f0(0) The contraction qmicroL

micro results in terms proportional to m` [20] and thus for` = e the terms proportionals to qmicro in Eq (8) are negligible For light leptons only the f+(q2)vector form factor is relevant and the dierential partial width is

dΓ(D rarr P`ν`)

dq2 d cos θ`=

G2F |Vcq|2

32π3plowast 3|f+(q2)|2 sin θ2

` (9)

where plowast is the magnitude of the momentum of the nal state hadron in the D rest frame andθ` is the angle of the lepton in the `ν rest frame with respect to the direction of the pseudoscalarmeson in the D rest frame

223 Form factor parameterizations

The form factor is traditionally parameterized with an explicit pole and a sum of eective poles

f+(q2) =f+(0)

(1minus α)

[(1

1minus q2m2pole

)+

Nsumk=1

ρk1minus q2(γkm2

pole)

] (10)

where ρk and γk are expansion parameters and α is a parameter that normalizes the formfactor at q2 = 0 f+(0) The parameter mpole is the mass of the lowest-lying cq resonance withthe vector quantum numbers this is expected to provide the largest contribution to the formfactor for the crarr q transition The sum over N gives the contribution of higher mass statesFor example for D rarr π transitions the dominant resonance is expected to be Dlowast(2010) andthus mpole = mDlowast(2010) For D rarr K transitions the dominant contribution is expected from

Dlowasts(2112) with mpole = mDlowasts (2112)

9

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Comparison between CLEO-c and BABAR results for the quantities q2H20 (q2) and

q2h0(q2)H0(q2)

Table 11 Results for rV and r2 from various experiments

Experiment Ref rV r2

D+ rarr Klowast0l+ν

E691 [54] 20plusmn 06plusmn 03 00plusmn 05plusmn 02E653 [55] 200plusmn 033plusmn 016 082plusmn 022plusmn 011E687 [56] 174plusmn 027plusmn 028 078plusmn 018plusmn 011

E791 (e) [57] 190plusmn 011plusmn 009 071plusmn 008plusmn 009E791 (micro) [58] 184plusmn011plusmn009 075plusmn008plusmn009Beatrice [59] 145plusmn 023plusmn 007 100plusmn 015plusmn 003FOCUS [60] 1504plusmn0057plusmn0039 0875plusmn0049plusmn0064

D0 rarr K0πminusmicro+ν

FOCUS [61] 1706plusmn0677plusmn0342 0912plusmn0370plusmn0104BABAR [62] 1493plusmn 0014plusmn 0021 0775plusmn 0011plusmn 0011

D+s rarr φ e+νBABAR [63] 1849plusmn0060plusmn0095 0763plusmn0071plusmn0065

D0 D+ rarr ρ eνCLEO [64] 140plusmn025plusmn003 057plusmn018plusmn006

23

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

HFLAV())+-amp

Figure 7 A comparison of r2 (lled inverted triangles) and rV (open triangles) values fromvarious experiments The rst seven measurements are for D+ rarr Kminusπ+l+νl decays Alsoshown as a line with 1-σ limits is the average of these The last two points are D+

s and D0

decays

24

23 Excited D(s) mesons

Excited charm meson states have received increased attention since the rst observation ofstates that could not be accommodated by QCD predictions [70 71 72 73] Tables 12 13and 14 summarize recent measurements of the masses and widths of excited D and Ds mesonsrespectively If a preferred assignment of spin and parity was measured it is listed in the columnJP where the label natural denotes JP = 0minus 1+ 2minus and unnatural JP = 0+ 1minus 2+ Ifpossible an average mass and width was calculated which is listed in the gray shaded rowThe calculation of the averages assumes no correlation between individual measurements Asummary of the averaged masses and widths is shown in Figure 8

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

0+ 1+ 2+ 1minus 1 3minus

unnatu

ral

Dlowast s0

(2317)plusmn

Ds1

(2460)plusmn

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn D

sJ(3

040)plusmn

HFAG-charmAugust 2016

(a)

Mas

s[M

eVc

2]

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

0+ 1+ 2+ 0minus 1minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ralDlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn

D(2

550)0

D(2

580)0

D(2

600)0

D(2

600)plusmn

Dlowast (

2640)plusmn

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(b)

Mas

s[M

eVc

2]

0

50

100

150

200

250

300

350

400

450

500

550

1+ 2+ 1minus 1 3minus

unnatu

ral

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn

DsJ

(3040)plusmn

HFAG-charmAugust 2016

(c)

Wid

th[M

eV]

50100150200250300350400450500550600650700

0+ 1+ 2+ 0minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ral

Dlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn D(2

550)0

D(2

580)0

D(2

600)0

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(d)

Wid

th[M

eV]

Figure 8 Averaged masses for Ds mesons are shown in subgure (a) and for D mesons insubgure (b) The average widths for Ds mesons are shown in subgure (c) and for D mesonsin subgure (d) The vertical shaded regions distinguish between dierent spin parity states

The masses and widths of narrow (Γ lt 50 MeV) orbitally excited D mesons (denotedDlowastlowast) both neutral and charged are well established Measurements of broad states (Γ sim200400 MeV) are less abundant as identifying the signal is more challenging There is aslight discrepancy between the Dlowast0(2400)0 masses measured by the Belle [74] and FOCUS [75]experiments No data exist yet for the D1(2430)plusmn state Dalitz plot analyses of B rarr D(lowast)ππ

25

decays strongly favor the assignments 0+ and 1+ for the spin-parity quantum numbers of theDlowast0(2400)0Dlowast0(2400)plusmn and D1(2430)0 states respectively The measured masses and widthsas well as the JP values are in agreement with theoretical predictions based on potentialmodels [76777879]

Tables 15 and 16 summarizes the branching fractions of B mesons decays to excited D andDs states respectively It can be noted that the branching fractions for B mesons decaying to anarrow Dlowastlowast state and a pion are similar for charged and neutral B initial states the branchingfractions to a broad Dlowastlowast state and π+ are much larger for B+ than for B0 This may be dueto the fact that color-suppressed amplitudes contribute only to the B+ decay and not to theB0 decay (for a theoretical discussion see Ref [8081]) Measurements of individual branchingfractions of D mesons are dicult due to the unknown fragmentation of cc rarr Dlowastlowast or due tothe unknown B rarr DlowastlowastX branching fractions

The discoveries of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn have triggered increased interest in prop-erties of and searches for excited Ds mesons (here generically denoted D

lowastlowasts ) While the masses

and widths of Ds1(2536)plusmn and Ds2(2573)plusmn states are in relatively good agreement with po-tential model predictions the masses of Dlowasts0(2317)plusmn and Ds1(2460)plusmn states are signicantlylower than expected (see Ref [82] for a discussion of cs models) Moreover the mass splittingbetween these two states greatly exceeds that between the Ds1(2536)plusmn and Ds2(2573)plusmn Theseunexpected properties have led to interpretations of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn as exoticfour-quark states [8384]

While there are few measurements of the JP values of Dlowasts0(2317)plusmn andDs1(2460)plusmn the avail-able data favor 0+ and 1+ respectively A molecule-like (DK) interpretation of the Dlowasts0(2317)plusmn

and Ds1(2460)plusmn [8384] that can account for their low masses and isospin-breaking decay modesis tested by searching for charged and neutral isospin partners of these states thus far suchsearches have yielded negative results Therefore the subset of models that predict equal pro-duction rates for dierent charged states is excluded The molecular picture can also be testedby measuring the rates for the radiative processes Dlowasts0(2317)plusmnDs1(2460)plusmn rarr D

(lowast)s γ and com-

paring to theoretical predictions The predicted rates however are below the sensitivity ofcurrent experiments

Another model successful in explaining the total widths and the Dlowasts0(2317)plusmn Ds1(2460)plusmn

mass splitting is based on the assumption that these states are chiral partners of the groundstates D+

s and Dlowasts [85] While some measured branching fraction ratios agree with predictedvalues further experimental tests with better sensitivity are needed to conrm or refute thisscenario A summary of the mass dierence measurements is given in Table 17

Measurements by BABAR [86] and LHCb [87] rst indicated the existence of a strange-charm DlowastsJ(2860)plusmn meson An LHCb study of B0

s rarr D0Kminusπ+ decays in which they searchedfor excited Ds mesons [88] showed with 10σ signicance that this state is comprised of twodierent particles one of spin 1 and one of spin 3 This represents the rst measurement of aheavy avored spin-3 particle and the rst observation B mesons decays to spin 3 particlesA subsequent study of DsJ mesons by the LHCb collaboration [89] supports the natural parityassignment for this state (JP = 3minus) This study also shows weak evidence for a further structureat a mass around 3040 MeVc2 with unnatural parity which was rst hinted at by a Babaranalysis [86]

Recent evidence shows that the 1D family of charm resonances can be explored in the Dalitzplot analyses of B-meson decays in the same way as seen for the charm-strange resonances TheLHCb collaboration performed an analysis of B0 rarr D0π+πminus decays in which they measured

26

the spin-parity assignment of the stateDlowast3(2760)plusmn which was observed previously by BABAR [29]and LHCb [30] to be JP = 3minus The measurement suggests a spectroscopic assignment of 3D3This is the second observation of a spin-3 charm meson

Other observed excited Ds states include Ds1(2700)plusmn and Ds2(2573)plusmn The properties ofboth (mass width JP ) have been measured and determined in several analyses A theoreticaldiscussion [90] investigates the possibility that theDs1(2700)plusmn could represent radial excitationsof the Dlowastplusmns Similarly the Ds1(2860)plusmn and DsJ(3040)plusmn could be excitations of Dlowasts0(2317)plusmn andDs1(2460)plusmn or Ds1(2536)plusmn respectively

Table 18 summarizes measurements of the polarization amplitude AD (sometimes also re-ferred as helicity parameter) which describes the initial polarization of the D meson In Dlowastlowast

meson decay the helicity distribution varies like 1 + AD cos2 θH where θH is the angle in theDlowast rest frame between the two pions emitted by decay Dlowastlowast rarr Dlowastπ and the Dlowast rarr Dπ Theparameter is sensitive to possible S-wave contributions in the decay In the case of an unpolar-ized D meson decay decaying purely via D-wave the polarization amplitude is predicted to giveAD = 3 Studies of the D1(2420)0 meson by the ZEUS and BABAR collaborations suggest thatthere is an S-wave admixture in the decay which is contrary to Heavy Quark Eective Theorycalculations [9192]

27

Table 12 Recent measurements of mass and width for dierent excited Ds mesons Thecolumn JP list the most signicant assignment of spin and parity If possible an average massor width is calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowasts0(2317)plusmn 0+

D+s π

0 23196plusmn 02plusmn 14 BABAR [93]D+s π

0 23173plusmn 04plusmn 08 BABAR [73]

23180plusmn 08 Our average

Ds1(2460)plusmn 1+

D+s π

0γD+s γD

+s π

+πminus 24601plusmn 02plusmn 08 BABAR [93]D+s π

0γ 2458plusmn 10plusmn 10 BABAR [73]

24596plusmn 07 Our average

Ds1(2536)plusmn 1+

Dlowast+K0S 25357plusmn 06plusmn 05 DOslash [94]

Dlowast+K0S D

lowast0K+ 253478plusmn 031plusmn 040 BABAR [95]D+s π

+πminus 25346plusmn 03plusmn 07 BABAR [93]Dlowast+K0

S Dlowast0K+ 25350plusmn 06plusmn 10 E687 [96]

Dlowast0K+ 25353plusmn 02plusmn 05 CLEO [97]Dlowast+K0

S 25348plusmn 06plusmn 06 CLEO [97]Dlowast0K+ 25352plusmn 05plusmn 15 ARGUS [98]Dlowast+K0

S 25356plusmn 07plusmn 04 CLEO [99]Dlowast+K0

S 25359plusmn 06plusmn 20 ARGUS [100]Dlowast+K0

S 092plusmn 003plusmn 004 BABAR [101]

253510plusmn 026 092plusmn 005 Our average

Dlowasts2(2573)plusmn 2+

D0K+ Dlowast+K0S 256839plusmn 029plusmn 026 169plusmn 05plusmn 06 LHCb [102]

D+K0S D

0K+ 25694plusmn 16plusmn 05 121plusmn 45plusmn 16 LHCb [103]D+K0

S D0K+ 25722plusmn 03plusmn 10 271plusmn 06plusmn 56 BABAR [104]

D0K+ 257425plusmn 33plusmn 16 104plusmn 83plusmn 30 ARGUS [105]D0K+ 25732+17

minus16 plusmn 09 16+5minus4 plusmn 3 CLEO [106]

256908plusmn 035 169plusmn 08 Our average

Dlowasts1(2700)plusmn 1minus

Dlowast+K0S D

lowast0K+ 27323plusmn 43plusmn 58 136plusmn 19plusmn 24 LHCb [89]D0K+ 2699+14

minus7 127+24minus19 BABAR [107]

Dlowast+K0S D

lowast0K+ 27092plusmn 19plusmn 45 1158plusmn 73plusmn 121 LHCb [87]DKDlowastK 2710plusmn 2+12

minus7 149plusmn 7+39minus52 BABAR [86]

D0K+ 2708plusmn 9+11minus10 108plusmn 2+36

minus31 Belle [108]

27120plusmn 15 1215plusmn 102 Our average

Dlowasts1(2860)plusmn 1 D0K+ 2859plusmn 12plusmn 24 159plusmn 23plusmn 77 LHCb [88]

Dlowasts3(2860)plusmn 3minusDlowast+K0

S Dlowast0K+ 28671plusmn 43plusmn 19 50plusmn 11plusmn 13 LHCb [89]

D0K+ 28605plusmn 26plusmn 65 53plusmn 7plusmn 7 LHCb [88]

28650plusmn 39 522plusmn 86 Our average

DsJ(3040)plusmn Unnatural DlowastK 3044plusmn 8+30minus5 239plusmn 35+46

minus42 BABAR (m amp Γ) + LHCb(JP ) [86]+ [89]

28

Table 13 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast0(2400)0 0+

D+πminus 2297plusmn 8plusmn 20 273plusmn 12plusmn 48 BABAR [109]D+πminus 2308plusmn 17plusmn 32 276plusmn 21plusmn 63 Belle [74]D+πminus 2407plusmn 21plusmn 35 240plusmn 55plusmn 59 Focus [75]

23182plusmn 169 2674plusmn 356 Our average

Dlowast0(2400)plusmn 0+

D0π+ 2349plusmn 6plusmn 1plusmn 4 217plusmn 13plusmn 5plusmn 12 LHCb [110]D0π+ 2360plusmn 15plusmn 12plusmn 28 255plusmn 26plusmn 20plusmn 47 LHCb [111]D0π+ 2403plusmn 14plusmn 35 283plusmn 24plusmn 34 Focus(m ampΓ) + Belle(JP ) [75] + [112]

23506plusmn 59 2337plusmn 155 Our average

D1(2420)0 1+

Dlowast+πminus 24196plusmn 01plusmn 07 352plusmn 04plusmn 09 LHCb [30]Dlowast+πminus 24231plusmn 15+04

minus10 388plusmn 5+19minus54 Zeus [113]

Dlowast+πminus 24201plusmn 01plusmn 08 314plusmn 05plusmn 13 BABAR [29]Dlowast+πminus 200plusmn 17plusmn 13 CDF [114]D0π+πminus 2426plusmn 3plusmn 1 24plusmn 7plusmn 8 Belle [115]Dlowast+πminus 24214plusmn 15plusmn 09 237plusmn 27plusmn 40 Belle [74]Dlowast+πminus 2421+1

minus2 plusmn 2 20+6minus5

+3minus3 CLEO [116]

Dlowast+πminus 2422plusmn 2plusmn 2 15plusmn 8plusmn 4 E687 [96]Dlowast+πminus 2428plusmn 3plusmn 2 23+8

minus6+10minus4 CLEO [99]

Dlowast+πminus 2414plusmn 2plusmn 5 13plusmn 6+10minus5 ARGUS [117]

Dlowast+πminus 2428plusmn 8plusmn 5 58plusmn 14plusmn 10 TPS [118]

24205plusmn 05 317plusmn 07 Our average

D1(2420)plusmn 1+

Dlowast0π+ 24219plusmn 47+34minus12 Zeus [113]

D+πminusπ+ 2421plusmn 2plusmn 1 21plusmn 5plusmn 8 Belle [115]Dlowast0π+ 2425plusmn 2plusmn 2 26+8

minus7 plusmn 4 CLEO [119]Dlowast0π+ 2443plusmn 7plusmn 5 41plusmn 19plusmn 8 TPS [118]

24232plusmn 16 252plusmn 60 Our average

D1(2430)0 1+ Dlowast+πminus 2427plusmn 26plusmn 25 384+107minus75 plusmn 74 Belle [74]

Dlowast2(2460)0 2+

Dlowast+πminus 24640plusmn 14plusmn 05plusmn 02 438plusmn 29plusmn 17plusmn 06 LHCb [120]Dlowast+πminus 24604plusmn 04plusmn 12 432plusmn 12plusmn 30 LHCb [30]D+πminus 24604plusmn 01plusmn 01 456plusmn 04plusmn 11 LHCb [30]

Dlowast+πminus D+πminus 24625plusmn 24+13minus11 466plusmn 81+59

minus38 Zeus [113]D+πminus 24622plusmn 01plusmn 08 505plusmn 06plusmn 07 BABAR [29]D+πminus 24604plusmn 12plusmn 22 418plusmn 25plusmn 29 BABAR [109]D+πminus 492plusmn 23plusmn 13 CDF [114]D+πminus 24616plusmn 21plusmn 33 456plusmn 44plusmn 67 Belle [74]D+πminus 24645plusmn 11plusmn 19 387plusmn 53plusmn 29 Focus [75]D+πminus 2465plusmn 3plusmn 3 28+8

minus7 plusmn 6 CLEO [116]D+πminus 2453plusmn 3plusmn 2 25plusmn 10plusmn 5 E687 [96]Dlowast+πminus 2461plusmn 3plusmn 1 20+9

minus12+9minus10 CLEO [99]

D+πminus 2455plusmn 3plusmn 5 15+13minus10

+5minus10 ARGUS [121]

D+πminus 2459plusmn 3plusmn 2 20plusmn 10plusmn 5 TPS [118]

246049plusmn 017 4752plusmn 065 Our average

29

Table 14 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast2(2460)plusmn 2+

D0π+ 24686plusmn 06plusmn 00plusmn 03 473plusmn 15plusmn 03plusmn 06 LHCb [110]D0π+ 24656plusmn 18plusmn 05plusmn 12 460plusmn 34plusmn 14plusmn 29 LHCb [111]D0π+ 24631plusmn 02plusmn 06 486plusmn 13plusmn 19 LHCb [30]

Dlowast0π+ D0π+ 24606plusmn 44+36minus08 Zeus [113]

D0π+ 24654plusmn 02plusmn 11 BABAR [29]D0π+ 24657plusmn 18+14

minus48 497plusmn 38plusmn 64 Belle [112]D0π+ 24676plusmn 15plusmn 08 341plusmn 65plusmn 42 Focus [75]D0π+ 2463plusmn 3plusmn 3 27+11

minus8 plusmn 5 CLEO [119]D0π+ 2453plusmn 3plusmn 2 23plusmn 9plusmn 5 E687 [96]D0π+ 2469plusmn 4plusmn 6 ARGUS [122]

246555plusmn 040 467plusmn 12 Our average

D(2550)0 0minus Dlowast+πminus 25394plusmn 45plusmn 68 130plusmn 12plusmn 13 BABAR [29]

D(2580)0 Unnatural Dlowast+πminus 25795plusmn 34plusmn 55 1175plusmn 178plusmn 460 LHCb [30]

D(2600)0 Natural D+πminus 26087plusmn 24plusmn 25 93plusmn 6plusmn 13 BABAR [29]

D(2600)plusmn Natural D0π+ 26213plusmn 37plusmn 42 BABAR [29]

Dlowast(2640)plusmn 1minus Dlowast+π+πminus 2637plusmn 2plusmn 6 Delphi [123]

Dlowast(2650)0 Natural Dlowast+πminus 26492plusmn 35plusmn 35 1402plusmn 171plusmn 186 LHCb [30]

D(2740)0 Unnatural Dlowast+πminus 27370plusmn 35plusmn 112 732plusmn 134plusmn 250 LHCb [30]

D(2750)0 Dlowast+πminus 27524plusmn 17plusmn 27 71plusmn 6plusmn 11 BABAR [29]

Dlowast1(2760)0 1+

D+πminus 2781plusmn 18plusmn 11plusmn 6 177plusmn 32plusmn 20plusmn 7 LHCb [120]Dlowast+πminus 27611plusmn 51plusmn 65 744plusmn 34plusmn 370 LHCb [30]D+πminus 27601plusmn 11plusmn 37 744plusmn 34plusmn 191 LHCb [30]D+πminus 27633plusmn 23plusmn 23 609plusmn 51plusmn 36 BABAR [29]

27621plusmn 24 651plusmn 58 Our average

Dlowast3(2760)plusmn 3minus

D0π+ 2798plusmn 7plusmn 1plusmn 7 105plusmn 18plusmn 6plusmn 23 LHCb [110]D0π+ 27717plusmn 17plusmn 38 667plusmn 66plusmn 105 LHCb [30]D0π+ 27697plusmn 38plusmn 15 BABAR [29]

27739plusmn 33 723plusmn 115 Our average

30

Table 15 Product of B meson branching fraction and (daughter) excited D meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowast0(2400)0

Bminus rarr Dlowast0(2400)0(rarr D+π+)πminus61plusmn 06plusmn 18 Belle [74]68plusmn 03plusmn 20 BABAR [109]

64plusmn 14 Our average

Bminus rarr Dlowast0(2400)0(rarr D+π+)Kminus 0061plusmn 0019plusmn 0005plusmn 0014plusmn 0004 LHCb [120]

Dlowast0(2400)plusmnB0 rarr Dlowast0(2400)+(rarr D0π+)πminus

077plusmn 005plusmn 003plusmn 003plusmn 004 LHCb [110]060plusmn 013plusmn 027 Belle [112]

076plusmn 007 Our average

B0 rarr Dlowast0(2400)+(rarr D0π+)Kminus 0177plusmn 0026plusmn 0019plusmn 0067plusmn 020 LHCb [111]

D1(2420)0

Bminus rarr D1(2420)0(rarr Dlowast+πminus)πminus 68plusmn 07plusmn 13 Belle [74]

Bminus rarr D1(2420)0(rarr D0π+πminus)πminus 185plusmn 029plusmn 027plusmn 041 Belle [115]

B0 rarr D1(2420)0(rarr Dlowast+πminus)ω 07plusmn 02+01minus00 plusmn 01 Belle [124]

D1(2420)plusmn B0 rarr D1(2420)+(rarr D+πminusπ+)πminus 089plusmn 015plusmn 022 Belle [115]

D1(2430)0Bminus rarr D1(2430)0(rarr Dlowast+πminus)πminus 50plusmn 04plusmn 108 Belle [74]

B0 rarr D1(2430)0(rarr Dlowast+πminus)ω 25plusmn 04+07minus02

+04minus01 Belle [124]

Dlowast2(2460)0

Bminus rarr Dlowast2(2460)0(rarr D+πminus)πminus34plusmn 03plusmn 07 Belle [74]35plusmn 02plusmn 05 BABAR [109]

34plusmn 03 Our average

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)πminus 18plusmn 03plusmn 04 Belle [74]

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)ω 04plusmn 01+00minus01 plusmn 01 Belle [124]

Bminus rarr Dlowast2(2460)0(rarr D+π+)Kminus 0232plusmn 0011plusmn 0006plusmn 0010plusmn 0016 LHCb [120]

Dlowast2(2460)plusmnB0 rarr Dlowast2(2460)+(rarr D0π+)πminus

244plusmn 007plusmn 010plusmn 004plusmn 012 LHCb [110]215plusmn 017plusmn 031 Belle [112]

238plusmn 016 Our average

B0 rarr Dlowast2(2460)+(rarr D0π+)Kminus 0212plusmn 0010plusmn 0011plusmn 0011plusmn 025 LHCb [111]

Dlowast1(2760)0 Bminus rarr Dlowast1(2760)0(rarr D+π+)Kminus 0036plusmn 0009plusmn 0003plusmn 0007plusmn 0002 LHCb [120]

Dlowast3(2760)plusmn B0 rarr Dlowast3(2760)0(rarr D0π+)πminus 0103plusmn 0016plusmn 0007plusmn 0008plusmn 0005 LHCb [110]

31

Table 16 Product of B meson branching fraction and (daughter) excited Ds meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowasts0(2317)plusmnB0 rarr Dlowasts0(2317)+(rarr D+

s π0)Dminus

86+33minus26 plusmn 26 Belle [125]

180plusmn 40+67minus50 BABAR [126]

101+13minus12 plusmn 10plusmn 04 Belle [127]

102plusmn 15 Our average

B+ rarr Dlowasts0(2317)+(rarr D+s π

0)D0 80+13minus12 plusmn 10plusmn 04 Belle [127]

B0 rarr Dlowasts0(2317)+(rarr D+s π

0)Kminus 053+015minus013 plusmn 016 Belle [128]

Ds1(2460)plusmn

B0 rarr Ds1(2460)+(rarr Dlowast+s π0)Dminus227+73

minus62 plusmn 68 Belle [125]280plusmn 80+112

minus78 BABAR [126]

247plusmn 76 Our average

B0 rarr Ds1(2460)+(rarr Dlowast+s γ)Dminus82+22minus19 plusmn 25 Belle [125]

80plusmn 20+32minus23 BABAR [126]

81plusmn 23 Our average

Ds1(2460)+ rarr Dlowast+s π0 (56plusmn 13plusmn 9) BABAR [129]

Ds1(2460)+ rarr Dlowast+s γ (16plusmn 4plusmn 3) BABAR [129]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dminus 171plusmn 048plusmn 032 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast+K0)Dminus 261plusmn 103plusmn 031 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dlowastminus 332plusmn 088plusmn 066 BABAR [95]

Ds1(2536)plusmnB0 rarr Ds1(2536)+(rarr Dlowast+K0)Dlowastminus 500plusmn 151plusmn 067 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)D0 216plusmn 052plusmn 045 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)D0 230plusmn 098plusmn 043 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)Dlowast0 546plusmn 117plusmn 104 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)Dlowast0 392plusmn 246plusmn 083 BABAR [95]

Ds2(2573)plusmnB0 rarr Ds2(2573)(rarr D0K+)Dminus 034plusmn 017plusmn 005 BABAR [107]

B+ rarr Ds2(2573)(rarr D0K+)D0 008plusmn 14plusmn 005 BABAR [107]

Ds1(2700)plusmn B+ rarr Ds1(2700)+(rarr D0K+)D0

113plusmn 22+14minus28 Belle [108]

502plusmn 071plusmn 093 BABAR [107]

583plusmn 109 Our average

B0 rarr Ds1(2700)+(rarr D0K+)Dminus 714plusmn 096plusmn 069 BABAR [107]

32

Table 17 Mass dierence measurements for excited D mesons

Resonance Relative to ∆m [MeVc2] Measured by Reference

Dlowast1(2420)0 Dlowast+4102plusmn 21plusmn 09 Zeus [130]4117plusmn 07plusmn 04 CDF [114]

4115plusmn 08 Our average

D1(2420)plusmn Dlowast1(2420)0 4+2minus3 plusmn 3 CLEO [119]

Dlowast2(2460)0 D+ 5939plusmn 06plusmn 05 CDF [114]

Dlowast+ 4588plusmn 37+12minus13 Zeus [130]

Dlowast2(2460)plusmn Dlowast2(2460)0

31plusmn 19plusmn 09 Focus [75]minus2plusmn 4plusmn 4 CLEO [119]14plusmn 5plusmn 8 ARGUS [122]

30plusmn 19 Our average

Dlowasts0(2317)plusmn Dplusmns

3487plusmn 05plusmn 07 Belle [72]3500plusmn 12plusmn 10 CLEO [71]3513plusmn 21plusmn 19 Belle [125]

3492plusmn 07 Our average

Ds1(2460)plusmn

Dlowastplusmns

3441plusmn 13plusmn 11 Belle [72]3512plusmn 17plusmn 10 CLEO [71]3468plusmn 16plusmn 19 Belle [125]

3471plusmn 11 Our average

Dplusmns

4910plusmn 13plusmn 19 Belle [72]4914plusmn 09plusmn 15 Belle [72]

4913plusmn 14 Our average

Ds1(2536)plusmnDlowast(2010)plusmn

52483plusmn 001plusmn 004 BABAR [101]52530+044

minus041 plusmn 010 Zeus [130]5253plusmn 06plusmn 01 ALEPH [131]

52484plusmn 004 Our average

Dlowast(2007)0 5287plusmn 19plusmn 05 ALEPH [131]

Dlowasts2(2573)plusmn D0 704plusmn 3plusmn 1 ALEPH [131]

33

Table 18 Measurements of polarization amplitudes for excited D mesons

Resonance AD Measured by Reference

D1(2420)0

78+67minus27

+46minus18 ZEUS [113]

572plusmn 025 BABAR [29]59+30minus17

+24minus10 ZEUS [130]

38plusmn 06plusmn 08 BABAR [132]

561plusmn 024 Our average

D1(2420)plusmn 38plusmn 06plusmn 08 BABAR [132]

Dlowast2(2460)0 minus116plusmn 035 ZEUS [113]

D(2750)0 minus033plusmn 028 BABAR [29]

34

24 Rare and forbidden decays

This section provides a summary of rare and forbidden charm decays in tabular form The decaymodes can be categorized as avor-changing neutral currents lepton-avor-violating lepton-number-violating and both baryon- and lepton-number-violating decays Figures 9-11 plot theupper limits for D0 D+ D+

s and Λ+c decays Tables 19-22 give the corresponding numerical

results Some theoretical predictions are given in Refs [133134135136137138139140]In several cases the rare-decay nal states have been observed with the di-lepton pair being

the decay product of a hadronic resonance For these measurements the quoted limits are thoseexpected for the non-resonant di-lepton spectrum For the extrapolation to the full spectruma phase-space distribution of the non-resonant component has been assumed This applies tothe CLEO measurement of the decays D+

(s) rarr (K+π+)e+eminus [141] to the D0 measurements

of the decays D+(s) rarr π+micro+microminus [142] and to the BABAR measurements of the decays D+

(s) rarr(K+π+)e+eminus and D+

(s) rarr (K+π+)micro+microminus where the contribution from φ rarr l+lminus (l = e micro) has

been excluded In the case of the LHCb measurements of the decays D0 rarr π+πminusmicro+microminus [143]as well as the decays D+

(s) rarr π+micro+microminus [144] the contributions from φ rarr l+lminus as well as from

ρ ω rarr l+lminus (l = e micro) have been excluded

Table 19 Upper limits at 90 CL for D0 decays

Decay Limit times106 Experiment Referenceγγ 260 CLEO II [145]

38 BESIII [146]22 BaBar [147]085 Belle [148]

e+eminus 2200 CLEO [149]1700 Argus [150]1300 Mark3 [151]130 CLEO II [152]819 E789 [153]62 E791 [154]12 BaBar [155]0079 Belle [156]

micro+microminus 700 Argus [150]440 E653 [157]340 CLEO II [152]156 E789 [153]52 E791 [154]20 HERAb [158]13 BaBar [155]021 CDF [159]014 Belle [156]00062 LHCb [160]

π0e+eminus 450 CLEO II [152]π0micro+microminus 5400 CLEO II [152]

1800 E653 [157]

35

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceη e+eminus 1100 CLEO II [152]η micro+microminus 5300 CLEO II [152]π+πminuse+eminus 3700 E791 [161]ρ0e+eminus 4500 CLEO [149]

1240 E791 [161]1000 CLEO II [152]

π+πminusmicro+microminus 300 E791 [161]055 LHCb [143]

ρ0micro+microminus 8100 CLEO [149]4900 CLEO II [152]2300 E653 [157]220 E791 [161]

ω e+eminus 1800 CLEO II [152]ω micro+microminus 8300 CLEO II [152]K+Kminuse+eminus 3150 E791 [161]φ e+eminus 590 E791 [161]

520 CLEO II [152]K+Kminusmicro+microminus 330 E791 [161]φmicro+microminus 4100 CLEO II [152]

310 E791 [161]

K0e+eminus 17000 Mark3 [162]

1100 CLEO II [152]

K0micro+microminus 6700 CLEO II [152]

2600 E653 [157]Kminusπ+e+eminus 3850 E791 [161]

Klowast0

(892)e+eminus 1400 CLEO II [152]470 E791 [161]

Kminusπ+micro+microminus 3600 E791 [161]

Klowast0

(892)micro+microminus 11800 CLEO II [152]240 E791 [161]

π+πminusπ0micro+microminus 8100 E653 [157]microplusmne∓ 2700 CLEO [149]

1200 Mark3 [163]1000 Argus [150]190 CLEO II [152]172 E789 [153]81 E791 [154]081 BaBar [155]026 Belle [156]0016 LHCb [164]

π0eplusmnmicro∓ 860 CLEO II [152]η eplusmnmicro∓ 1000 CLEO II [152]

36

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceπ+πminuseplusmnmicro∓ 150 E791 [161]ρ0eplusmnmicro∓ 660 E791 [161]

490 CLEO II [152]ω eplusmnmicro∓ 1200 CLEO II [152]K+Kminuseplusmnmicro∓ 1800 E791 [161]φ eplusmnmicro∓ 470 E791 [161]

340 CLEO II [152]

K0eplusmnmicro∓ 1000 CLEO II [152]

Kminusπ+eplusmnmicro∓ 5500 E791 [161]Klowast0(892)eplusmnmicro∓ 1000 CLEO II [152]

830 E791 [161]π∓π∓eplusmneplusmn 1120 E791 [161]π∓π∓microplusmnmicroplusmn 290 E791 [161]K∓π∓eplusmneplusmn 2060 E791 [161]K∓π∓microplusmnmicroplusmn 3900 E791 [161]K∓K∓eplusmneplusmn 1520 E791 [161]K∓K∓microplusmnmicroplusmn 940 E791 [161]π∓π∓eplusmnmicroplusmn 790 E791 [161]K∓π∓eplusmnmicroplusmn 2180 E791 [161]K∓K∓eplusmnmicroplusmn 570 E791 [161]p eminus 100 CLEO [165]p e+ 110 CLEO [165]

37

γγ

ρ0micro

+microminus

π+πminusπ

0micro

+microminus

K+K

minuse

+eminus

ηe

+eminus

φmicro

+microminus

π0e

+eminus

φe

+eminus

ωmicro

+microminus

Kminusπ

+micro

+microminus

ρ0e

+eminus

K0micro

+microminus

Klowast0

(892

)e+eminus

π+πminusmicro

+microminus

micro+microminus

π+πminuse

+eminus

e+eminus

Klowast0

(892

)micro+microminus

K+K

minusmicro

+microminus

Kminusπ

+e

+eminus

π0micro

+microminus

K0e

+eminus

ωe

+eminus

ηmicro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

HFAG-charm

Belle

BESIII

CLEO II

BaBar

E791

CLEO

E653

LHCb

E789

HERAB

CDF

Argus

Mark3

June 16

K∓π∓microplusmnmicroplusmn

ωeplusmnmicro∓

Kminusπ

+eplusmnmicro∓

K∓K∓eplusmnmicroplusmn

π∓π∓eplusmnmicroplusmn

peminus

K∓π∓eplusmnmicroplusmn

π∓π∓eplusmneplusmn

ηeplusmnmicro∓

π∓π∓microplusmnmicroplusmn

K∓K∓eplusmneplusmn

K0eplusmnmicro∓

π+πminuseplusmnmicro∓

K∓K∓microplusmnmicroplusmn

ρ0eplusmnmicro∓

pe

+

φeplusmnmicro∓

microplusmne∓

K+K

minuseplusmnmicro∓

Klowast0

(892

)eplusmnmicro∓

π0eplusmnmicro∓

K∓π∓eplusmneplusmn

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

L BLHFAG-charm

E791

CLEO II

CLEO

Belle

E789

Mark3

Argus

LHCb

BaBar

June 16

Figure 9 Upper limits at 90 CL for D0 decays The top plot shows avor-changing neu-tral current decays and the bottom plot shows lepton-avor-changing (LF) lepton-number-changing (L) and both baryon- and lepton-number-changing (BL) decays38

Kminuse

+micro

+

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminusmicro

+micro

+

K+e

+eminus

π+e

+eminus

πminuse

+micro

+

Kminuse

+e

+

K+micro

+eminus

ρminusmicro

+micro

+

K+e

+microminus

K+eplusmnmicro∓

π+micro

+eminus

π+e

+microminus

πminusmicro

+micro

+

πminuse

+e

+

π+micro

+microminus

ρ+micro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E687

E653

E791

BaBar

Focus

CLEO

BESIII

LHCb

D0

June 16

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminuse

+micro

+

K+e

+eminus

π+e

+eminus

K+eplusmnmicro∓

Kminuse

+e

+

K+micro

+eminus

K+e

+microminus

Klowast+

(892

)micro+microminus

π+micro

+eminus

Kminusmicro

+micro

+

πminusmicro

+micro

+

πminuse

+e

+

πminuse

+micro

+

π+micro

+microminus

K+micro

+microminus

π+e

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E653

E791

CLEO

BaBar

Focus

LHCb

June 16

Figure 10 Upper limits at 90 CL for D+ (top) and D+s (bottom) decays Each plot shows

avor-changing neutral current decays lepton-avor-changing decays (LF) and lepton-number-changing (L) decays 39

pmicro

+microminus

pe

+microminus

σ+micro

+microminus

pe

+e

+

pe

+eminus

pe

+micro

+

pmicro

+micro

+

pmicro

+eminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

LHFAG-charm

BaBar E653

June 16

Figure 11 Upper limits at 90 CL for Λ+c decays Shown are avor-changing neutral current

decays lepton-avor-changing (LF) decays and lepton-number-changing (L) decays

40

Table 20 Upper limits at 90 CL for D+ decays

Decay Limit times106 Experiment Referenceπ+e+eminus 1100 E687 [166]

520 E791 [154]59 CLEO [141]11 BaBar [167]03 BESIII [168]

π+micro+microminus 2200 E653 [157]890 E687 [166]150 E791 [154]88 Focus [169]65 BaBar [167]39 D0 [142]0073 LHCb [144]

ρ+micro+microminus 5600 E653 [157]K+e+eminus 2000 E687 [166]

30 CLEO [141]12 BESIII [168]10 BaBar [167]

π+eplusmnmicro∓ 340 E791 [154]π+e+microminus 1100 E687 [166]

29 BaBar [167]π+micro+eminus 1300 E687 [166]

36 BaBar [167]K+eplusmnmicro∓ 680 E791 [154]K+e+microminus 1300 E687 [166]

12 BaBar [167]K+micro+eminus 1200 E687 [166]

28 BaBar [167]πminuse+e+ 1100 E687 [166]

960 E791 [154]19 BaBar [167]12 BESIII [168]11 CLEO [141]

πminusmicro+micro+ 870 E687 [166]170 E791 [154]48 Focus [169]20 BaBar [167]0022 LHCb [144]

πminuse+micro+ 1100 E687 [166]500 E791 [154]

ρminusmicro+micro+ 5600 E653 [157]Kminuse+e+ 1200 E687 [166]

35 CLEO [141]09 BaBar [167]

41

Table 20 continued from previous pageDecay Limit times106 Experiment Reference

06 BESIII [168]Kminusmicro+micro+ 3200 E653 [157]

1200 E687 [166]130 Focus [169]100 BaBar [167]

Kminuse+micro+ 1300 E687 [166]Klowastminus(892)micro+micro+ 8500 E653 [157]

Table 21 Upper limits at 90 CL for D+s decays

Decay Limit times106 Experiment Referenceπ+e+eminus 2700 E791 [154]

220 CLEO [141]130 BaBar [167]

π+micro+microminus 4300 E653 [157]1400 E791 [154]430 BaBar [167]260 Focus [169]041 LHCb [144]

K+e+eminus 16000 E791 [154]520 CLEO [141]37 BaBar [167]

K+micro+microminus 1400 E791 [154]360 Focus [169]210 BaBar [167]

Klowast+(892)micro+microminus 14000 E653 [157]π+eplusmnmicro∓ 6100 E791 [154]π+e+microminus 120 BaBar [167]π+micro+eminus 200 BaBar [167]K+eplusmnmicro∓ 6300 E791 [154]K+e+microminus 140 BaBar [167]K+micro+eminus 97 BaBar [167]πminuse+e+ 6900 E791 [154]

180 CLEO [141]41 BaBar [167]

πminusmicro+micro+ 4300 E653 [157]820 E791 [154]290 Focus [169]140 BaBar [167]012 LHCb [144]

πminuse+micro+ 7300 E791 [154]Kminuse+e+ 6300 E791 [154]

170 CLEO [141]

42

Table 21 continued from previous pageDecay Limit times106 Experiment Reference

52 BaBar [167]Kminusmicro+micro+ 5900 E653 [157]

1800 E791 [154]130 BaBar [167]

Kminuse+micro+ 6800 E791 [154]Klowastminus(892)micro+micro+ 14000 E653 [157]

Table 22 Upper limits at 90 CL for Λ+c decays

Decay Limit times106 Experiment Referencepe+eminus 55 BaBar [167]pmicro+microminus 3400 E653 [157]

440 BaBar [167]σ+micro+microminus 7000 E653 [157]pe+microminus 99 BaBar [167]pmicro+eminus 190 BaBar [167]p e+e+ 27 BaBar [167]p micro+micro+ 94 BaBar [167]

43

References

[1] N Cabibbo Phys Rev Lett 10 531533 (1963)

[2] M Kobayashi and T Maskawa Prog Theor Phys 49 652657 (1973)

[3] D Abbaneo et al (ALEPH CDF DELPHI L3 OPAL and SLD collaborations)arXivhep-ex0009052 (2000) CERN-EP-2000-096 arXivhep-ex0112028 (2001)CERN-EP-2001-050

[4] Y Amhis et al (Heavy Flavor Averaging Group) (2012) arXiv12071158 [hep-ex]

[5] K Olive et al (Particle Data Group) Chin Phys C38 090001 (2014)

[6] A L Kagan and M D Sokolo Phys Rev D80 076008 (2009) arXiv09073917 [hep-ph]

[7] Y Grossman A L Kagan and Y Nir Phys Rev D75 036008 (2007)arXivhep-ph0609178 [hep-ph]

[8] M Gersabeck M Alexander S Borghi V Gligorov and C Parkes J Phys G39 045005(2012) arXiv11116515 [hep-ex]

[9] J P Lees et al (BABAR collaboration) Phys Rev D87 012004 (2013) arXiv12093896[hep-ex]

[10] R Aaij et al (LHCb collaboration) Phys Rev Lett 112 041801 (2014) arXiv13107201[hep-ex]

[11] T A Aaltonen et al (CDF collaboration) Phys Rev D90 no 11 111103 (2014)arXiv14105435 [hep-ex]

[12] R Aaij et al (LHCb collaboration) JHEP 04 043 (2015) arXiv150106777 [hep-ex]

[13] M Staripound et al (Belle collaboration) Phys Lett B753 412418 (2016) arXiv150908266[hep-ex]

[14] B Aubert et al (BABAR collaboration) Phys Rev Lett 100 061803 (2008)arXiv07092715 [hep-ex]

[15] B Ko (Belle collaboration) PoS ICHEP2012 353 (2013) arXiv12121975

[16] T Aaltonen et al (CDF collaboration) Phys Rev Lett 109 111801 (2012)arXiv12072158 [hep-ex]

[17] R Aaij et al (LHCb collaboration) JHEP 07 041 (2014) arXiv14052797 [hep-ex]

[18] R Aaij et al (LHCb collaboration) Phys Rev Lett 116 no 19 191601 (2016)arXiv160203160 [hep-ex]

[19] T Becher and R J Hill Phys Lett B633 6169 (2006) arXivhep-ph0509090 [hep-ph]

[20] F J Gilman and R L Singleton Phys Rev D41 142 (1990)

[21] R J Hill eConf C060409 027 (2006) arXivhep-ph0606023 [hep-ph]

[22] D Becirevic and A B Kaidalov Phys Lett B478 417423 (2000) arXivhep-ph9904490[hep-ph]

44

[23] C G Boyd B Grinstein and R F Lebed Phys Rev Lett 74 46034606 (1995)arXivhep-ph9412324 [hep-ph]

[24] C G Boyd and M J Savage Phys Rev D56 303311 (1997) arXivhep-ph9702300[hep-ph]

[25] M C Arnesen B Grinstein I Z Rothstein and I W Stewart Phys Rev Lett 95 071802(2005)

[26] C Bourrely B Machet and E de Rafael Nucl Phys B189 157 (1981)

[27] D Becirevic A L Yaouanc A Oyanguren P Roudeau and F Sanlippo (2014)arXiv14071019 [hep-ph]

[28] J P Lees et al (BABAR collaboration) Phys Rev D88 052003 (2013) arXiv13045009[hep-ex]

[29] P del Amo Sanchez et al (BaBar Collaboration collaboration) PhysRev D82 111101(2010) arXiv10092076 [hep-ex]

[30] R Aaij et al (LHCb collaboration) JHEP 1309 145 (2013) arXiv13074556

[31] G Burdman and J Kambor Phys Rev D55 28172826 (1997) arXivhep-ph9602353[hep-ph]

[32] D Becirevic A Le Yaouanc L Oliver J-C Raynal P Roudeau and J Serrano Phys RevD87 no 5 054007 (2013) arXiv12065869 [hep-ph]

[33] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052022 (2015)arXiv14125502 [hep-ex]

[34] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 7 072012 (2015)arXiv150807560 [hep-ex]

[35] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 11 112008 (2015)arXiv151000308 [hep-ex]

[36] L Widhalm et al (Belle collaboration) Phys Rev Lett 97 061804 (2006)arXivhep-ex0604049 [hep-ex]

[37] B Aubert et al (BABAR collaboration) Phys Rev D76 052005 (2007) arXiv07040020[hep-ex]

[38] D Besson et al (CLEO collaboration) Phys Rev D80 032005 (2009) arXiv09062983[hep-ex]

[39] S Dobbs et al (CLEO collaboration) Phys Rev D77 112005 (2008) arXiv07121020[hep-ex]

[40] G Huang et al (CLEO collaboration) Phys Rev Lett 94 011802 (2005)arXivhep-ex0407035 [hep-ex]

[41] J Link et al (FOCUS collaboration) Phys Lett B607 233242 (2005)arXivhep-ex0410037 [hep-ex]

[42] J Adler et al (MARK-III collaboration) Phys Rev Lett 62 1821 (1989)

45

[43] K Kodama et al (Fermilab E653 collaboration) Phys Rev Lett 66 18191822 (1991)

[44] K Kodama et al (E653 collaboration) Phys Lett B336 605613 (1994)

[45] P L Frabetti et al (E687 collaboration) Phys Lett B364 127136 (1995)

[46] P L Frabetti et al (E687 collaboration) Phys Lett B315 203208 (1993)

[47] J C Anjos et al (Tagged Photon Spectrometer collaboration) Phys Rev Lett 6215871590 (1989)

[48] M Ablikim et al (BES collaboration) Phys Lett B597 3946 (2004)arXivhep-ex0406028 [hep-ex]

[49] M Ablikim et al (BES collaboration) (2006) arXivhep-ex0610019 [hep-ex]

[50] A Bean et al (CLEO collaboration) Phys Lett B317 647654 (1993)

[51] BESIII collaboration presented at ICHEP 2014 conference 2014httpindicoificuvesindicogetFilepyaccesscontribId=69ampsessionId=25ampresId=

0ampmaterialId=slidesampconfId=2025

[52] J G Korner and G A Schuler Z Phys C46 93 (1990)

[53] FLAG collaboration httpitpwikiunibechagimages44bFLAGpdf 2014httpitpwikiunibechflagimages44bFLAGpdf

[54] J Anjos et al (Fermilab E691 collaboration) Phys Rev Lett 65 26302633 (1990)

[55] K Kodama et al (Fermilab E653 collaboration) Phys Lett B274 246252 (1992)

[56] P Frabetti et al (Fermilab E687 collaboration) Phys Lett B307 262268 (1993)

[57] E Aitala et al (E791 collaboration) Phys Rev Lett 80 13931397 (1998)arXivhep-ph9710216 [hep-ph]

[58] E Aitala et al (E791 collaboration) Phys Lett B440 435441 (1998)arXivhep-ex9809026 [hep-ex]

[59] M Adamovich et al (BEATRICE collaboration) Eur Phys J C6 3541 (1999)

[60] J Link et al (FOCUS collaboration) Phys Lett B544 8996 (2002)arXivhep-ex0207049 [hep-ex]

[61] J Link et al (FOCUS collaboration) Phys Lett B607 6777 (2005)arXivhep-ex0410067 [hep-ex]

[62] P del Amo Sanchez et al (BABAR collaboration) Phys Rev D83 072001 (2011)arXiv10121810 [hep-ex]

[63] B Aubert et al (BABAR collaboration) Phys Rev D78 051101 (2008) arXiv08071599[hep-ex]

[64] H Mahlke eConf C0610161 014 (2006) arXivhep-ex0702014 [hep-ex]

[65] J Link et al (FOCUS collaboration) Phys Lett B535 4351 (2002)arXivhep-ex0203031 [hep-ex]

46

[66] K M Ecklund et al (CLEO collaboration) Phys Rev D80 052009 (2009)arXiv09073201 [hep-ex]

[67] R A Briere et al (CLEO collaboration) Phys Rev D81 112001 (2010) arXiv10041954[hep-ex]

[68] P Estabrooks R Carnegie A D Martin W Dunwoodie T Lasinski et al Nucl PhysB133 490 (1978)

[69] D Aston et al Nucl Phys B296 493 (1988)

[70] B Aubert et al (BABAR collaboration) Phys Rev Lett 90 242001 (2003)arXivhep-ex0304021 [hep-ex]

[71] D Besson et al (CLEO Collaboration collaboration) PhysRev D68 032002 (2003)arXivhep-ex0305100 [hep-ex]

[72] K Abe et al (Belle Collaboration collaboration) PhysRevLett 92 012002 (2004)arXivhep-ex0307052 [hep-ex]

[73] B Aubert et al (BaBar Collaboration collaboration) PhysRev D69 031101 (2004)arXivhep-ex0310050 [hep-ex]

[74] K Abe et al (Belle collaboration) Phys Rev D69 112002 (2004) arXivhep-ex0307021[hep-ex]

[75] J M Link et al (FOCUS Collaboration collaboration) PhysLett B586 1120 (2004)arXivhep-ex0312060 [hep-ex]

[76] S Godfrey and N Isgur Phys Rev D32 189231 (1985)

[77] S Godfrey and R Kokoski Phys Rev D43 16791687 (1991)

[78] N Isgur and M B Wise Phys Rev Lett 66 11301133 (1991)

[79] P Schweitzer S Bo and M Radici Phys Rev D66 114004 (2002)arXivhep-ph0207230 [hep-ph]

[80] F Jugeau A Le Yaouanc L Oliver and J-C Raynal Phys Rev D72 094010 (2005)arXivhep-ph0504206 [hep-ph]

[81] P Colangelo F De Fazio and R Ferrandes ModPhysLett A19 20832102 (2004)arXivhep-ph0407137 [hep-ph]

[82] R N Cahn and J D Jackson Phys Rev D68 037502 (2003) arXivhep-ph0305012[hep-ph]

[83] T Barnes F E Close and H J Lipkin PhysRev D68 054006 (2003)arXivhep-ph0305025 [hep-ph]

[84] H Lipkin PhysLett B580 5053 (2004) arXivhep-ph0306204 [hep-ph]

[85] W A Bardeen E J Eichten and C T Hill Phys Rev D68 054024 (2003)arXivhep-ph0305049 [hep-ph]

[86] B Aubert et al (BaBar Collaboration collaboration) PhysRev D80 092003 (2009)arXiv09080806 [hep-ex]

47

[87] R Aaij et al (LHCb Collaboration collaboration) JHEP 1210 151 (2012) arXiv12076016[hep-ex]

[88] R Aaij et al (LHCb collaboration) Phys Rev Lett 113 162001 (2014) arXiv14077574[hep-ex]

[89] R Aaij et al (LHCb collaboration) JHEP 02 133 (2016) arXiv160101495 [hep-ex]

[90] T Matsuki T Morii and K Sudoh EurPhysJ A31 701704 (2007)arXivhep-ph0610186 [hep-ph]

[91] N Isgur and M B Wise PhysLett B232 113117 (1989)

[92] M Neubert PhysRept 245 259396 (1994) arXivhep-ph9306320 [hep-ph]

[93] B Aubert et al (BaBar Collaboration collaboration) PhysRev D74 032007 (2006)arXivhep-ex0604030 [hep-ex]

[94] V M Abazov et al (D0 Collaboration collaboration) PhysRevLett 102 051801 (2009)arXiv07123789 [hep-ex]

[95] B Aubert et al (BABAR collaboration) Phys Rev D77 011102 (2008) arXiv07081565[hep-ex]

[96] P L Frabetti et al (E687 Collaboration collaboration) PhysRevLett 72 324327 (1994)

[97] J P Alexander et al (CLEO Collaboration collaboration) PhysLett B303 377384 (1993)

[98] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B297 425431 (1992)

[99] P Avery et al (CLEO Collaboration collaboration) PhysRev D41 774 (1990)

[100] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B230 162 (1989)

[101] J P Lees et al (BaBar Collaboration collaboration) PhysRev D83 072003 (2011)arXiv11032675 [hep-ex]

[102] R Aaij et al (LHCb collaboration) Phys Rev D90 no 7 072003 (2014) arXiv14077712[hep-ex]

[103] R Aaij et al (LHCb collaboration) PhysLett B698 1420 (2011) arXiv11020348[hep-ex]

[104] B Aubert et al (BaBar Collaboration collaboration) PhysRevLett 97 222001 (2006)arXivhep-ex0607082 [hep-ex]

[105] H Albrecht et al (ARGUS Collaboration collaboration) ZPhys C69 405408 (1996)

[106] Y Kubota et al (CLEO Collaboration collaboration) PhysRevLett 72 19721976 (1994)arXivhep-ph9403325 [hep-ph]

[107] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052002 (2015)arXiv14126751 [hep-ex]

[108] J Brodzicka et al (Belle collaboration) Phys Rev Lett 100 092001 (2008)arXiv07073491 [hep-ex]

48

[109] B Aubert et al (BABAR collaboration) Phys Rev D79 112004 (2009) arXiv09011291[hep-ex]

[110] R Aaij et al (LHCb collaboration) Phys Rev D92 no 3 032002 (2015)arXiv150501710 [hep-ex]

[111] R Aaij et al (LHCb collaboration) Phys Rev D92 no 1 012012 (2015)arXiv150501505 [hep-ex]

[112] A Kuzmin et al (Belle Collaboration collaboration) PhysRev D76 012006 (2007)arXivhep-ex0611054 [hep-ex]

[113] H Abramowicz et al (ZEUS Collaboration collaboration) NuclPhys B866 229254 (2013)arXiv12084468 [hep-ex]

[114] A Abulencia et al (CDF Collaboration collaboration) PhysRev D73 051104 (2006)arXivhep-ex0512069 [hep-ex]

[115] K Abe et al (Belle collaboration) Phys Rev Lett 94 221805 (2005)arXivhep-ex0410091 [hep-ex]

[116] P Avery et al (CLEO Collaboration collaboration) PhysLett B331 236244 (1994)arXivhep-ph9403359 [hep-ph]

[117] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B232 398 (1989)

[118] J C Anjos et al (Tagged Photon Spectrometer Collaboration collaboration) PhysRevLett62 1717 (1989)

[119] T Bergfeld et al (CLEO Collaboration collaboration) PhysLett B340 194204 (1994)

[120] R Aaij et al (LHCb collaboration) Phys Rev D91 no 9 092002 (2015)arXiv150302995 [hep-ex] [Erratum Phys RevD93no11119901(2016)]

[121] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B221 422 (1989)

[122] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B231 208 (1989)

[123] P Abreu et al (DELPHI Collaboration collaboration) PhysLett B426 231242 (1998)

[124] D Matvienko et al (Belle collaboration) Phys Rev D92 no 1 012013 (2015)arXiv150503362 [hep-ex]

[125] P Krokovny et al (Belle collaboration) Phys Rev Lett 91 262002 (2003)arXivhep-ex0308019 [hep-ex]

[126] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 181801 (2004)arXivhep-ex0408041 [hep-ex]

[127] S K Choi et al (Belle collaboration) Phys Rev D91 no 9 092011 (2015)arXiv150402637 [hep-ex] [Addendum Phys RevD92no3039905(2015)]

[128] A Drutskoy et al (Belle collaboration) Phys Rev Lett 94 061802 (2005)arXivhep-ex0409026 [hep-ex]

[129] B Aubert et al (BABAR collaboration) Phys Rev D74 031103 (2006)arXivhep-ex0605036 [hep-ex]

49

[130] S Chekanov et al (ZEUS Collaboration collaboration) EurPhysJ C60 2545 (2009)arXiv08071290 [hep-ex]

[131] A Heister et al (ALEPH Collaboration collaboration) PhysLett B526 3449 (2002)arXivhep-ex0112010 [hep-ex]

[132] B Aubert et al (BABAR collaboration) Phys Rev Lett 103 051803 (2009)arXiv08080333 [hep-ex]

[133] G Burdman E Golowich J L Hewett and S Pakvasa Phys Rev D66 014009 (2002)arXivhep-ph0112235 [hep-ph]

[134] S Fajfer A Prapotnik S Prelovsek P Singer and J Zupan Nucl Phys Proc Suppl 1159397 (2003) arXivhep-ph0208201 [hep-ph]

[135] S Fajfer N Kosnik and S Prelovsek Phys Rev D76 074010 (2007) arXiv07061133[hep-ph]

[136] E Golowich J Hewett S Pakvasa and A A Petrov Phys Rev D79 114030 (2009)arXiv09032830 [hep-ph]

[137] A Paul I I Bigi and S Recksiegel Phys Rev D82 094006 (2010) arXiv10083141[hep-ph]

[138] A Borisov (2011) arXiv11123269 [hep-ph]

[139] R-M Wang J-H Sheng J Zhu Y-Y Fan and Y Gao Int J Mod Phys A29 no 291450169 (2014)

[140] S de Boer and G Hiller Phys Rev D93 no 7 074001 (2016) arXiv151000311 [hep-ph]

[141] P Rubin et al (CLEO collaboration) Phys Rev D82 092007 (2010) arXiv10091606[hep-ex]

[142] V Abazov et al (D0 collaboration) Phys Rev Lett 100 101801 (2008) arXiv07082094[hep-ex]

[143] R Aaij et al (LHCb collaboration) Phys Lett B728 234243 (2014) arXiv13102535[hep-ex]

[144] R Aaij et al (LHCb collaboration) Phys Lett B724 203212 (2013) arXiv13046365[hep-ex]

[145] T Coan et al (CLEO collaboration) Phys Rev Lett 90 101801 (2003)arXivhep-ex0212045 [hep-ex]

[146] M Ablikim et al (BESIII collaboration) Phys Rev D91 no 11 112015 (2015)arXiv150503087 [hep-ex]

[147] J P Lees et al (BABAR collaboration) Phys Rev D85 091107 (2012) arXiv11106480[hep-ex]

[148] N K Nisar et al (Belle collaboration) Phys Rev D93 no 5 051102 (2016)arXiv151202992 [hep-ex]

[149] P Haas et al (CLEO collaboration) Phys Rev Lett 60 1614 (1988)

50

[150] H Albrecht et al (ARGUS collaboration) Phys Lett B209 380 (1988)

[151] J Adler et al (MARK-III collaboration) Phys Rev D37 2023 (1988) Erratum ibid D40(1989) 3788

[152] A Freyberger et al (CLEO collaboration) Phys Rev Lett 76 30653069 (1996)

[153] D Pripstein et al (E789 collaboration) Phys Rev D61 032005 (2000)arXivhep-ex9906022 [hep-ex]

[154] E Aitala et al (E791 collaboration) Phys Lett B462 401409 (1999)arXivhep-ex9906045 [hep-ex]

[155] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 191801 (2004)arXivhep-ex0408023 [hep-ex]

[156] M Petric et al (Belle collaboration) Phys Rev D81 091102 (2010) arXiv10032345[hep-ex]

[157] K Kodama et al (E653 collaboration) Phys Lett B345 8592 (1995)

[158] I Abt et al (HERA-B collaboration) Phys Lett B596 173183 (2004)arXivhep-ex0405059 [hep-ex]

[159] T Aaltonen et al (CDF collaboration) Phys Rev D82 091105 (2010) arXiv10085077[hep-ex]

[160] R Aaij et al (LHCb collaboration) Phys Lett B725 1524 (2013) arXiv13055059[hep-ex]

[161] E Aitala et al (E791 collaboration) Phys Rev Lett 86 39693972 (2001)arXivhep-ex0011077 [hep-ex]

[162] J Adler et al (MARK-III collaboration) Phys Rev D40 906 (1989)

[163] J Becker et al (MARK-III collaboration) Phys Lett B193 147 (1987)

[164] R Aaij et al (LHCb collaboration) Phys Lett B754 167175 (2016) arXiv151200322[hep-ex]

[165] P Rubin et al (CLEO collaboration) Phys Rev D79 097101 (2009) arXiv09041619[hep-ex]

[166] P Frabetti et al (E687 collaboration) Phys Lett B398 239244 (1997)

[167] J P Lees et al (BABAR collaboration) Phys Rev D84 072006 (2011) arXiv11074465[hep-ex]

[168] (BESIII collaboration) M-G Zhao D rareforbidden decays at BESIII in 7th International

Workshop on Charm Physics (Charm 2015) Detroit MI USA May 18-22 2015 2016arXiv160508952 [hep-ex]httpinspirehepnetrecord1466292filesarXiv160508952pdf

[169] J Link et al (FOCUS collaboration) Phys Lett B572 2131 (2003)arXivhep-ex0306049 [hep-ex]

51

  • Introduction
  • D decays
    • Interplay of direct and indirect CP violation
    • Semileptonic decays
      • Introduction
      • DP decays
      • Form factor parameterizations
      • Simple pole
      • z expansion
      • Three-pole formalism
      • Experimental techniques and results
      • Combined results for the DK channel
      • Combined results for the D channel
      • Vcs and Vcd determination
      • DV decays
      • Form factor measurements
        • Excited D(s) mesons
        • Rare and forbidden decays
          • References
Page 2: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

Contents

1 Introduction 3

2 D decays 521 Interplay of direct and indirect CP violation 622 Semileptonic decays 9

221 Introduction 9222 DrarrP`ν` decays 9223 Form factor parameterizations 9224 Simple pole 10225 z expansion 10226 Three-pole formalism 11227 Experimental techniques and results 12228 Combined results for the D rarr K`ν` channel 14229 Combined results for the D rarr π`ν` channel 162210 Vcs and Vcd determination 162211 DrarrV `ν` decays 202212 Form factor measurements 21

23 Excited D(s) mesons 2524 Rare and forbidden decays 35

References 44

2

1 Introduction

Flavor dynamics is an important element in understanding the nature of particle physics Theaccurate knowledge of properties of heavy avor hadrons especially b hadrons plays an essentialrole for determining the elements of the Cabibbo-Kobayashi-Maskawa (CKM) weak-mixingmatrix [12] The operation of the Belle and BABAR e+eminus B factory experiments led to a largeincrease in the size of available B-meson D-hadron and τ -lepton samples enabling dramaticimprovement in the accuracies of related measurements The CDF and D0 experiments at theFermilab Tevatron have also provided important results in heavy avour physics most notablyin the B0

s sector In the D-meson sector the dedicated e+eminus charm factory experiments CLEOc

and BESIII have made signicant contributions Run I of the CERN Large Hadron Colliderdelivered high luminosity enabling the collection of even higher statistics samples of b andc hadrons and thus a further leap in precision in many areas at the ATLAS CMS and(especially) LHCb experiments With the LHC Run II ongoing further improvements arekeenly anticipated

The Heavy Flavor Averaging Group (HFAG) was formed in 2002 to continue the activities ofthe LEP Heavy Flavor Steering group [3] This group was responsible for calculating averages ofmeasurements of b-avor related quantities HFAG has evolved since its inception and currentlyconsists of seven subgroups

bull the B Lifetime and Oscillations subgroup provides averages for b-hadron lifetimes b-hadron fractions in Υ (4S) decay and pp or pp collisions and various parameters governingB0-B0 and BsB

0s mixing

bull the Unitarity Triangle Parameters subgroup provides averages for time-dependent CPasymmetry parameters and studies of B rarr DK decays and resulting determinations ofthe angles of the CKM unitarity triangle

bull the Semileptonic B Decays subgroup provides averages for inclusive and exclusive B-decay branching fractions and subsequent determinations of the CKM matrix elements|Vcb| and |Vub|

bull the B to Charm Decays subgroup provides averages of branching fractions for B decaysto nal states involving open charm or charmonium mesons

bull the Rare Decays subgroup provides averages of branching fractions and CP asymmetriesfor charmless radiative leptonic and baryonic B-meson and b-baryon decays

bull the Charm Physics subgroup provides averages of numerous quantities in the charmsector including branching fractions properties of charm baryons and of excited Dlowastlowast andDsJ mesons averages of D0-D0 mixing and CP and T violation parameters and anaverage value for the Ds decay constant fDs

bull the Tau Physics subgroup provides documentation and averages for a selection of τlepton quantities that most prot from the adoption of the HFAG prescriptions Inparticular the τ lepton branching fractions uncertainties and correlations are obtainedfrom a global t of the experimental results and this information is further elaboratedto compute several lepton universality tests and the CKM matrix element |Vus| The

3

τ lepton-avor-violating decays are documented and combinations of upper limits arecomputed

The Lifetime and Oscillations and Semileptonic subgroups were formed from the mergerof four LEP working groups The Unitary Triangle B to Charm Decays and Rare De-cays subgroups were formed to provide averages for new results obtained from the B factoryexperiments (and now also from the Fermilab Tevatron and CERN LHC experiments) TheCharm and Tau subgroups were formed more recently in response to the wealth of new dataconcerning D and τ physics Subgroups typically include representatives from Belle BABARand LHCb plus when relevant CLEO CDF and D0

This article is an update of the last HFAG preprint which used results available at leastthrough early 2012 [4] Here we report world averages using results available at least throughsummer 2014 In some cases results made available in the latter part of 2014 have been in-cluded1 In general we use all publicly available results that have written documentationThese include preliminary results presented at conferences or workshops However we do notuse preliminary results that remain unpublished for an extended period of time or for whichno publication is planned Close contacts have been established between representatives fromthe experiments and members of subgroups that perform averaging to ensure that the data areprepared in a form suitable for combinations

In the case of obtaining a world average for which χ2dof gt 1 where dof is the numberof degrees of freedom in the average calculation we do not usually scale the resulting erroras is presently done by the Particle Data Group [5] Rather we examine the systematics ofeach measurement to better understand them Unless we nd possible systematic discrepanciesbetween the measurements we do not apply any additional correction to the calculated errorWe provide the condence level of the t as an indicator for the consistency of the measurementsincluded in the average In case some special treatment was necessary to calculate an averageor if an approximation used in an average calculation might not be suciently accurate (egassuming Gaussian errors when the likelihood function indicates non-Gaussian behavior) weinclude a warning message

Chapter describes the methodology used for calculating averages In the averagingprocedure common input parameters used in the various analyses are adjusted (rescaled) tocommon values and where possible known correlations are taken into account Chapters present world average values from each of the subgroups listed above A brief summary ofthe averages presented is given in Chapter A complete listing of the averages and plotsincluding updates since this document was prepared are also available on the HFAG web site

httpwwwslacstanfordeduxorghfag

1 Particularly important new results have been included whenever possible The precise cut-o date forincluding results in the averages varies between subgroups

4

2 D decays

5

21 Interplay of direct and indirect CP violation

In decays of D0 mesons CP asymmetry measurements have contributions from both directand indirect CP violation as discussed in Sec The contribution from indirect CP viola-tion depends on the decay-time distribution of the data sample [6] This section describes acombination of measurements that allows the extraction of the individual contributions of thetwo types of CP violation At the same time the level of agreement for a no-CP -violationhypothesis is tested The observables are

AΓ equivτ(D 0rarrh+hminus)minus τ(D0rarrh+hminus)

τ(D 0rarrh+hminus) + τ(D0rarrh+hminus) (1)

where h+hminus can be K+Kminus or π+πminus and

∆ACP equiv ACP(K+Kminus)minus ACP(π+πminus) (2)

where ACP are time-integrated CP asymmetries The underlying theoretical parameters are

adirCP equiv

|AD0rarrf |2 minus |AD 0rarrf |2

|AD0rarrf |2 + |AD 0rarrf |2

aindCP equiv 1

2

[(∣∣∣∣qp∣∣∣∣+

∣∣∣∣pq∣∣∣∣)x sinφminus

(∣∣∣∣qp∣∣∣∣minus ∣∣∣∣pq

∣∣∣∣) y cosφ

] (3)

where ADrarrf is the amplitude for D rarr f [7] We use the following relations between theobservables and the underlying parameters [8]

AΓ = minusaindCP minus adir

CPyCP

∆ACP = ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

+ adirCPyCP

∆〈t〉τ

(4)

asymp ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

(5)

The rst relation constrains mostly indirect CP violation and the direct CP violation contri-bution can dier for dierent nal states In the second relation 〈t〉τ denotes the mean decaytime in units of the D0 lifetime ∆X denotes the dierence in quantity X between K+Kminus andπ+πminus nal states and X denotes the average for quantity X We neglect the last term in thisrelation as all three factors are O(10minus2) or smaller and thus this term is negligible with respectto the other two terms Note that ∆〈t〉τ 〈t〉τ and it is expected that |adir

CP| lt |∆adirCP|

because adirCP(K+Kminus) and adir

CP(π+πminus) are expected to have opposite signs [7]A χ2 t is performed in the plane ∆adir

CP vs aindCP For the BABAR result the dierence of

the quoted values for ACP(K+Kminus) and ACP(π+πminus) is calculated adding all uncertainties inquadrature This may overestimate the systematic uncertainty for the dierence as it neglectscorrelated errors however the result is conservative and the eect is small as all measurementsare statistically limited For all measurements statistical and systematic uncertainties areadded in quadrature when calculating the χ2 We use the current world average value yCP =(0866plusmn 0155) (see Sec ) and the measurements listed in Table 1

6

Table 1 Inputs to the t for direct and indirect CP violation The rst uncertainty listed isstatistical and the second is systematic

Year Experiment Results ∆〈t〉τ 〈t〉τ Reference2012 BABAR AΓ = (009plusmn 026plusmn 006) - - [9]2013 LHCb prompt AΓ(KK) = (minus0035plusmn 0062plusmn 0012) - - [10]

AΓ(ππ) = (0033plusmn 0106plusmn 0014) - -2014 CDF AΓ = (minus012plusmn 012) - - [11]2015 LHCb SL AΓ = (minus0125plusmn 0073) - - [12]2015 Belle AΓ = (minus003plusmn 020plusmn 007) - - [13]2008 BABAR ACP(KK) = (000plusmn 034plusmn 013)

ACP(ππ) = (minus024plusmn 052plusmn 022) 000 100 [14]2012 Belle prel ∆ACP = (minus087plusmn 041plusmn 006) 000 100 [15]2012 CDF ∆ACP = (minus062plusmn 021plusmn 010) 025 258 [16]2014 LHCb SL ∆ACP = (014plusmn 016plusmn 008) 001 107 [17]2016 LHCb prompt ∆ACP = (minus010plusmn 008plusmn 003) 012 210 [18]

In this t AΓ(KK) and AΓ(ππ) are assumed to be identical This assumption is sup-ported by all measurements to date A signicant relative shift due to nal-state dependentAΓ values between ∆ACP measurements with dierent mean decay times is excluded by thesemeasurements

The combination plot (see Fig 1) shows the measurements listed in Table 1 for ∆ACP andAΓ where the bands represent plusmn1σ intervals The point of no CP violation (00) is shownas a lled circle and two-dimensional 68 CL 95 CL and 997 CL regions are plotted asellipses The best t value is indicated by a cross showing the one-dimensional errors

From the t the change in χ2 from the minimum value for the no-CPV point (00) is55 which corresponds to a CL of 65 times 10minus2 for two degrees of freedom Thus the data areconsistent with the no-CP -violation hypothesis at 65 CL This p-value corresponds to 18σThe central values and plusmn1σ uncertainties for the individual parameters are

aindCP = (0056plusmn 0040)

∆adirCP = (minus0137plusmn 0070) (6)

Compared to the previous average the tension in the dierence between direct CP violationin the two nal states reduced while the common indirect CP violation moved away from theno CP violation point by about one standard deviation

7

0015 0010 0005 0000 0005 0010

aindCP

0015

0010

0005

0000

0005

0010

0015

∆adirCP

Contours contain 68 95 99 CL

CD

F

LHC

b S

L

LHC

b p

rom

pt

BaBarBelleCDF KK+ππLHCb SL KK+ππ

LHCb prompt KKLHCb prompt ππ

HFAG-charmWinter 16

no CPV

BaBar

Belle

CDF

LHCb

Figure 1 Plot of all data and the t result Individual measurements are plotted as bandsshowing their plusmn1σ range The no-CPV point (00) is shown as a lled circle and the best tvalue is indicated by a cross showing the one-dimensional uncertainties Two-dimensional 68CL 95 CL and 997 CL regions are plotted as ellipses

8

22 Semileptonic decays

221 Introduction

Semileptonic decays of D mesons involve the interaction of a leptonic current with a hadroniccurrent The latter is nonperturbative and cannot be calculated from rst principles thus it isusually parameterized in terms of form factors The transition matrix element is written

M = minusi GFradic2Vcq L

microHmicro (7)

where GF is the Fermi constant and Vcq is a CKM matrix element The leptonic current Lmicro isevaluated directly from the lepton spinors and has a simple structure this allows one to extractinformation about the form factors (in Hmicro) from data on semileptonic decays [19] Converselybecause there are no strong nal-state interactions between the leptonic and hadronic systemssemileptonic decays for which the form factors can be calculated allow one to determine Vcq [2]

222 DrarrP`ν` decays

When the nal state hadron is a pseudoscalar the hadronic current is given by

Hmicro = 〈P (p)|qγmicroc|D(pprime)〉 = f+(q2)

[(pprime + p)micro minus

m2D minusm2

P

q2qmicro

]+ f0(q2)

m2D minusm2

P

q2qmicro (8)

where mD and pprime are the mass and four momentum of the parent D meson mP and p are thoseof the daughter meson f+(q2) and f0(q2) are form factors and q = pprime minus p Kinematics requirethat f+(0) = f0(0) The contraction qmicroL

micro results in terms proportional to m` [20] and thus for` = e the terms proportionals to qmicro in Eq (8) are negligible For light leptons only the f+(q2)vector form factor is relevant and the dierential partial width is

dΓ(D rarr P`ν`)

dq2 d cos θ`=

G2F |Vcq|2

32π3plowast 3|f+(q2)|2 sin θ2

` (9)

where plowast is the magnitude of the momentum of the nal state hadron in the D rest frame andθ` is the angle of the lepton in the `ν rest frame with respect to the direction of the pseudoscalarmeson in the D rest frame

223 Form factor parameterizations

The form factor is traditionally parameterized with an explicit pole and a sum of eective poles

f+(q2) =f+(0)

(1minus α)

[(1

1minus q2m2pole

)+

Nsumk=1

ρk1minus q2(γkm2

pole)

] (10)

where ρk and γk are expansion parameters and α is a parameter that normalizes the formfactor at q2 = 0 f+(0) The parameter mpole is the mass of the lowest-lying cq resonance withthe vector quantum numbers this is expected to provide the largest contribution to the formfactor for the crarr q transition The sum over N gives the contribution of higher mass statesFor example for D rarr π transitions the dominant resonance is expected to be Dlowast(2010) andthus mpole = mDlowast(2010) For D rarr K transitions the dominant contribution is expected from

Dlowasts(2112) with mpole = mDlowasts (2112)

9

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Comparison between CLEO-c and BABAR results for the quantities q2H20 (q2) and

q2h0(q2)H0(q2)

Table 11 Results for rV and r2 from various experiments

Experiment Ref rV r2

D+ rarr Klowast0l+ν

E691 [54] 20plusmn 06plusmn 03 00plusmn 05plusmn 02E653 [55] 200plusmn 033plusmn 016 082plusmn 022plusmn 011E687 [56] 174plusmn 027plusmn 028 078plusmn 018plusmn 011

E791 (e) [57] 190plusmn 011plusmn 009 071plusmn 008plusmn 009E791 (micro) [58] 184plusmn011plusmn009 075plusmn008plusmn009Beatrice [59] 145plusmn 023plusmn 007 100plusmn 015plusmn 003FOCUS [60] 1504plusmn0057plusmn0039 0875plusmn0049plusmn0064

D0 rarr K0πminusmicro+ν

FOCUS [61] 1706plusmn0677plusmn0342 0912plusmn0370plusmn0104BABAR [62] 1493plusmn 0014plusmn 0021 0775plusmn 0011plusmn 0011

D+s rarr φ e+νBABAR [63] 1849plusmn0060plusmn0095 0763plusmn0071plusmn0065

D0 D+ rarr ρ eνCLEO [64] 140plusmn025plusmn003 057plusmn018plusmn006

23

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

HFLAV())+-amp

Figure 7 A comparison of r2 (lled inverted triangles) and rV (open triangles) values fromvarious experiments The rst seven measurements are for D+ rarr Kminusπ+l+νl decays Alsoshown as a line with 1-σ limits is the average of these The last two points are D+

s and D0

decays

24

23 Excited D(s) mesons

Excited charm meson states have received increased attention since the rst observation ofstates that could not be accommodated by QCD predictions [70 71 72 73] Tables 12 13and 14 summarize recent measurements of the masses and widths of excited D and Ds mesonsrespectively If a preferred assignment of spin and parity was measured it is listed in the columnJP where the label natural denotes JP = 0minus 1+ 2minus and unnatural JP = 0+ 1minus 2+ Ifpossible an average mass and width was calculated which is listed in the gray shaded rowThe calculation of the averages assumes no correlation between individual measurements Asummary of the averaged masses and widths is shown in Figure 8

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

0+ 1+ 2+ 1minus 1 3minus

unnatu

ral

Dlowast s0

(2317)plusmn

Ds1

(2460)plusmn

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn D

sJ(3

040)plusmn

HFAG-charmAugust 2016

(a)

Mas

s[M

eVc

2]

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

0+ 1+ 2+ 0minus 1minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ralDlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn

D(2

550)0

D(2

580)0

D(2

600)0

D(2

600)plusmn

Dlowast (

2640)plusmn

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(b)

Mas

s[M

eVc

2]

0

50

100

150

200

250

300

350

400

450

500

550

1+ 2+ 1minus 1 3minus

unnatu

ral

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn

DsJ

(3040)plusmn

HFAG-charmAugust 2016

(c)

Wid

th[M

eV]

50100150200250300350400450500550600650700

0+ 1+ 2+ 0minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ral

Dlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn D(2

550)0

D(2

580)0

D(2

600)0

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(d)

Wid

th[M

eV]

Figure 8 Averaged masses for Ds mesons are shown in subgure (a) and for D mesons insubgure (b) The average widths for Ds mesons are shown in subgure (c) and for D mesonsin subgure (d) The vertical shaded regions distinguish between dierent spin parity states

The masses and widths of narrow (Γ lt 50 MeV) orbitally excited D mesons (denotedDlowastlowast) both neutral and charged are well established Measurements of broad states (Γ sim200400 MeV) are less abundant as identifying the signal is more challenging There is aslight discrepancy between the Dlowast0(2400)0 masses measured by the Belle [74] and FOCUS [75]experiments No data exist yet for the D1(2430)plusmn state Dalitz plot analyses of B rarr D(lowast)ππ

25

decays strongly favor the assignments 0+ and 1+ for the spin-parity quantum numbers of theDlowast0(2400)0Dlowast0(2400)plusmn and D1(2430)0 states respectively The measured masses and widthsas well as the JP values are in agreement with theoretical predictions based on potentialmodels [76777879]

Tables 15 and 16 summarizes the branching fractions of B mesons decays to excited D andDs states respectively It can be noted that the branching fractions for B mesons decaying to anarrow Dlowastlowast state and a pion are similar for charged and neutral B initial states the branchingfractions to a broad Dlowastlowast state and π+ are much larger for B+ than for B0 This may be dueto the fact that color-suppressed amplitudes contribute only to the B+ decay and not to theB0 decay (for a theoretical discussion see Ref [8081]) Measurements of individual branchingfractions of D mesons are dicult due to the unknown fragmentation of cc rarr Dlowastlowast or due tothe unknown B rarr DlowastlowastX branching fractions

The discoveries of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn have triggered increased interest in prop-erties of and searches for excited Ds mesons (here generically denoted D

lowastlowasts ) While the masses

and widths of Ds1(2536)plusmn and Ds2(2573)plusmn states are in relatively good agreement with po-tential model predictions the masses of Dlowasts0(2317)plusmn and Ds1(2460)plusmn states are signicantlylower than expected (see Ref [82] for a discussion of cs models) Moreover the mass splittingbetween these two states greatly exceeds that between the Ds1(2536)plusmn and Ds2(2573)plusmn Theseunexpected properties have led to interpretations of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn as exoticfour-quark states [8384]

While there are few measurements of the JP values of Dlowasts0(2317)plusmn andDs1(2460)plusmn the avail-able data favor 0+ and 1+ respectively A molecule-like (DK) interpretation of the Dlowasts0(2317)plusmn

and Ds1(2460)plusmn [8384] that can account for their low masses and isospin-breaking decay modesis tested by searching for charged and neutral isospin partners of these states thus far suchsearches have yielded negative results Therefore the subset of models that predict equal pro-duction rates for dierent charged states is excluded The molecular picture can also be testedby measuring the rates for the radiative processes Dlowasts0(2317)plusmnDs1(2460)plusmn rarr D

(lowast)s γ and com-

paring to theoretical predictions The predicted rates however are below the sensitivity ofcurrent experiments

Another model successful in explaining the total widths and the Dlowasts0(2317)plusmn Ds1(2460)plusmn

mass splitting is based on the assumption that these states are chiral partners of the groundstates D+

s and Dlowasts [85] While some measured branching fraction ratios agree with predictedvalues further experimental tests with better sensitivity are needed to conrm or refute thisscenario A summary of the mass dierence measurements is given in Table 17

Measurements by BABAR [86] and LHCb [87] rst indicated the existence of a strange-charm DlowastsJ(2860)plusmn meson An LHCb study of B0

s rarr D0Kminusπ+ decays in which they searchedfor excited Ds mesons [88] showed with 10σ signicance that this state is comprised of twodierent particles one of spin 1 and one of spin 3 This represents the rst measurement of aheavy avored spin-3 particle and the rst observation B mesons decays to spin 3 particlesA subsequent study of DsJ mesons by the LHCb collaboration [89] supports the natural parityassignment for this state (JP = 3minus) This study also shows weak evidence for a further structureat a mass around 3040 MeVc2 with unnatural parity which was rst hinted at by a Babaranalysis [86]

Recent evidence shows that the 1D family of charm resonances can be explored in the Dalitzplot analyses of B-meson decays in the same way as seen for the charm-strange resonances TheLHCb collaboration performed an analysis of B0 rarr D0π+πminus decays in which they measured

26

the spin-parity assignment of the stateDlowast3(2760)plusmn which was observed previously by BABAR [29]and LHCb [30] to be JP = 3minus The measurement suggests a spectroscopic assignment of 3D3This is the second observation of a spin-3 charm meson

Other observed excited Ds states include Ds1(2700)plusmn and Ds2(2573)plusmn The properties ofboth (mass width JP ) have been measured and determined in several analyses A theoreticaldiscussion [90] investigates the possibility that theDs1(2700)plusmn could represent radial excitationsof the Dlowastplusmns Similarly the Ds1(2860)plusmn and DsJ(3040)plusmn could be excitations of Dlowasts0(2317)plusmn andDs1(2460)plusmn or Ds1(2536)plusmn respectively

Table 18 summarizes measurements of the polarization amplitude AD (sometimes also re-ferred as helicity parameter) which describes the initial polarization of the D meson In Dlowastlowast

meson decay the helicity distribution varies like 1 + AD cos2 θH where θH is the angle in theDlowast rest frame between the two pions emitted by decay Dlowastlowast rarr Dlowastπ and the Dlowast rarr Dπ Theparameter is sensitive to possible S-wave contributions in the decay In the case of an unpolar-ized D meson decay decaying purely via D-wave the polarization amplitude is predicted to giveAD = 3 Studies of the D1(2420)0 meson by the ZEUS and BABAR collaborations suggest thatthere is an S-wave admixture in the decay which is contrary to Heavy Quark Eective Theorycalculations [9192]

27

Table 12 Recent measurements of mass and width for dierent excited Ds mesons Thecolumn JP list the most signicant assignment of spin and parity If possible an average massor width is calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowasts0(2317)plusmn 0+

D+s π

0 23196plusmn 02plusmn 14 BABAR [93]D+s π

0 23173plusmn 04plusmn 08 BABAR [73]

23180plusmn 08 Our average

Ds1(2460)plusmn 1+

D+s π

0γD+s γD

+s π

+πminus 24601plusmn 02plusmn 08 BABAR [93]D+s π

0γ 2458plusmn 10plusmn 10 BABAR [73]

24596plusmn 07 Our average

Ds1(2536)plusmn 1+

Dlowast+K0S 25357plusmn 06plusmn 05 DOslash [94]

Dlowast+K0S D

lowast0K+ 253478plusmn 031plusmn 040 BABAR [95]D+s π

+πminus 25346plusmn 03plusmn 07 BABAR [93]Dlowast+K0

S Dlowast0K+ 25350plusmn 06plusmn 10 E687 [96]

Dlowast0K+ 25353plusmn 02plusmn 05 CLEO [97]Dlowast+K0

S 25348plusmn 06plusmn 06 CLEO [97]Dlowast0K+ 25352plusmn 05plusmn 15 ARGUS [98]Dlowast+K0

S 25356plusmn 07plusmn 04 CLEO [99]Dlowast+K0

S 25359plusmn 06plusmn 20 ARGUS [100]Dlowast+K0

S 092plusmn 003plusmn 004 BABAR [101]

253510plusmn 026 092plusmn 005 Our average

Dlowasts2(2573)plusmn 2+

D0K+ Dlowast+K0S 256839plusmn 029plusmn 026 169plusmn 05plusmn 06 LHCb [102]

D+K0S D

0K+ 25694plusmn 16plusmn 05 121plusmn 45plusmn 16 LHCb [103]D+K0

S D0K+ 25722plusmn 03plusmn 10 271plusmn 06plusmn 56 BABAR [104]

D0K+ 257425plusmn 33plusmn 16 104plusmn 83plusmn 30 ARGUS [105]D0K+ 25732+17

minus16 plusmn 09 16+5minus4 plusmn 3 CLEO [106]

256908plusmn 035 169plusmn 08 Our average

Dlowasts1(2700)plusmn 1minus

Dlowast+K0S D

lowast0K+ 27323plusmn 43plusmn 58 136plusmn 19plusmn 24 LHCb [89]D0K+ 2699+14

minus7 127+24minus19 BABAR [107]

Dlowast+K0S D

lowast0K+ 27092plusmn 19plusmn 45 1158plusmn 73plusmn 121 LHCb [87]DKDlowastK 2710plusmn 2+12

minus7 149plusmn 7+39minus52 BABAR [86]

D0K+ 2708plusmn 9+11minus10 108plusmn 2+36

minus31 Belle [108]

27120plusmn 15 1215plusmn 102 Our average

Dlowasts1(2860)plusmn 1 D0K+ 2859plusmn 12plusmn 24 159plusmn 23plusmn 77 LHCb [88]

Dlowasts3(2860)plusmn 3minusDlowast+K0

S Dlowast0K+ 28671plusmn 43plusmn 19 50plusmn 11plusmn 13 LHCb [89]

D0K+ 28605plusmn 26plusmn 65 53plusmn 7plusmn 7 LHCb [88]

28650plusmn 39 522plusmn 86 Our average

DsJ(3040)plusmn Unnatural DlowastK 3044plusmn 8+30minus5 239plusmn 35+46

minus42 BABAR (m amp Γ) + LHCb(JP ) [86]+ [89]

28

Table 13 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast0(2400)0 0+

D+πminus 2297plusmn 8plusmn 20 273plusmn 12plusmn 48 BABAR [109]D+πminus 2308plusmn 17plusmn 32 276plusmn 21plusmn 63 Belle [74]D+πminus 2407plusmn 21plusmn 35 240plusmn 55plusmn 59 Focus [75]

23182plusmn 169 2674plusmn 356 Our average

Dlowast0(2400)plusmn 0+

D0π+ 2349plusmn 6plusmn 1plusmn 4 217plusmn 13plusmn 5plusmn 12 LHCb [110]D0π+ 2360plusmn 15plusmn 12plusmn 28 255plusmn 26plusmn 20plusmn 47 LHCb [111]D0π+ 2403plusmn 14plusmn 35 283plusmn 24plusmn 34 Focus(m ampΓ) + Belle(JP ) [75] + [112]

23506plusmn 59 2337plusmn 155 Our average

D1(2420)0 1+

Dlowast+πminus 24196plusmn 01plusmn 07 352plusmn 04plusmn 09 LHCb [30]Dlowast+πminus 24231plusmn 15+04

minus10 388plusmn 5+19minus54 Zeus [113]

Dlowast+πminus 24201plusmn 01plusmn 08 314plusmn 05plusmn 13 BABAR [29]Dlowast+πminus 200plusmn 17plusmn 13 CDF [114]D0π+πminus 2426plusmn 3plusmn 1 24plusmn 7plusmn 8 Belle [115]Dlowast+πminus 24214plusmn 15plusmn 09 237plusmn 27plusmn 40 Belle [74]Dlowast+πminus 2421+1

minus2 plusmn 2 20+6minus5

+3minus3 CLEO [116]

Dlowast+πminus 2422plusmn 2plusmn 2 15plusmn 8plusmn 4 E687 [96]Dlowast+πminus 2428plusmn 3plusmn 2 23+8

minus6+10minus4 CLEO [99]

Dlowast+πminus 2414plusmn 2plusmn 5 13plusmn 6+10minus5 ARGUS [117]

Dlowast+πminus 2428plusmn 8plusmn 5 58plusmn 14plusmn 10 TPS [118]

24205plusmn 05 317plusmn 07 Our average

D1(2420)plusmn 1+

Dlowast0π+ 24219plusmn 47+34minus12 Zeus [113]

D+πminusπ+ 2421plusmn 2plusmn 1 21plusmn 5plusmn 8 Belle [115]Dlowast0π+ 2425plusmn 2plusmn 2 26+8

minus7 plusmn 4 CLEO [119]Dlowast0π+ 2443plusmn 7plusmn 5 41plusmn 19plusmn 8 TPS [118]

24232plusmn 16 252plusmn 60 Our average

D1(2430)0 1+ Dlowast+πminus 2427plusmn 26plusmn 25 384+107minus75 plusmn 74 Belle [74]

Dlowast2(2460)0 2+

Dlowast+πminus 24640plusmn 14plusmn 05plusmn 02 438plusmn 29plusmn 17plusmn 06 LHCb [120]Dlowast+πminus 24604plusmn 04plusmn 12 432plusmn 12plusmn 30 LHCb [30]D+πminus 24604plusmn 01plusmn 01 456plusmn 04plusmn 11 LHCb [30]

Dlowast+πminus D+πminus 24625plusmn 24+13minus11 466plusmn 81+59

minus38 Zeus [113]D+πminus 24622plusmn 01plusmn 08 505plusmn 06plusmn 07 BABAR [29]D+πminus 24604plusmn 12plusmn 22 418plusmn 25plusmn 29 BABAR [109]D+πminus 492plusmn 23plusmn 13 CDF [114]D+πminus 24616plusmn 21plusmn 33 456plusmn 44plusmn 67 Belle [74]D+πminus 24645plusmn 11plusmn 19 387plusmn 53plusmn 29 Focus [75]D+πminus 2465plusmn 3plusmn 3 28+8

minus7 plusmn 6 CLEO [116]D+πminus 2453plusmn 3plusmn 2 25plusmn 10plusmn 5 E687 [96]Dlowast+πminus 2461plusmn 3plusmn 1 20+9

minus12+9minus10 CLEO [99]

D+πminus 2455plusmn 3plusmn 5 15+13minus10

+5minus10 ARGUS [121]

D+πminus 2459plusmn 3plusmn 2 20plusmn 10plusmn 5 TPS [118]

246049plusmn 017 4752plusmn 065 Our average

29

Table 14 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast2(2460)plusmn 2+

D0π+ 24686plusmn 06plusmn 00plusmn 03 473plusmn 15plusmn 03plusmn 06 LHCb [110]D0π+ 24656plusmn 18plusmn 05plusmn 12 460plusmn 34plusmn 14plusmn 29 LHCb [111]D0π+ 24631plusmn 02plusmn 06 486plusmn 13plusmn 19 LHCb [30]

Dlowast0π+ D0π+ 24606plusmn 44+36minus08 Zeus [113]

D0π+ 24654plusmn 02plusmn 11 BABAR [29]D0π+ 24657plusmn 18+14

minus48 497plusmn 38plusmn 64 Belle [112]D0π+ 24676plusmn 15plusmn 08 341plusmn 65plusmn 42 Focus [75]D0π+ 2463plusmn 3plusmn 3 27+11

minus8 plusmn 5 CLEO [119]D0π+ 2453plusmn 3plusmn 2 23plusmn 9plusmn 5 E687 [96]D0π+ 2469plusmn 4plusmn 6 ARGUS [122]

246555plusmn 040 467plusmn 12 Our average

D(2550)0 0minus Dlowast+πminus 25394plusmn 45plusmn 68 130plusmn 12plusmn 13 BABAR [29]

D(2580)0 Unnatural Dlowast+πminus 25795plusmn 34plusmn 55 1175plusmn 178plusmn 460 LHCb [30]

D(2600)0 Natural D+πminus 26087plusmn 24plusmn 25 93plusmn 6plusmn 13 BABAR [29]

D(2600)plusmn Natural D0π+ 26213plusmn 37plusmn 42 BABAR [29]

Dlowast(2640)plusmn 1minus Dlowast+π+πminus 2637plusmn 2plusmn 6 Delphi [123]

Dlowast(2650)0 Natural Dlowast+πminus 26492plusmn 35plusmn 35 1402plusmn 171plusmn 186 LHCb [30]

D(2740)0 Unnatural Dlowast+πminus 27370plusmn 35plusmn 112 732plusmn 134plusmn 250 LHCb [30]

D(2750)0 Dlowast+πminus 27524plusmn 17plusmn 27 71plusmn 6plusmn 11 BABAR [29]

Dlowast1(2760)0 1+

D+πminus 2781plusmn 18plusmn 11plusmn 6 177plusmn 32plusmn 20plusmn 7 LHCb [120]Dlowast+πminus 27611plusmn 51plusmn 65 744plusmn 34plusmn 370 LHCb [30]D+πminus 27601plusmn 11plusmn 37 744plusmn 34plusmn 191 LHCb [30]D+πminus 27633plusmn 23plusmn 23 609plusmn 51plusmn 36 BABAR [29]

27621plusmn 24 651plusmn 58 Our average

Dlowast3(2760)plusmn 3minus

D0π+ 2798plusmn 7plusmn 1plusmn 7 105plusmn 18plusmn 6plusmn 23 LHCb [110]D0π+ 27717plusmn 17plusmn 38 667plusmn 66plusmn 105 LHCb [30]D0π+ 27697plusmn 38plusmn 15 BABAR [29]

27739plusmn 33 723plusmn 115 Our average

30

Table 15 Product of B meson branching fraction and (daughter) excited D meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowast0(2400)0

Bminus rarr Dlowast0(2400)0(rarr D+π+)πminus61plusmn 06plusmn 18 Belle [74]68plusmn 03plusmn 20 BABAR [109]

64plusmn 14 Our average

Bminus rarr Dlowast0(2400)0(rarr D+π+)Kminus 0061plusmn 0019plusmn 0005plusmn 0014plusmn 0004 LHCb [120]

Dlowast0(2400)plusmnB0 rarr Dlowast0(2400)+(rarr D0π+)πminus

077plusmn 005plusmn 003plusmn 003plusmn 004 LHCb [110]060plusmn 013plusmn 027 Belle [112]

076plusmn 007 Our average

B0 rarr Dlowast0(2400)+(rarr D0π+)Kminus 0177plusmn 0026plusmn 0019plusmn 0067plusmn 020 LHCb [111]

D1(2420)0

Bminus rarr D1(2420)0(rarr Dlowast+πminus)πminus 68plusmn 07plusmn 13 Belle [74]

Bminus rarr D1(2420)0(rarr D0π+πminus)πminus 185plusmn 029plusmn 027plusmn 041 Belle [115]

B0 rarr D1(2420)0(rarr Dlowast+πminus)ω 07plusmn 02+01minus00 plusmn 01 Belle [124]

D1(2420)plusmn B0 rarr D1(2420)+(rarr D+πminusπ+)πminus 089plusmn 015plusmn 022 Belle [115]

D1(2430)0Bminus rarr D1(2430)0(rarr Dlowast+πminus)πminus 50plusmn 04plusmn 108 Belle [74]

B0 rarr D1(2430)0(rarr Dlowast+πminus)ω 25plusmn 04+07minus02

+04minus01 Belle [124]

Dlowast2(2460)0

Bminus rarr Dlowast2(2460)0(rarr D+πminus)πminus34plusmn 03plusmn 07 Belle [74]35plusmn 02plusmn 05 BABAR [109]

34plusmn 03 Our average

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)πminus 18plusmn 03plusmn 04 Belle [74]

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)ω 04plusmn 01+00minus01 plusmn 01 Belle [124]

Bminus rarr Dlowast2(2460)0(rarr D+π+)Kminus 0232plusmn 0011plusmn 0006plusmn 0010plusmn 0016 LHCb [120]

Dlowast2(2460)plusmnB0 rarr Dlowast2(2460)+(rarr D0π+)πminus

244plusmn 007plusmn 010plusmn 004plusmn 012 LHCb [110]215plusmn 017plusmn 031 Belle [112]

238plusmn 016 Our average

B0 rarr Dlowast2(2460)+(rarr D0π+)Kminus 0212plusmn 0010plusmn 0011plusmn 0011plusmn 025 LHCb [111]

Dlowast1(2760)0 Bminus rarr Dlowast1(2760)0(rarr D+π+)Kminus 0036plusmn 0009plusmn 0003plusmn 0007plusmn 0002 LHCb [120]

Dlowast3(2760)plusmn B0 rarr Dlowast3(2760)0(rarr D0π+)πminus 0103plusmn 0016plusmn 0007plusmn 0008plusmn 0005 LHCb [110]

31

Table 16 Product of B meson branching fraction and (daughter) excited Ds meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowasts0(2317)plusmnB0 rarr Dlowasts0(2317)+(rarr D+

s π0)Dminus

86+33minus26 plusmn 26 Belle [125]

180plusmn 40+67minus50 BABAR [126]

101+13minus12 plusmn 10plusmn 04 Belle [127]

102plusmn 15 Our average

B+ rarr Dlowasts0(2317)+(rarr D+s π

0)D0 80+13minus12 plusmn 10plusmn 04 Belle [127]

B0 rarr Dlowasts0(2317)+(rarr D+s π

0)Kminus 053+015minus013 plusmn 016 Belle [128]

Ds1(2460)plusmn

B0 rarr Ds1(2460)+(rarr Dlowast+s π0)Dminus227+73

minus62 plusmn 68 Belle [125]280plusmn 80+112

minus78 BABAR [126]

247plusmn 76 Our average

B0 rarr Ds1(2460)+(rarr Dlowast+s γ)Dminus82+22minus19 plusmn 25 Belle [125]

80plusmn 20+32minus23 BABAR [126]

81plusmn 23 Our average

Ds1(2460)+ rarr Dlowast+s π0 (56plusmn 13plusmn 9) BABAR [129]

Ds1(2460)+ rarr Dlowast+s γ (16plusmn 4plusmn 3) BABAR [129]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dminus 171plusmn 048plusmn 032 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast+K0)Dminus 261plusmn 103plusmn 031 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dlowastminus 332plusmn 088plusmn 066 BABAR [95]

Ds1(2536)plusmnB0 rarr Ds1(2536)+(rarr Dlowast+K0)Dlowastminus 500plusmn 151plusmn 067 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)D0 216plusmn 052plusmn 045 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)D0 230plusmn 098plusmn 043 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)Dlowast0 546plusmn 117plusmn 104 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)Dlowast0 392plusmn 246plusmn 083 BABAR [95]

Ds2(2573)plusmnB0 rarr Ds2(2573)(rarr D0K+)Dminus 034plusmn 017plusmn 005 BABAR [107]

B+ rarr Ds2(2573)(rarr D0K+)D0 008plusmn 14plusmn 005 BABAR [107]

Ds1(2700)plusmn B+ rarr Ds1(2700)+(rarr D0K+)D0

113plusmn 22+14minus28 Belle [108]

502plusmn 071plusmn 093 BABAR [107]

583plusmn 109 Our average

B0 rarr Ds1(2700)+(rarr D0K+)Dminus 714plusmn 096plusmn 069 BABAR [107]

32

Table 17 Mass dierence measurements for excited D mesons

Resonance Relative to ∆m [MeVc2] Measured by Reference

Dlowast1(2420)0 Dlowast+4102plusmn 21plusmn 09 Zeus [130]4117plusmn 07plusmn 04 CDF [114]

4115plusmn 08 Our average

D1(2420)plusmn Dlowast1(2420)0 4+2minus3 plusmn 3 CLEO [119]

Dlowast2(2460)0 D+ 5939plusmn 06plusmn 05 CDF [114]

Dlowast+ 4588plusmn 37+12minus13 Zeus [130]

Dlowast2(2460)plusmn Dlowast2(2460)0

31plusmn 19plusmn 09 Focus [75]minus2plusmn 4plusmn 4 CLEO [119]14plusmn 5plusmn 8 ARGUS [122]

30plusmn 19 Our average

Dlowasts0(2317)plusmn Dplusmns

3487plusmn 05plusmn 07 Belle [72]3500plusmn 12plusmn 10 CLEO [71]3513plusmn 21plusmn 19 Belle [125]

3492plusmn 07 Our average

Ds1(2460)plusmn

Dlowastplusmns

3441plusmn 13plusmn 11 Belle [72]3512plusmn 17plusmn 10 CLEO [71]3468plusmn 16plusmn 19 Belle [125]

3471plusmn 11 Our average

Dplusmns

4910plusmn 13plusmn 19 Belle [72]4914plusmn 09plusmn 15 Belle [72]

4913plusmn 14 Our average

Ds1(2536)plusmnDlowast(2010)plusmn

52483plusmn 001plusmn 004 BABAR [101]52530+044

minus041 plusmn 010 Zeus [130]5253plusmn 06plusmn 01 ALEPH [131]

52484plusmn 004 Our average

Dlowast(2007)0 5287plusmn 19plusmn 05 ALEPH [131]

Dlowasts2(2573)plusmn D0 704plusmn 3plusmn 1 ALEPH [131]

33

Table 18 Measurements of polarization amplitudes for excited D mesons

Resonance AD Measured by Reference

D1(2420)0

78+67minus27

+46minus18 ZEUS [113]

572plusmn 025 BABAR [29]59+30minus17

+24minus10 ZEUS [130]

38plusmn 06plusmn 08 BABAR [132]

561plusmn 024 Our average

D1(2420)plusmn 38plusmn 06plusmn 08 BABAR [132]

Dlowast2(2460)0 minus116plusmn 035 ZEUS [113]

D(2750)0 minus033plusmn 028 BABAR [29]

34

24 Rare and forbidden decays

This section provides a summary of rare and forbidden charm decays in tabular form The decaymodes can be categorized as avor-changing neutral currents lepton-avor-violating lepton-number-violating and both baryon- and lepton-number-violating decays Figures 9-11 plot theupper limits for D0 D+ D+

s and Λ+c decays Tables 19-22 give the corresponding numerical

results Some theoretical predictions are given in Refs [133134135136137138139140]In several cases the rare-decay nal states have been observed with the di-lepton pair being

the decay product of a hadronic resonance For these measurements the quoted limits are thoseexpected for the non-resonant di-lepton spectrum For the extrapolation to the full spectruma phase-space distribution of the non-resonant component has been assumed This applies tothe CLEO measurement of the decays D+

(s) rarr (K+π+)e+eminus [141] to the D0 measurements

of the decays D+(s) rarr π+micro+microminus [142] and to the BABAR measurements of the decays D+

(s) rarr(K+π+)e+eminus and D+

(s) rarr (K+π+)micro+microminus where the contribution from φ rarr l+lminus (l = e micro) has

been excluded In the case of the LHCb measurements of the decays D0 rarr π+πminusmicro+microminus [143]as well as the decays D+

(s) rarr π+micro+microminus [144] the contributions from φ rarr l+lminus as well as from

ρ ω rarr l+lminus (l = e micro) have been excluded

Table 19 Upper limits at 90 CL for D0 decays

Decay Limit times106 Experiment Referenceγγ 260 CLEO II [145]

38 BESIII [146]22 BaBar [147]085 Belle [148]

e+eminus 2200 CLEO [149]1700 Argus [150]1300 Mark3 [151]130 CLEO II [152]819 E789 [153]62 E791 [154]12 BaBar [155]0079 Belle [156]

micro+microminus 700 Argus [150]440 E653 [157]340 CLEO II [152]156 E789 [153]52 E791 [154]20 HERAb [158]13 BaBar [155]021 CDF [159]014 Belle [156]00062 LHCb [160]

π0e+eminus 450 CLEO II [152]π0micro+microminus 5400 CLEO II [152]

1800 E653 [157]

35

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceη e+eminus 1100 CLEO II [152]η micro+microminus 5300 CLEO II [152]π+πminuse+eminus 3700 E791 [161]ρ0e+eminus 4500 CLEO [149]

1240 E791 [161]1000 CLEO II [152]

π+πminusmicro+microminus 300 E791 [161]055 LHCb [143]

ρ0micro+microminus 8100 CLEO [149]4900 CLEO II [152]2300 E653 [157]220 E791 [161]

ω e+eminus 1800 CLEO II [152]ω micro+microminus 8300 CLEO II [152]K+Kminuse+eminus 3150 E791 [161]φ e+eminus 590 E791 [161]

520 CLEO II [152]K+Kminusmicro+microminus 330 E791 [161]φmicro+microminus 4100 CLEO II [152]

310 E791 [161]

K0e+eminus 17000 Mark3 [162]

1100 CLEO II [152]

K0micro+microminus 6700 CLEO II [152]

2600 E653 [157]Kminusπ+e+eminus 3850 E791 [161]

Klowast0

(892)e+eminus 1400 CLEO II [152]470 E791 [161]

Kminusπ+micro+microminus 3600 E791 [161]

Klowast0

(892)micro+microminus 11800 CLEO II [152]240 E791 [161]

π+πminusπ0micro+microminus 8100 E653 [157]microplusmne∓ 2700 CLEO [149]

1200 Mark3 [163]1000 Argus [150]190 CLEO II [152]172 E789 [153]81 E791 [154]081 BaBar [155]026 Belle [156]0016 LHCb [164]

π0eplusmnmicro∓ 860 CLEO II [152]η eplusmnmicro∓ 1000 CLEO II [152]

36

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceπ+πminuseplusmnmicro∓ 150 E791 [161]ρ0eplusmnmicro∓ 660 E791 [161]

490 CLEO II [152]ω eplusmnmicro∓ 1200 CLEO II [152]K+Kminuseplusmnmicro∓ 1800 E791 [161]φ eplusmnmicro∓ 470 E791 [161]

340 CLEO II [152]

K0eplusmnmicro∓ 1000 CLEO II [152]

Kminusπ+eplusmnmicro∓ 5500 E791 [161]Klowast0(892)eplusmnmicro∓ 1000 CLEO II [152]

830 E791 [161]π∓π∓eplusmneplusmn 1120 E791 [161]π∓π∓microplusmnmicroplusmn 290 E791 [161]K∓π∓eplusmneplusmn 2060 E791 [161]K∓π∓microplusmnmicroplusmn 3900 E791 [161]K∓K∓eplusmneplusmn 1520 E791 [161]K∓K∓microplusmnmicroplusmn 940 E791 [161]π∓π∓eplusmnmicroplusmn 790 E791 [161]K∓π∓eplusmnmicroplusmn 2180 E791 [161]K∓K∓eplusmnmicroplusmn 570 E791 [161]p eminus 100 CLEO [165]p e+ 110 CLEO [165]

37

γγ

ρ0micro

+microminus

π+πminusπ

0micro

+microminus

K+K

minuse

+eminus

ηe

+eminus

φmicro

+microminus

π0e

+eminus

φe

+eminus

ωmicro

+microminus

Kminusπ

+micro

+microminus

ρ0e

+eminus

K0micro

+microminus

Klowast0

(892

)e+eminus

π+πminusmicro

+microminus

micro+microminus

π+πminuse

+eminus

e+eminus

Klowast0

(892

)micro+microminus

K+K

minusmicro

+microminus

Kminusπ

+e

+eminus

π0micro

+microminus

K0e

+eminus

ωe

+eminus

ηmicro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

HFAG-charm

Belle

BESIII

CLEO II

BaBar

E791

CLEO

E653

LHCb

E789

HERAB

CDF

Argus

Mark3

June 16

K∓π∓microplusmnmicroplusmn

ωeplusmnmicro∓

Kminusπ

+eplusmnmicro∓

K∓K∓eplusmnmicroplusmn

π∓π∓eplusmnmicroplusmn

peminus

K∓π∓eplusmnmicroplusmn

π∓π∓eplusmneplusmn

ηeplusmnmicro∓

π∓π∓microplusmnmicroplusmn

K∓K∓eplusmneplusmn

K0eplusmnmicro∓

π+πminuseplusmnmicro∓

K∓K∓microplusmnmicroplusmn

ρ0eplusmnmicro∓

pe

+

φeplusmnmicro∓

microplusmne∓

K+K

minuseplusmnmicro∓

Klowast0

(892

)eplusmnmicro∓

π0eplusmnmicro∓

K∓π∓eplusmneplusmn

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

L BLHFAG-charm

E791

CLEO II

CLEO

Belle

E789

Mark3

Argus

LHCb

BaBar

June 16

Figure 9 Upper limits at 90 CL for D0 decays The top plot shows avor-changing neu-tral current decays and the bottom plot shows lepton-avor-changing (LF) lepton-number-changing (L) and both baryon- and lepton-number-changing (BL) decays38

Kminuse

+micro

+

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminusmicro

+micro

+

K+e

+eminus

π+e

+eminus

πminuse

+micro

+

Kminuse

+e

+

K+micro

+eminus

ρminusmicro

+micro

+

K+e

+microminus

K+eplusmnmicro∓

π+micro

+eminus

π+e

+microminus

πminusmicro

+micro

+

πminuse

+e

+

π+micro

+microminus

ρ+micro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E687

E653

E791

BaBar

Focus

CLEO

BESIII

LHCb

D0

June 16

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminuse

+micro

+

K+e

+eminus

π+e

+eminus

K+eplusmnmicro∓

Kminuse

+e

+

K+micro

+eminus

K+e

+microminus

Klowast+

(892

)micro+microminus

π+micro

+eminus

Kminusmicro

+micro

+

πminusmicro

+micro

+

πminuse

+e

+

πminuse

+micro

+

π+micro

+microminus

K+micro

+microminus

π+e

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E653

E791

CLEO

BaBar

Focus

LHCb

June 16

Figure 10 Upper limits at 90 CL for D+ (top) and D+s (bottom) decays Each plot shows

avor-changing neutral current decays lepton-avor-changing decays (LF) and lepton-number-changing (L) decays 39

pmicro

+microminus

pe

+microminus

σ+micro

+microminus

pe

+e

+

pe

+eminus

pe

+micro

+

pmicro

+micro

+

pmicro

+eminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

LHFAG-charm

BaBar E653

June 16

Figure 11 Upper limits at 90 CL for Λ+c decays Shown are avor-changing neutral current

decays lepton-avor-changing (LF) decays and lepton-number-changing (L) decays

40

Table 20 Upper limits at 90 CL for D+ decays

Decay Limit times106 Experiment Referenceπ+e+eminus 1100 E687 [166]

520 E791 [154]59 CLEO [141]11 BaBar [167]03 BESIII [168]

π+micro+microminus 2200 E653 [157]890 E687 [166]150 E791 [154]88 Focus [169]65 BaBar [167]39 D0 [142]0073 LHCb [144]

ρ+micro+microminus 5600 E653 [157]K+e+eminus 2000 E687 [166]

30 CLEO [141]12 BESIII [168]10 BaBar [167]

π+eplusmnmicro∓ 340 E791 [154]π+e+microminus 1100 E687 [166]

29 BaBar [167]π+micro+eminus 1300 E687 [166]

36 BaBar [167]K+eplusmnmicro∓ 680 E791 [154]K+e+microminus 1300 E687 [166]

12 BaBar [167]K+micro+eminus 1200 E687 [166]

28 BaBar [167]πminuse+e+ 1100 E687 [166]

960 E791 [154]19 BaBar [167]12 BESIII [168]11 CLEO [141]

πminusmicro+micro+ 870 E687 [166]170 E791 [154]48 Focus [169]20 BaBar [167]0022 LHCb [144]

πminuse+micro+ 1100 E687 [166]500 E791 [154]

ρminusmicro+micro+ 5600 E653 [157]Kminuse+e+ 1200 E687 [166]

35 CLEO [141]09 BaBar [167]

41

Table 20 continued from previous pageDecay Limit times106 Experiment Reference

06 BESIII [168]Kminusmicro+micro+ 3200 E653 [157]

1200 E687 [166]130 Focus [169]100 BaBar [167]

Kminuse+micro+ 1300 E687 [166]Klowastminus(892)micro+micro+ 8500 E653 [157]

Table 21 Upper limits at 90 CL for D+s decays

Decay Limit times106 Experiment Referenceπ+e+eminus 2700 E791 [154]

220 CLEO [141]130 BaBar [167]

π+micro+microminus 4300 E653 [157]1400 E791 [154]430 BaBar [167]260 Focus [169]041 LHCb [144]

K+e+eminus 16000 E791 [154]520 CLEO [141]37 BaBar [167]

K+micro+microminus 1400 E791 [154]360 Focus [169]210 BaBar [167]

Klowast+(892)micro+microminus 14000 E653 [157]π+eplusmnmicro∓ 6100 E791 [154]π+e+microminus 120 BaBar [167]π+micro+eminus 200 BaBar [167]K+eplusmnmicro∓ 6300 E791 [154]K+e+microminus 140 BaBar [167]K+micro+eminus 97 BaBar [167]πminuse+e+ 6900 E791 [154]

180 CLEO [141]41 BaBar [167]

πminusmicro+micro+ 4300 E653 [157]820 E791 [154]290 Focus [169]140 BaBar [167]012 LHCb [144]

πminuse+micro+ 7300 E791 [154]Kminuse+e+ 6300 E791 [154]

170 CLEO [141]

42

Table 21 continued from previous pageDecay Limit times106 Experiment Reference

52 BaBar [167]Kminusmicro+micro+ 5900 E653 [157]

1800 E791 [154]130 BaBar [167]

Kminuse+micro+ 6800 E791 [154]Klowastminus(892)micro+micro+ 14000 E653 [157]

Table 22 Upper limits at 90 CL for Λ+c decays

Decay Limit times106 Experiment Referencepe+eminus 55 BaBar [167]pmicro+microminus 3400 E653 [157]

440 BaBar [167]σ+micro+microminus 7000 E653 [157]pe+microminus 99 BaBar [167]pmicro+eminus 190 BaBar [167]p e+e+ 27 BaBar [167]p micro+micro+ 94 BaBar [167]

43

References

[1] N Cabibbo Phys Rev Lett 10 531533 (1963)

[2] M Kobayashi and T Maskawa Prog Theor Phys 49 652657 (1973)

[3] D Abbaneo et al (ALEPH CDF DELPHI L3 OPAL and SLD collaborations)arXivhep-ex0009052 (2000) CERN-EP-2000-096 arXivhep-ex0112028 (2001)CERN-EP-2001-050

[4] Y Amhis et al (Heavy Flavor Averaging Group) (2012) arXiv12071158 [hep-ex]

[5] K Olive et al (Particle Data Group) Chin Phys C38 090001 (2014)

[6] A L Kagan and M D Sokolo Phys Rev D80 076008 (2009) arXiv09073917 [hep-ph]

[7] Y Grossman A L Kagan and Y Nir Phys Rev D75 036008 (2007)arXivhep-ph0609178 [hep-ph]

[8] M Gersabeck M Alexander S Borghi V Gligorov and C Parkes J Phys G39 045005(2012) arXiv11116515 [hep-ex]

[9] J P Lees et al (BABAR collaboration) Phys Rev D87 012004 (2013) arXiv12093896[hep-ex]

[10] R Aaij et al (LHCb collaboration) Phys Rev Lett 112 041801 (2014) arXiv13107201[hep-ex]

[11] T A Aaltonen et al (CDF collaboration) Phys Rev D90 no 11 111103 (2014)arXiv14105435 [hep-ex]

[12] R Aaij et al (LHCb collaboration) JHEP 04 043 (2015) arXiv150106777 [hep-ex]

[13] M Staripound et al (Belle collaboration) Phys Lett B753 412418 (2016) arXiv150908266[hep-ex]

[14] B Aubert et al (BABAR collaboration) Phys Rev Lett 100 061803 (2008)arXiv07092715 [hep-ex]

[15] B Ko (Belle collaboration) PoS ICHEP2012 353 (2013) arXiv12121975

[16] T Aaltonen et al (CDF collaboration) Phys Rev Lett 109 111801 (2012)arXiv12072158 [hep-ex]

[17] R Aaij et al (LHCb collaboration) JHEP 07 041 (2014) arXiv14052797 [hep-ex]

[18] R Aaij et al (LHCb collaboration) Phys Rev Lett 116 no 19 191601 (2016)arXiv160203160 [hep-ex]

[19] T Becher and R J Hill Phys Lett B633 6169 (2006) arXivhep-ph0509090 [hep-ph]

[20] F J Gilman and R L Singleton Phys Rev D41 142 (1990)

[21] R J Hill eConf C060409 027 (2006) arXivhep-ph0606023 [hep-ph]

[22] D Becirevic and A B Kaidalov Phys Lett B478 417423 (2000) arXivhep-ph9904490[hep-ph]

44

[23] C G Boyd B Grinstein and R F Lebed Phys Rev Lett 74 46034606 (1995)arXivhep-ph9412324 [hep-ph]

[24] C G Boyd and M J Savage Phys Rev D56 303311 (1997) arXivhep-ph9702300[hep-ph]

[25] M C Arnesen B Grinstein I Z Rothstein and I W Stewart Phys Rev Lett 95 071802(2005)

[26] C Bourrely B Machet and E de Rafael Nucl Phys B189 157 (1981)

[27] D Becirevic A L Yaouanc A Oyanguren P Roudeau and F Sanlippo (2014)arXiv14071019 [hep-ph]

[28] J P Lees et al (BABAR collaboration) Phys Rev D88 052003 (2013) arXiv13045009[hep-ex]

[29] P del Amo Sanchez et al (BaBar Collaboration collaboration) PhysRev D82 111101(2010) arXiv10092076 [hep-ex]

[30] R Aaij et al (LHCb collaboration) JHEP 1309 145 (2013) arXiv13074556

[31] G Burdman and J Kambor Phys Rev D55 28172826 (1997) arXivhep-ph9602353[hep-ph]

[32] D Becirevic A Le Yaouanc L Oliver J-C Raynal P Roudeau and J Serrano Phys RevD87 no 5 054007 (2013) arXiv12065869 [hep-ph]

[33] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052022 (2015)arXiv14125502 [hep-ex]

[34] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 7 072012 (2015)arXiv150807560 [hep-ex]

[35] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 11 112008 (2015)arXiv151000308 [hep-ex]

[36] L Widhalm et al (Belle collaboration) Phys Rev Lett 97 061804 (2006)arXivhep-ex0604049 [hep-ex]

[37] B Aubert et al (BABAR collaboration) Phys Rev D76 052005 (2007) arXiv07040020[hep-ex]

[38] D Besson et al (CLEO collaboration) Phys Rev D80 032005 (2009) arXiv09062983[hep-ex]

[39] S Dobbs et al (CLEO collaboration) Phys Rev D77 112005 (2008) arXiv07121020[hep-ex]

[40] G Huang et al (CLEO collaboration) Phys Rev Lett 94 011802 (2005)arXivhep-ex0407035 [hep-ex]

[41] J Link et al (FOCUS collaboration) Phys Lett B607 233242 (2005)arXivhep-ex0410037 [hep-ex]

[42] J Adler et al (MARK-III collaboration) Phys Rev Lett 62 1821 (1989)

45

[43] K Kodama et al (Fermilab E653 collaboration) Phys Rev Lett 66 18191822 (1991)

[44] K Kodama et al (E653 collaboration) Phys Lett B336 605613 (1994)

[45] P L Frabetti et al (E687 collaboration) Phys Lett B364 127136 (1995)

[46] P L Frabetti et al (E687 collaboration) Phys Lett B315 203208 (1993)

[47] J C Anjos et al (Tagged Photon Spectrometer collaboration) Phys Rev Lett 6215871590 (1989)

[48] M Ablikim et al (BES collaboration) Phys Lett B597 3946 (2004)arXivhep-ex0406028 [hep-ex]

[49] M Ablikim et al (BES collaboration) (2006) arXivhep-ex0610019 [hep-ex]

[50] A Bean et al (CLEO collaboration) Phys Lett B317 647654 (1993)

[51] BESIII collaboration presented at ICHEP 2014 conference 2014httpindicoificuvesindicogetFilepyaccesscontribId=69ampsessionId=25ampresId=

0ampmaterialId=slidesampconfId=2025

[52] J G Korner and G A Schuler Z Phys C46 93 (1990)

[53] FLAG collaboration httpitpwikiunibechagimages44bFLAGpdf 2014httpitpwikiunibechflagimages44bFLAGpdf

[54] J Anjos et al (Fermilab E691 collaboration) Phys Rev Lett 65 26302633 (1990)

[55] K Kodama et al (Fermilab E653 collaboration) Phys Lett B274 246252 (1992)

[56] P Frabetti et al (Fermilab E687 collaboration) Phys Lett B307 262268 (1993)

[57] E Aitala et al (E791 collaboration) Phys Rev Lett 80 13931397 (1998)arXivhep-ph9710216 [hep-ph]

[58] E Aitala et al (E791 collaboration) Phys Lett B440 435441 (1998)arXivhep-ex9809026 [hep-ex]

[59] M Adamovich et al (BEATRICE collaboration) Eur Phys J C6 3541 (1999)

[60] J Link et al (FOCUS collaboration) Phys Lett B544 8996 (2002)arXivhep-ex0207049 [hep-ex]

[61] J Link et al (FOCUS collaboration) Phys Lett B607 6777 (2005)arXivhep-ex0410067 [hep-ex]

[62] P del Amo Sanchez et al (BABAR collaboration) Phys Rev D83 072001 (2011)arXiv10121810 [hep-ex]

[63] B Aubert et al (BABAR collaboration) Phys Rev D78 051101 (2008) arXiv08071599[hep-ex]

[64] H Mahlke eConf C0610161 014 (2006) arXivhep-ex0702014 [hep-ex]

[65] J Link et al (FOCUS collaboration) Phys Lett B535 4351 (2002)arXivhep-ex0203031 [hep-ex]

46

[66] K M Ecklund et al (CLEO collaboration) Phys Rev D80 052009 (2009)arXiv09073201 [hep-ex]

[67] R A Briere et al (CLEO collaboration) Phys Rev D81 112001 (2010) arXiv10041954[hep-ex]

[68] P Estabrooks R Carnegie A D Martin W Dunwoodie T Lasinski et al Nucl PhysB133 490 (1978)

[69] D Aston et al Nucl Phys B296 493 (1988)

[70] B Aubert et al (BABAR collaboration) Phys Rev Lett 90 242001 (2003)arXivhep-ex0304021 [hep-ex]

[71] D Besson et al (CLEO Collaboration collaboration) PhysRev D68 032002 (2003)arXivhep-ex0305100 [hep-ex]

[72] K Abe et al (Belle Collaboration collaboration) PhysRevLett 92 012002 (2004)arXivhep-ex0307052 [hep-ex]

[73] B Aubert et al (BaBar Collaboration collaboration) PhysRev D69 031101 (2004)arXivhep-ex0310050 [hep-ex]

[74] K Abe et al (Belle collaboration) Phys Rev D69 112002 (2004) arXivhep-ex0307021[hep-ex]

[75] J M Link et al (FOCUS Collaboration collaboration) PhysLett B586 1120 (2004)arXivhep-ex0312060 [hep-ex]

[76] S Godfrey and N Isgur Phys Rev D32 189231 (1985)

[77] S Godfrey and R Kokoski Phys Rev D43 16791687 (1991)

[78] N Isgur and M B Wise Phys Rev Lett 66 11301133 (1991)

[79] P Schweitzer S Bo and M Radici Phys Rev D66 114004 (2002)arXivhep-ph0207230 [hep-ph]

[80] F Jugeau A Le Yaouanc L Oliver and J-C Raynal Phys Rev D72 094010 (2005)arXivhep-ph0504206 [hep-ph]

[81] P Colangelo F De Fazio and R Ferrandes ModPhysLett A19 20832102 (2004)arXivhep-ph0407137 [hep-ph]

[82] R N Cahn and J D Jackson Phys Rev D68 037502 (2003) arXivhep-ph0305012[hep-ph]

[83] T Barnes F E Close and H J Lipkin PhysRev D68 054006 (2003)arXivhep-ph0305025 [hep-ph]

[84] H Lipkin PhysLett B580 5053 (2004) arXivhep-ph0306204 [hep-ph]

[85] W A Bardeen E J Eichten and C T Hill Phys Rev D68 054024 (2003)arXivhep-ph0305049 [hep-ph]

[86] B Aubert et al (BaBar Collaboration collaboration) PhysRev D80 092003 (2009)arXiv09080806 [hep-ex]

47

[87] R Aaij et al (LHCb Collaboration collaboration) JHEP 1210 151 (2012) arXiv12076016[hep-ex]

[88] R Aaij et al (LHCb collaboration) Phys Rev Lett 113 162001 (2014) arXiv14077574[hep-ex]

[89] R Aaij et al (LHCb collaboration) JHEP 02 133 (2016) arXiv160101495 [hep-ex]

[90] T Matsuki T Morii and K Sudoh EurPhysJ A31 701704 (2007)arXivhep-ph0610186 [hep-ph]

[91] N Isgur and M B Wise PhysLett B232 113117 (1989)

[92] M Neubert PhysRept 245 259396 (1994) arXivhep-ph9306320 [hep-ph]

[93] B Aubert et al (BaBar Collaboration collaboration) PhysRev D74 032007 (2006)arXivhep-ex0604030 [hep-ex]

[94] V M Abazov et al (D0 Collaboration collaboration) PhysRevLett 102 051801 (2009)arXiv07123789 [hep-ex]

[95] B Aubert et al (BABAR collaboration) Phys Rev D77 011102 (2008) arXiv07081565[hep-ex]

[96] P L Frabetti et al (E687 Collaboration collaboration) PhysRevLett 72 324327 (1994)

[97] J P Alexander et al (CLEO Collaboration collaboration) PhysLett B303 377384 (1993)

[98] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B297 425431 (1992)

[99] P Avery et al (CLEO Collaboration collaboration) PhysRev D41 774 (1990)

[100] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B230 162 (1989)

[101] J P Lees et al (BaBar Collaboration collaboration) PhysRev D83 072003 (2011)arXiv11032675 [hep-ex]

[102] R Aaij et al (LHCb collaboration) Phys Rev D90 no 7 072003 (2014) arXiv14077712[hep-ex]

[103] R Aaij et al (LHCb collaboration) PhysLett B698 1420 (2011) arXiv11020348[hep-ex]

[104] B Aubert et al (BaBar Collaboration collaboration) PhysRevLett 97 222001 (2006)arXivhep-ex0607082 [hep-ex]

[105] H Albrecht et al (ARGUS Collaboration collaboration) ZPhys C69 405408 (1996)

[106] Y Kubota et al (CLEO Collaboration collaboration) PhysRevLett 72 19721976 (1994)arXivhep-ph9403325 [hep-ph]

[107] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052002 (2015)arXiv14126751 [hep-ex]

[108] J Brodzicka et al (Belle collaboration) Phys Rev Lett 100 092001 (2008)arXiv07073491 [hep-ex]

48

[109] B Aubert et al (BABAR collaboration) Phys Rev D79 112004 (2009) arXiv09011291[hep-ex]

[110] R Aaij et al (LHCb collaboration) Phys Rev D92 no 3 032002 (2015)arXiv150501710 [hep-ex]

[111] R Aaij et al (LHCb collaboration) Phys Rev D92 no 1 012012 (2015)arXiv150501505 [hep-ex]

[112] A Kuzmin et al (Belle Collaboration collaboration) PhysRev D76 012006 (2007)arXivhep-ex0611054 [hep-ex]

[113] H Abramowicz et al (ZEUS Collaboration collaboration) NuclPhys B866 229254 (2013)arXiv12084468 [hep-ex]

[114] A Abulencia et al (CDF Collaboration collaboration) PhysRev D73 051104 (2006)arXivhep-ex0512069 [hep-ex]

[115] K Abe et al (Belle collaboration) Phys Rev Lett 94 221805 (2005)arXivhep-ex0410091 [hep-ex]

[116] P Avery et al (CLEO Collaboration collaboration) PhysLett B331 236244 (1994)arXivhep-ph9403359 [hep-ph]

[117] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B232 398 (1989)

[118] J C Anjos et al (Tagged Photon Spectrometer Collaboration collaboration) PhysRevLett62 1717 (1989)

[119] T Bergfeld et al (CLEO Collaboration collaboration) PhysLett B340 194204 (1994)

[120] R Aaij et al (LHCb collaboration) Phys Rev D91 no 9 092002 (2015)arXiv150302995 [hep-ex] [Erratum Phys RevD93no11119901(2016)]

[121] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B221 422 (1989)

[122] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B231 208 (1989)

[123] P Abreu et al (DELPHI Collaboration collaboration) PhysLett B426 231242 (1998)

[124] D Matvienko et al (Belle collaboration) Phys Rev D92 no 1 012013 (2015)arXiv150503362 [hep-ex]

[125] P Krokovny et al (Belle collaboration) Phys Rev Lett 91 262002 (2003)arXivhep-ex0308019 [hep-ex]

[126] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 181801 (2004)arXivhep-ex0408041 [hep-ex]

[127] S K Choi et al (Belle collaboration) Phys Rev D91 no 9 092011 (2015)arXiv150402637 [hep-ex] [Addendum Phys RevD92no3039905(2015)]

[128] A Drutskoy et al (Belle collaboration) Phys Rev Lett 94 061802 (2005)arXivhep-ex0409026 [hep-ex]

[129] B Aubert et al (BABAR collaboration) Phys Rev D74 031103 (2006)arXivhep-ex0605036 [hep-ex]

49

[130] S Chekanov et al (ZEUS Collaboration collaboration) EurPhysJ C60 2545 (2009)arXiv08071290 [hep-ex]

[131] A Heister et al (ALEPH Collaboration collaboration) PhysLett B526 3449 (2002)arXivhep-ex0112010 [hep-ex]

[132] B Aubert et al (BABAR collaboration) Phys Rev Lett 103 051803 (2009)arXiv08080333 [hep-ex]

[133] G Burdman E Golowich J L Hewett and S Pakvasa Phys Rev D66 014009 (2002)arXivhep-ph0112235 [hep-ph]

[134] S Fajfer A Prapotnik S Prelovsek P Singer and J Zupan Nucl Phys Proc Suppl 1159397 (2003) arXivhep-ph0208201 [hep-ph]

[135] S Fajfer N Kosnik and S Prelovsek Phys Rev D76 074010 (2007) arXiv07061133[hep-ph]

[136] E Golowich J Hewett S Pakvasa and A A Petrov Phys Rev D79 114030 (2009)arXiv09032830 [hep-ph]

[137] A Paul I I Bigi and S Recksiegel Phys Rev D82 094006 (2010) arXiv10083141[hep-ph]

[138] A Borisov (2011) arXiv11123269 [hep-ph]

[139] R-M Wang J-H Sheng J Zhu Y-Y Fan and Y Gao Int J Mod Phys A29 no 291450169 (2014)

[140] S de Boer and G Hiller Phys Rev D93 no 7 074001 (2016) arXiv151000311 [hep-ph]

[141] P Rubin et al (CLEO collaboration) Phys Rev D82 092007 (2010) arXiv10091606[hep-ex]

[142] V Abazov et al (D0 collaboration) Phys Rev Lett 100 101801 (2008) arXiv07082094[hep-ex]

[143] R Aaij et al (LHCb collaboration) Phys Lett B728 234243 (2014) arXiv13102535[hep-ex]

[144] R Aaij et al (LHCb collaboration) Phys Lett B724 203212 (2013) arXiv13046365[hep-ex]

[145] T Coan et al (CLEO collaboration) Phys Rev Lett 90 101801 (2003)arXivhep-ex0212045 [hep-ex]

[146] M Ablikim et al (BESIII collaboration) Phys Rev D91 no 11 112015 (2015)arXiv150503087 [hep-ex]

[147] J P Lees et al (BABAR collaboration) Phys Rev D85 091107 (2012) arXiv11106480[hep-ex]

[148] N K Nisar et al (Belle collaboration) Phys Rev D93 no 5 051102 (2016)arXiv151202992 [hep-ex]

[149] P Haas et al (CLEO collaboration) Phys Rev Lett 60 1614 (1988)

50

[150] H Albrecht et al (ARGUS collaboration) Phys Lett B209 380 (1988)

[151] J Adler et al (MARK-III collaboration) Phys Rev D37 2023 (1988) Erratum ibid D40(1989) 3788

[152] A Freyberger et al (CLEO collaboration) Phys Rev Lett 76 30653069 (1996)

[153] D Pripstein et al (E789 collaboration) Phys Rev D61 032005 (2000)arXivhep-ex9906022 [hep-ex]

[154] E Aitala et al (E791 collaboration) Phys Lett B462 401409 (1999)arXivhep-ex9906045 [hep-ex]

[155] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 191801 (2004)arXivhep-ex0408023 [hep-ex]

[156] M Petric et al (Belle collaboration) Phys Rev D81 091102 (2010) arXiv10032345[hep-ex]

[157] K Kodama et al (E653 collaboration) Phys Lett B345 8592 (1995)

[158] I Abt et al (HERA-B collaboration) Phys Lett B596 173183 (2004)arXivhep-ex0405059 [hep-ex]

[159] T Aaltonen et al (CDF collaboration) Phys Rev D82 091105 (2010) arXiv10085077[hep-ex]

[160] R Aaij et al (LHCb collaboration) Phys Lett B725 1524 (2013) arXiv13055059[hep-ex]

[161] E Aitala et al (E791 collaboration) Phys Rev Lett 86 39693972 (2001)arXivhep-ex0011077 [hep-ex]

[162] J Adler et al (MARK-III collaboration) Phys Rev D40 906 (1989)

[163] J Becker et al (MARK-III collaboration) Phys Lett B193 147 (1987)

[164] R Aaij et al (LHCb collaboration) Phys Lett B754 167175 (2016) arXiv151200322[hep-ex]

[165] P Rubin et al (CLEO collaboration) Phys Rev D79 097101 (2009) arXiv09041619[hep-ex]

[166] P Frabetti et al (E687 collaboration) Phys Lett B398 239244 (1997)

[167] J P Lees et al (BABAR collaboration) Phys Rev D84 072006 (2011) arXiv11074465[hep-ex]

[168] (BESIII collaboration) M-G Zhao D rareforbidden decays at BESIII in 7th International

Workshop on Charm Physics (Charm 2015) Detroit MI USA May 18-22 2015 2016arXiv160508952 [hep-ex]httpinspirehepnetrecord1466292filesarXiv160508952pdf

[169] J Link et al (FOCUS collaboration) Phys Lett B572 2131 (2003)arXivhep-ex0306049 [hep-ex]

51

  • Introduction
  • D decays
    • Interplay of direct and indirect CP violation
    • Semileptonic decays
      • Introduction
      • DP decays
      • Form factor parameterizations
      • Simple pole
      • z expansion
      • Three-pole formalism
      • Experimental techniques and results
      • Combined results for the DK channel
      • Combined results for the D channel
      • Vcs and Vcd determination
      • DV decays
      • Form factor measurements
        • Excited D(s) mesons
        • Rare and forbidden decays
          • References
Page 3: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

1 Introduction

Flavor dynamics is an important element in understanding the nature of particle physics Theaccurate knowledge of properties of heavy avor hadrons especially b hadrons plays an essentialrole for determining the elements of the Cabibbo-Kobayashi-Maskawa (CKM) weak-mixingmatrix [12] The operation of the Belle and BABAR e+eminus B factory experiments led to a largeincrease in the size of available B-meson D-hadron and τ -lepton samples enabling dramaticimprovement in the accuracies of related measurements The CDF and D0 experiments at theFermilab Tevatron have also provided important results in heavy avour physics most notablyin the B0

s sector In the D-meson sector the dedicated e+eminus charm factory experiments CLEOc

and BESIII have made signicant contributions Run I of the CERN Large Hadron Colliderdelivered high luminosity enabling the collection of even higher statistics samples of b andc hadrons and thus a further leap in precision in many areas at the ATLAS CMS and(especially) LHCb experiments With the LHC Run II ongoing further improvements arekeenly anticipated

The Heavy Flavor Averaging Group (HFAG) was formed in 2002 to continue the activities ofthe LEP Heavy Flavor Steering group [3] This group was responsible for calculating averages ofmeasurements of b-avor related quantities HFAG has evolved since its inception and currentlyconsists of seven subgroups

bull the B Lifetime and Oscillations subgroup provides averages for b-hadron lifetimes b-hadron fractions in Υ (4S) decay and pp or pp collisions and various parameters governingB0-B0 and BsB

0s mixing

bull the Unitarity Triangle Parameters subgroup provides averages for time-dependent CPasymmetry parameters and studies of B rarr DK decays and resulting determinations ofthe angles of the CKM unitarity triangle

bull the Semileptonic B Decays subgroup provides averages for inclusive and exclusive B-decay branching fractions and subsequent determinations of the CKM matrix elements|Vcb| and |Vub|

bull the B to Charm Decays subgroup provides averages of branching fractions for B decaysto nal states involving open charm or charmonium mesons

bull the Rare Decays subgroup provides averages of branching fractions and CP asymmetriesfor charmless radiative leptonic and baryonic B-meson and b-baryon decays

bull the Charm Physics subgroup provides averages of numerous quantities in the charmsector including branching fractions properties of charm baryons and of excited Dlowastlowast andDsJ mesons averages of D0-D0 mixing and CP and T violation parameters and anaverage value for the Ds decay constant fDs

bull the Tau Physics subgroup provides documentation and averages for a selection of τlepton quantities that most prot from the adoption of the HFAG prescriptions Inparticular the τ lepton branching fractions uncertainties and correlations are obtainedfrom a global t of the experimental results and this information is further elaboratedto compute several lepton universality tests and the CKM matrix element |Vus| The

3

τ lepton-avor-violating decays are documented and combinations of upper limits arecomputed

The Lifetime and Oscillations and Semileptonic subgroups were formed from the mergerof four LEP working groups The Unitary Triangle B to Charm Decays and Rare De-cays subgroups were formed to provide averages for new results obtained from the B factoryexperiments (and now also from the Fermilab Tevatron and CERN LHC experiments) TheCharm and Tau subgroups were formed more recently in response to the wealth of new dataconcerning D and τ physics Subgroups typically include representatives from Belle BABARand LHCb plus when relevant CLEO CDF and D0

This article is an update of the last HFAG preprint which used results available at leastthrough early 2012 [4] Here we report world averages using results available at least throughsummer 2014 In some cases results made available in the latter part of 2014 have been in-cluded1 In general we use all publicly available results that have written documentationThese include preliminary results presented at conferences or workshops However we do notuse preliminary results that remain unpublished for an extended period of time or for whichno publication is planned Close contacts have been established between representatives fromthe experiments and members of subgroups that perform averaging to ensure that the data areprepared in a form suitable for combinations

In the case of obtaining a world average for which χ2dof gt 1 where dof is the numberof degrees of freedom in the average calculation we do not usually scale the resulting erroras is presently done by the Particle Data Group [5] Rather we examine the systematics ofeach measurement to better understand them Unless we nd possible systematic discrepanciesbetween the measurements we do not apply any additional correction to the calculated errorWe provide the condence level of the t as an indicator for the consistency of the measurementsincluded in the average In case some special treatment was necessary to calculate an averageor if an approximation used in an average calculation might not be suciently accurate (egassuming Gaussian errors when the likelihood function indicates non-Gaussian behavior) weinclude a warning message

Chapter describes the methodology used for calculating averages In the averagingprocedure common input parameters used in the various analyses are adjusted (rescaled) tocommon values and where possible known correlations are taken into account Chapters present world average values from each of the subgroups listed above A brief summary ofthe averages presented is given in Chapter A complete listing of the averages and plotsincluding updates since this document was prepared are also available on the HFAG web site

httpwwwslacstanfordeduxorghfag

1 Particularly important new results have been included whenever possible The precise cut-o date forincluding results in the averages varies between subgroups

4

2 D decays

5

21 Interplay of direct and indirect CP violation

In decays of D0 mesons CP asymmetry measurements have contributions from both directand indirect CP violation as discussed in Sec The contribution from indirect CP viola-tion depends on the decay-time distribution of the data sample [6] This section describes acombination of measurements that allows the extraction of the individual contributions of thetwo types of CP violation At the same time the level of agreement for a no-CP -violationhypothesis is tested The observables are

AΓ equivτ(D 0rarrh+hminus)minus τ(D0rarrh+hminus)

τ(D 0rarrh+hminus) + τ(D0rarrh+hminus) (1)

where h+hminus can be K+Kminus or π+πminus and

∆ACP equiv ACP(K+Kminus)minus ACP(π+πminus) (2)

where ACP are time-integrated CP asymmetries The underlying theoretical parameters are

adirCP equiv

|AD0rarrf |2 minus |AD 0rarrf |2

|AD0rarrf |2 + |AD 0rarrf |2

aindCP equiv 1

2

[(∣∣∣∣qp∣∣∣∣+

∣∣∣∣pq∣∣∣∣)x sinφminus

(∣∣∣∣qp∣∣∣∣minus ∣∣∣∣pq

∣∣∣∣) y cosφ

] (3)

where ADrarrf is the amplitude for D rarr f [7] We use the following relations between theobservables and the underlying parameters [8]

AΓ = minusaindCP minus adir

CPyCP

∆ACP = ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

+ adirCPyCP

∆〈t〉τ

(4)

asymp ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

(5)

The rst relation constrains mostly indirect CP violation and the direct CP violation contri-bution can dier for dierent nal states In the second relation 〈t〉τ denotes the mean decaytime in units of the D0 lifetime ∆X denotes the dierence in quantity X between K+Kminus andπ+πminus nal states and X denotes the average for quantity X We neglect the last term in thisrelation as all three factors are O(10minus2) or smaller and thus this term is negligible with respectto the other two terms Note that ∆〈t〉τ 〈t〉τ and it is expected that |adir

CP| lt |∆adirCP|

because adirCP(K+Kminus) and adir

CP(π+πminus) are expected to have opposite signs [7]A χ2 t is performed in the plane ∆adir

CP vs aindCP For the BABAR result the dierence of

the quoted values for ACP(K+Kminus) and ACP(π+πminus) is calculated adding all uncertainties inquadrature This may overestimate the systematic uncertainty for the dierence as it neglectscorrelated errors however the result is conservative and the eect is small as all measurementsare statistically limited For all measurements statistical and systematic uncertainties areadded in quadrature when calculating the χ2 We use the current world average value yCP =(0866plusmn 0155) (see Sec ) and the measurements listed in Table 1

6

Table 1 Inputs to the t for direct and indirect CP violation The rst uncertainty listed isstatistical and the second is systematic

Year Experiment Results ∆〈t〉τ 〈t〉τ Reference2012 BABAR AΓ = (009plusmn 026plusmn 006) - - [9]2013 LHCb prompt AΓ(KK) = (minus0035plusmn 0062plusmn 0012) - - [10]

AΓ(ππ) = (0033plusmn 0106plusmn 0014) - -2014 CDF AΓ = (minus012plusmn 012) - - [11]2015 LHCb SL AΓ = (minus0125plusmn 0073) - - [12]2015 Belle AΓ = (minus003plusmn 020plusmn 007) - - [13]2008 BABAR ACP(KK) = (000plusmn 034plusmn 013)

ACP(ππ) = (minus024plusmn 052plusmn 022) 000 100 [14]2012 Belle prel ∆ACP = (minus087plusmn 041plusmn 006) 000 100 [15]2012 CDF ∆ACP = (minus062plusmn 021plusmn 010) 025 258 [16]2014 LHCb SL ∆ACP = (014plusmn 016plusmn 008) 001 107 [17]2016 LHCb prompt ∆ACP = (minus010plusmn 008plusmn 003) 012 210 [18]

In this t AΓ(KK) and AΓ(ππ) are assumed to be identical This assumption is sup-ported by all measurements to date A signicant relative shift due to nal-state dependentAΓ values between ∆ACP measurements with dierent mean decay times is excluded by thesemeasurements

The combination plot (see Fig 1) shows the measurements listed in Table 1 for ∆ACP andAΓ where the bands represent plusmn1σ intervals The point of no CP violation (00) is shownas a lled circle and two-dimensional 68 CL 95 CL and 997 CL regions are plotted asellipses The best t value is indicated by a cross showing the one-dimensional errors

From the t the change in χ2 from the minimum value for the no-CPV point (00) is55 which corresponds to a CL of 65 times 10minus2 for two degrees of freedom Thus the data areconsistent with the no-CP -violation hypothesis at 65 CL This p-value corresponds to 18σThe central values and plusmn1σ uncertainties for the individual parameters are

aindCP = (0056plusmn 0040)

∆adirCP = (minus0137plusmn 0070) (6)

Compared to the previous average the tension in the dierence between direct CP violationin the two nal states reduced while the common indirect CP violation moved away from theno CP violation point by about one standard deviation

7

0015 0010 0005 0000 0005 0010

aindCP

0015

0010

0005

0000

0005

0010

0015

∆adirCP

Contours contain 68 95 99 CL

CD

F

LHC

b S

L

LHC

b p

rom

pt

BaBarBelleCDF KK+ππLHCb SL KK+ππ

LHCb prompt KKLHCb prompt ππ

HFAG-charmWinter 16

no CPV

BaBar

Belle

CDF

LHCb

Figure 1 Plot of all data and the t result Individual measurements are plotted as bandsshowing their plusmn1σ range The no-CPV point (00) is shown as a lled circle and the best tvalue is indicated by a cross showing the one-dimensional uncertainties Two-dimensional 68CL 95 CL and 997 CL regions are plotted as ellipses

8

22 Semileptonic decays

221 Introduction

Semileptonic decays of D mesons involve the interaction of a leptonic current with a hadroniccurrent The latter is nonperturbative and cannot be calculated from rst principles thus it isusually parameterized in terms of form factors The transition matrix element is written

M = minusi GFradic2Vcq L

microHmicro (7)

where GF is the Fermi constant and Vcq is a CKM matrix element The leptonic current Lmicro isevaluated directly from the lepton spinors and has a simple structure this allows one to extractinformation about the form factors (in Hmicro) from data on semileptonic decays [19] Converselybecause there are no strong nal-state interactions between the leptonic and hadronic systemssemileptonic decays for which the form factors can be calculated allow one to determine Vcq [2]

222 DrarrP`ν` decays

When the nal state hadron is a pseudoscalar the hadronic current is given by

Hmicro = 〈P (p)|qγmicroc|D(pprime)〉 = f+(q2)

[(pprime + p)micro minus

m2D minusm2

P

q2qmicro

]+ f0(q2)

m2D minusm2

P

q2qmicro (8)

where mD and pprime are the mass and four momentum of the parent D meson mP and p are thoseof the daughter meson f+(q2) and f0(q2) are form factors and q = pprime minus p Kinematics requirethat f+(0) = f0(0) The contraction qmicroL

micro results in terms proportional to m` [20] and thus for` = e the terms proportionals to qmicro in Eq (8) are negligible For light leptons only the f+(q2)vector form factor is relevant and the dierential partial width is

dΓ(D rarr P`ν`)

dq2 d cos θ`=

G2F |Vcq|2

32π3plowast 3|f+(q2)|2 sin θ2

` (9)

where plowast is the magnitude of the momentum of the nal state hadron in the D rest frame andθ` is the angle of the lepton in the `ν rest frame with respect to the direction of the pseudoscalarmeson in the D rest frame

223 Form factor parameterizations

The form factor is traditionally parameterized with an explicit pole and a sum of eective poles

f+(q2) =f+(0)

(1minus α)

[(1

1minus q2m2pole

)+

Nsumk=1

ρk1minus q2(γkm2

pole)

] (10)

where ρk and γk are expansion parameters and α is a parameter that normalizes the formfactor at q2 = 0 f+(0) The parameter mpole is the mass of the lowest-lying cq resonance withthe vector quantum numbers this is expected to provide the largest contribution to the formfactor for the crarr q transition The sum over N gives the contribution of higher mass statesFor example for D rarr π transitions the dominant resonance is expected to be Dlowast(2010) andthus mpole = mDlowast(2010) For D rarr K transitions the dominant contribution is expected from

Dlowasts(2112) with mpole = mDlowasts (2112)

9

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Comparison between CLEO-c and BABAR results for the quantities q2H20 (q2) and

q2h0(q2)H0(q2)

Table 11 Results for rV and r2 from various experiments

Experiment Ref rV r2

D+ rarr Klowast0l+ν

E691 [54] 20plusmn 06plusmn 03 00plusmn 05plusmn 02E653 [55] 200plusmn 033plusmn 016 082plusmn 022plusmn 011E687 [56] 174plusmn 027plusmn 028 078plusmn 018plusmn 011

E791 (e) [57] 190plusmn 011plusmn 009 071plusmn 008plusmn 009E791 (micro) [58] 184plusmn011plusmn009 075plusmn008plusmn009Beatrice [59] 145plusmn 023plusmn 007 100plusmn 015plusmn 003FOCUS [60] 1504plusmn0057plusmn0039 0875plusmn0049plusmn0064

D0 rarr K0πminusmicro+ν

FOCUS [61] 1706plusmn0677plusmn0342 0912plusmn0370plusmn0104BABAR [62] 1493plusmn 0014plusmn 0021 0775plusmn 0011plusmn 0011

D+s rarr φ e+νBABAR [63] 1849plusmn0060plusmn0095 0763plusmn0071plusmn0065

D0 D+ rarr ρ eνCLEO [64] 140plusmn025plusmn003 057plusmn018plusmn006

23

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

HFLAV())+-amp

Figure 7 A comparison of r2 (lled inverted triangles) and rV (open triangles) values fromvarious experiments The rst seven measurements are for D+ rarr Kminusπ+l+νl decays Alsoshown as a line with 1-σ limits is the average of these The last two points are D+

s and D0

decays

24

23 Excited D(s) mesons

Excited charm meson states have received increased attention since the rst observation ofstates that could not be accommodated by QCD predictions [70 71 72 73] Tables 12 13and 14 summarize recent measurements of the masses and widths of excited D and Ds mesonsrespectively If a preferred assignment of spin and parity was measured it is listed in the columnJP where the label natural denotes JP = 0minus 1+ 2minus and unnatural JP = 0+ 1minus 2+ Ifpossible an average mass and width was calculated which is listed in the gray shaded rowThe calculation of the averages assumes no correlation between individual measurements Asummary of the averaged masses and widths is shown in Figure 8

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

0+ 1+ 2+ 1minus 1 3minus

unnatu

ral

Dlowast s0

(2317)plusmn

Ds1

(2460)plusmn

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn D

sJ(3

040)plusmn

HFAG-charmAugust 2016

(a)

Mas

s[M

eVc

2]

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

0+ 1+ 2+ 0minus 1minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ralDlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn

D(2

550)0

D(2

580)0

D(2

600)0

D(2

600)plusmn

Dlowast (

2640)plusmn

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(b)

Mas

s[M

eVc

2]

0

50

100

150

200

250

300

350

400

450

500

550

1+ 2+ 1minus 1 3minus

unnatu

ral

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn

DsJ

(3040)plusmn

HFAG-charmAugust 2016

(c)

Wid

th[M

eV]

50100150200250300350400450500550600650700

0+ 1+ 2+ 0minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ral

Dlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn D(2

550)0

D(2

580)0

D(2

600)0

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(d)

Wid

th[M

eV]

Figure 8 Averaged masses for Ds mesons are shown in subgure (a) and for D mesons insubgure (b) The average widths for Ds mesons are shown in subgure (c) and for D mesonsin subgure (d) The vertical shaded regions distinguish between dierent spin parity states

The masses and widths of narrow (Γ lt 50 MeV) orbitally excited D mesons (denotedDlowastlowast) both neutral and charged are well established Measurements of broad states (Γ sim200400 MeV) are less abundant as identifying the signal is more challenging There is aslight discrepancy between the Dlowast0(2400)0 masses measured by the Belle [74] and FOCUS [75]experiments No data exist yet for the D1(2430)plusmn state Dalitz plot analyses of B rarr D(lowast)ππ

25

decays strongly favor the assignments 0+ and 1+ for the spin-parity quantum numbers of theDlowast0(2400)0Dlowast0(2400)plusmn and D1(2430)0 states respectively The measured masses and widthsas well as the JP values are in agreement with theoretical predictions based on potentialmodels [76777879]

Tables 15 and 16 summarizes the branching fractions of B mesons decays to excited D andDs states respectively It can be noted that the branching fractions for B mesons decaying to anarrow Dlowastlowast state and a pion are similar for charged and neutral B initial states the branchingfractions to a broad Dlowastlowast state and π+ are much larger for B+ than for B0 This may be dueto the fact that color-suppressed amplitudes contribute only to the B+ decay and not to theB0 decay (for a theoretical discussion see Ref [8081]) Measurements of individual branchingfractions of D mesons are dicult due to the unknown fragmentation of cc rarr Dlowastlowast or due tothe unknown B rarr DlowastlowastX branching fractions

The discoveries of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn have triggered increased interest in prop-erties of and searches for excited Ds mesons (here generically denoted D

lowastlowasts ) While the masses

and widths of Ds1(2536)plusmn and Ds2(2573)plusmn states are in relatively good agreement with po-tential model predictions the masses of Dlowasts0(2317)plusmn and Ds1(2460)plusmn states are signicantlylower than expected (see Ref [82] for a discussion of cs models) Moreover the mass splittingbetween these two states greatly exceeds that between the Ds1(2536)plusmn and Ds2(2573)plusmn Theseunexpected properties have led to interpretations of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn as exoticfour-quark states [8384]

While there are few measurements of the JP values of Dlowasts0(2317)plusmn andDs1(2460)plusmn the avail-able data favor 0+ and 1+ respectively A molecule-like (DK) interpretation of the Dlowasts0(2317)plusmn

and Ds1(2460)plusmn [8384] that can account for their low masses and isospin-breaking decay modesis tested by searching for charged and neutral isospin partners of these states thus far suchsearches have yielded negative results Therefore the subset of models that predict equal pro-duction rates for dierent charged states is excluded The molecular picture can also be testedby measuring the rates for the radiative processes Dlowasts0(2317)plusmnDs1(2460)plusmn rarr D

(lowast)s γ and com-

paring to theoretical predictions The predicted rates however are below the sensitivity ofcurrent experiments

Another model successful in explaining the total widths and the Dlowasts0(2317)plusmn Ds1(2460)plusmn

mass splitting is based on the assumption that these states are chiral partners of the groundstates D+

s and Dlowasts [85] While some measured branching fraction ratios agree with predictedvalues further experimental tests with better sensitivity are needed to conrm or refute thisscenario A summary of the mass dierence measurements is given in Table 17

Measurements by BABAR [86] and LHCb [87] rst indicated the existence of a strange-charm DlowastsJ(2860)plusmn meson An LHCb study of B0

s rarr D0Kminusπ+ decays in which they searchedfor excited Ds mesons [88] showed with 10σ signicance that this state is comprised of twodierent particles one of spin 1 and one of spin 3 This represents the rst measurement of aheavy avored spin-3 particle and the rst observation B mesons decays to spin 3 particlesA subsequent study of DsJ mesons by the LHCb collaboration [89] supports the natural parityassignment for this state (JP = 3minus) This study also shows weak evidence for a further structureat a mass around 3040 MeVc2 with unnatural parity which was rst hinted at by a Babaranalysis [86]

Recent evidence shows that the 1D family of charm resonances can be explored in the Dalitzplot analyses of B-meson decays in the same way as seen for the charm-strange resonances TheLHCb collaboration performed an analysis of B0 rarr D0π+πminus decays in which they measured

26

the spin-parity assignment of the stateDlowast3(2760)plusmn which was observed previously by BABAR [29]and LHCb [30] to be JP = 3minus The measurement suggests a spectroscopic assignment of 3D3This is the second observation of a spin-3 charm meson

Other observed excited Ds states include Ds1(2700)plusmn and Ds2(2573)plusmn The properties ofboth (mass width JP ) have been measured and determined in several analyses A theoreticaldiscussion [90] investigates the possibility that theDs1(2700)plusmn could represent radial excitationsof the Dlowastplusmns Similarly the Ds1(2860)plusmn and DsJ(3040)plusmn could be excitations of Dlowasts0(2317)plusmn andDs1(2460)plusmn or Ds1(2536)plusmn respectively

Table 18 summarizes measurements of the polarization amplitude AD (sometimes also re-ferred as helicity parameter) which describes the initial polarization of the D meson In Dlowastlowast

meson decay the helicity distribution varies like 1 + AD cos2 θH where θH is the angle in theDlowast rest frame between the two pions emitted by decay Dlowastlowast rarr Dlowastπ and the Dlowast rarr Dπ Theparameter is sensitive to possible S-wave contributions in the decay In the case of an unpolar-ized D meson decay decaying purely via D-wave the polarization amplitude is predicted to giveAD = 3 Studies of the D1(2420)0 meson by the ZEUS and BABAR collaborations suggest thatthere is an S-wave admixture in the decay which is contrary to Heavy Quark Eective Theorycalculations [9192]

27

Table 12 Recent measurements of mass and width for dierent excited Ds mesons Thecolumn JP list the most signicant assignment of spin and parity If possible an average massor width is calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowasts0(2317)plusmn 0+

D+s π

0 23196plusmn 02plusmn 14 BABAR [93]D+s π

0 23173plusmn 04plusmn 08 BABAR [73]

23180plusmn 08 Our average

Ds1(2460)plusmn 1+

D+s π

0γD+s γD

+s π

+πminus 24601plusmn 02plusmn 08 BABAR [93]D+s π

0γ 2458plusmn 10plusmn 10 BABAR [73]

24596plusmn 07 Our average

Ds1(2536)plusmn 1+

Dlowast+K0S 25357plusmn 06plusmn 05 DOslash [94]

Dlowast+K0S D

lowast0K+ 253478plusmn 031plusmn 040 BABAR [95]D+s π

+πminus 25346plusmn 03plusmn 07 BABAR [93]Dlowast+K0

S Dlowast0K+ 25350plusmn 06plusmn 10 E687 [96]

Dlowast0K+ 25353plusmn 02plusmn 05 CLEO [97]Dlowast+K0

S 25348plusmn 06plusmn 06 CLEO [97]Dlowast0K+ 25352plusmn 05plusmn 15 ARGUS [98]Dlowast+K0

S 25356plusmn 07plusmn 04 CLEO [99]Dlowast+K0

S 25359plusmn 06plusmn 20 ARGUS [100]Dlowast+K0

S 092plusmn 003plusmn 004 BABAR [101]

253510plusmn 026 092plusmn 005 Our average

Dlowasts2(2573)plusmn 2+

D0K+ Dlowast+K0S 256839plusmn 029plusmn 026 169plusmn 05plusmn 06 LHCb [102]

D+K0S D

0K+ 25694plusmn 16plusmn 05 121plusmn 45plusmn 16 LHCb [103]D+K0

S D0K+ 25722plusmn 03plusmn 10 271plusmn 06plusmn 56 BABAR [104]

D0K+ 257425plusmn 33plusmn 16 104plusmn 83plusmn 30 ARGUS [105]D0K+ 25732+17

minus16 plusmn 09 16+5minus4 plusmn 3 CLEO [106]

256908plusmn 035 169plusmn 08 Our average

Dlowasts1(2700)plusmn 1minus

Dlowast+K0S D

lowast0K+ 27323plusmn 43plusmn 58 136plusmn 19plusmn 24 LHCb [89]D0K+ 2699+14

minus7 127+24minus19 BABAR [107]

Dlowast+K0S D

lowast0K+ 27092plusmn 19plusmn 45 1158plusmn 73plusmn 121 LHCb [87]DKDlowastK 2710plusmn 2+12

minus7 149plusmn 7+39minus52 BABAR [86]

D0K+ 2708plusmn 9+11minus10 108plusmn 2+36

minus31 Belle [108]

27120plusmn 15 1215plusmn 102 Our average

Dlowasts1(2860)plusmn 1 D0K+ 2859plusmn 12plusmn 24 159plusmn 23plusmn 77 LHCb [88]

Dlowasts3(2860)plusmn 3minusDlowast+K0

S Dlowast0K+ 28671plusmn 43plusmn 19 50plusmn 11plusmn 13 LHCb [89]

D0K+ 28605plusmn 26plusmn 65 53plusmn 7plusmn 7 LHCb [88]

28650plusmn 39 522plusmn 86 Our average

DsJ(3040)plusmn Unnatural DlowastK 3044plusmn 8+30minus5 239plusmn 35+46

minus42 BABAR (m amp Γ) + LHCb(JP ) [86]+ [89]

28

Table 13 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast0(2400)0 0+

D+πminus 2297plusmn 8plusmn 20 273plusmn 12plusmn 48 BABAR [109]D+πminus 2308plusmn 17plusmn 32 276plusmn 21plusmn 63 Belle [74]D+πminus 2407plusmn 21plusmn 35 240plusmn 55plusmn 59 Focus [75]

23182plusmn 169 2674plusmn 356 Our average

Dlowast0(2400)plusmn 0+

D0π+ 2349plusmn 6plusmn 1plusmn 4 217plusmn 13plusmn 5plusmn 12 LHCb [110]D0π+ 2360plusmn 15plusmn 12plusmn 28 255plusmn 26plusmn 20plusmn 47 LHCb [111]D0π+ 2403plusmn 14plusmn 35 283plusmn 24plusmn 34 Focus(m ampΓ) + Belle(JP ) [75] + [112]

23506plusmn 59 2337plusmn 155 Our average

D1(2420)0 1+

Dlowast+πminus 24196plusmn 01plusmn 07 352plusmn 04plusmn 09 LHCb [30]Dlowast+πminus 24231plusmn 15+04

minus10 388plusmn 5+19minus54 Zeus [113]

Dlowast+πminus 24201plusmn 01plusmn 08 314plusmn 05plusmn 13 BABAR [29]Dlowast+πminus 200plusmn 17plusmn 13 CDF [114]D0π+πminus 2426plusmn 3plusmn 1 24plusmn 7plusmn 8 Belle [115]Dlowast+πminus 24214plusmn 15plusmn 09 237plusmn 27plusmn 40 Belle [74]Dlowast+πminus 2421+1

minus2 plusmn 2 20+6minus5

+3minus3 CLEO [116]

Dlowast+πminus 2422plusmn 2plusmn 2 15plusmn 8plusmn 4 E687 [96]Dlowast+πminus 2428plusmn 3plusmn 2 23+8

minus6+10minus4 CLEO [99]

Dlowast+πminus 2414plusmn 2plusmn 5 13plusmn 6+10minus5 ARGUS [117]

Dlowast+πminus 2428plusmn 8plusmn 5 58plusmn 14plusmn 10 TPS [118]

24205plusmn 05 317plusmn 07 Our average

D1(2420)plusmn 1+

Dlowast0π+ 24219plusmn 47+34minus12 Zeus [113]

D+πminusπ+ 2421plusmn 2plusmn 1 21plusmn 5plusmn 8 Belle [115]Dlowast0π+ 2425plusmn 2plusmn 2 26+8

minus7 plusmn 4 CLEO [119]Dlowast0π+ 2443plusmn 7plusmn 5 41plusmn 19plusmn 8 TPS [118]

24232plusmn 16 252plusmn 60 Our average

D1(2430)0 1+ Dlowast+πminus 2427plusmn 26plusmn 25 384+107minus75 plusmn 74 Belle [74]

Dlowast2(2460)0 2+

Dlowast+πminus 24640plusmn 14plusmn 05plusmn 02 438plusmn 29plusmn 17plusmn 06 LHCb [120]Dlowast+πminus 24604plusmn 04plusmn 12 432plusmn 12plusmn 30 LHCb [30]D+πminus 24604plusmn 01plusmn 01 456plusmn 04plusmn 11 LHCb [30]

Dlowast+πminus D+πminus 24625plusmn 24+13minus11 466plusmn 81+59

minus38 Zeus [113]D+πminus 24622plusmn 01plusmn 08 505plusmn 06plusmn 07 BABAR [29]D+πminus 24604plusmn 12plusmn 22 418plusmn 25plusmn 29 BABAR [109]D+πminus 492plusmn 23plusmn 13 CDF [114]D+πminus 24616plusmn 21plusmn 33 456plusmn 44plusmn 67 Belle [74]D+πminus 24645plusmn 11plusmn 19 387plusmn 53plusmn 29 Focus [75]D+πminus 2465plusmn 3plusmn 3 28+8

minus7 plusmn 6 CLEO [116]D+πminus 2453plusmn 3plusmn 2 25plusmn 10plusmn 5 E687 [96]Dlowast+πminus 2461plusmn 3plusmn 1 20+9

minus12+9minus10 CLEO [99]

D+πminus 2455plusmn 3plusmn 5 15+13minus10

+5minus10 ARGUS [121]

D+πminus 2459plusmn 3plusmn 2 20plusmn 10plusmn 5 TPS [118]

246049plusmn 017 4752plusmn 065 Our average

29

Table 14 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast2(2460)plusmn 2+

D0π+ 24686plusmn 06plusmn 00plusmn 03 473plusmn 15plusmn 03plusmn 06 LHCb [110]D0π+ 24656plusmn 18plusmn 05plusmn 12 460plusmn 34plusmn 14plusmn 29 LHCb [111]D0π+ 24631plusmn 02plusmn 06 486plusmn 13plusmn 19 LHCb [30]

Dlowast0π+ D0π+ 24606plusmn 44+36minus08 Zeus [113]

D0π+ 24654plusmn 02plusmn 11 BABAR [29]D0π+ 24657plusmn 18+14

minus48 497plusmn 38plusmn 64 Belle [112]D0π+ 24676plusmn 15plusmn 08 341plusmn 65plusmn 42 Focus [75]D0π+ 2463plusmn 3plusmn 3 27+11

minus8 plusmn 5 CLEO [119]D0π+ 2453plusmn 3plusmn 2 23plusmn 9plusmn 5 E687 [96]D0π+ 2469plusmn 4plusmn 6 ARGUS [122]

246555plusmn 040 467plusmn 12 Our average

D(2550)0 0minus Dlowast+πminus 25394plusmn 45plusmn 68 130plusmn 12plusmn 13 BABAR [29]

D(2580)0 Unnatural Dlowast+πminus 25795plusmn 34plusmn 55 1175plusmn 178plusmn 460 LHCb [30]

D(2600)0 Natural D+πminus 26087plusmn 24plusmn 25 93plusmn 6plusmn 13 BABAR [29]

D(2600)plusmn Natural D0π+ 26213plusmn 37plusmn 42 BABAR [29]

Dlowast(2640)plusmn 1minus Dlowast+π+πminus 2637plusmn 2plusmn 6 Delphi [123]

Dlowast(2650)0 Natural Dlowast+πminus 26492plusmn 35plusmn 35 1402plusmn 171plusmn 186 LHCb [30]

D(2740)0 Unnatural Dlowast+πminus 27370plusmn 35plusmn 112 732plusmn 134plusmn 250 LHCb [30]

D(2750)0 Dlowast+πminus 27524plusmn 17plusmn 27 71plusmn 6plusmn 11 BABAR [29]

Dlowast1(2760)0 1+

D+πminus 2781plusmn 18plusmn 11plusmn 6 177plusmn 32plusmn 20plusmn 7 LHCb [120]Dlowast+πminus 27611plusmn 51plusmn 65 744plusmn 34plusmn 370 LHCb [30]D+πminus 27601plusmn 11plusmn 37 744plusmn 34plusmn 191 LHCb [30]D+πminus 27633plusmn 23plusmn 23 609plusmn 51plusmn 36 BABAR [29]

27621plusmn 24 651plusmn 58 Our average

Dlowast3(2760)plusmn 3minus

D0π+ 2798plusmn 7plusmn 1plusmn 7 105plusmn 18plusmn 6plusmn 23 LHCb [110]D0π+ 27717plusmn 17plusmn 38 667plusmn 66plusmn 105 LHCb [30]D0π+ 27697plusmn 38plusmn 15 BABAR [29]

27739plusmn 33 723plusmn 115 Our average

30

Table 15 Product of B meson branching fraction and (daughter) excited D meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowast0(2400)0

Bminus rarr Dlowast0(2400)0(rarr D+π+)πminus61plusmn 06plusmn 18 Belle [74]68plusmn 03plusmn 20 BABAR [109]

64plusmn 14 Our average

Bminus rarr Dlowast0(2400)0(rarr D+π+)Kminus 0061plusmn 0019plusmn 0005plusmn 0014plusmn 0004 LHCb [120]

Dlowast0(2400)plusmnB0 rarr Dlowast0(2400)+(rarr D0π+)πminus

077plusmn 005plusmn 003plusmn 003plusmn 004 LHCb [110]060plusmn 013plusmn 027 Belle [112]

076plusmn 007 Our average

B0 rarr Dlowast0(2400)+(rarr D0π+)Kminus 0177plusmn 0026plusmn 0019plusmn 0067plusmn 020 LHCb [111]

D1(2420)0

Bminus rarr D1(2420)0(rarr Dlowast+πminus)πminus 68plusmn 07plusmn 13 Belle [74]

Bminus rarr D1(2420)0(rarr D0π+πminus)πminus 185plusmn 029plusmn 027plusmn 041 Belle [115]

B0 rarr D1(2420)0(rarr Dlowast+πminus)ω 07plusmn 02+01minus00 plusmn 01 Belle [124]

D1(2420)plusmn B0 rarr D1(2420)+(rarr D+πminusπ+)πminus 089plusmn 015plusmn 022 Belle [115]

D1(2430)0Bminus rarr D1(2430)0(rarr Dlowast+πminus)πminus 50plusmn 04plusmn 108 Belle [74]

B0 rarr D1(2430)0(rarr Dlowast+πminus)ω 25plusmn 04+07minus02

+04minus01 Belle [124]

Dlowast2(2460)0

Bminus rarr Dlowast2(2460)0(rarr D+πminus)πminus34plusmn 03plusmn 07 Belle [74]35plusmn 02plusmn 05 BABAR [109]

34plusmn 03 Our average

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)πminus 18plusmn 03plusmn 04 Belle [74]

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)ω 04plusmn 01+00minus01 plusmn 01 Belle [124]

Bminus rarr Dlowast2(2460)0(rarr D+π+)Kminus 0232plusmn 0011plusmn 0006plusmn 0010plusmn 0016 LHCb [120]

Dlowast2(2460)plusmnB0 rarr Dlowast2(2460)+(rarr D0π+)πminus

244plusmn 007plusmn 010plusmn 004plusmn 012 LHCb [110]215plusmn 017plusmn 031 Belle [112]

238plusmn 016 Our average

B0 rarr Dlowast2(2460)+(rarr D0π+)Kminus 0212plusmn 0010plusmn 0011plusmn 0011plusmn 025 LHCb [111]

Dlowast1(2760)0 Bminus rarr Dlowast1(2760)0(rarr D+π+)Kminus 0036plusmn 0009plusmn 0003plusmn 0007plusmn 0002 LHCb [120]

Dlowast3(2760)plusmn B0 rarr Dlowast3(2760)0(rarr D0π+)πminus 0103plusmn 0016plusmn 0007plusmn 0008plusmn 0005 LHCb [110]

31

Table 16 Product of B meson branching fraction and (daughter) excited Ds meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowasts0(2317)plusmnB0 rarr Dlowasts0(2317)+(rarr D+

s π0)Dminus

86+33minus26 plusmn 26 Belle [125]

180plusmn 40+67minus50 BABAR [126]

101+13minus12 plusmn 10plusmn 04 Belle [127]

102plusmn 15 Our average

B+ rarr Dlowasts0(2317)+(rarr D+s π

0)D0 80+13minus12 plusmn 10plusmn 04 Belle [127]

B0 rarr Dlowasts0(2317)+(rarr D+s π

0)Kminus 053+015minus013 plusmn 016 Belle [128]

Ds1(2460)plusmn

B0 rarr Ds1(2460)+(rarr Dlowast+s π0)Dminus227+73

minus62 plusmn 68 Belle [125]280plusmn 80+112

minus78 BABAR [126]

247plusmn 76 Our average

B0 rarr Ds1(2460)+(rarr Dlowast+s γ)Dminus82+22minus19 plusmn 25 Belle [125]

80plusmn 20+32minus23 BABAR [126]

81plusmn 23 Our average

Ds1(2460)+ rarr Dlowast+s π0 (56plusmn 13plusmn 9) BABAR [129]

Ds1(2460)+ rarr Dlowast+s γ (16plusmn 4plusmn 3) BABAR [129]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dminus 171plusmn 048plusmn 032 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast+K0)Dminus 261plusmn 103plusmn 031 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dlowastminus 332plusmn 088plusmn 066 BABAR [95]

Ds1(2536)plusmnB0 rarr Ds1(2536)+(rarr Dlowast+K0)Dlowastminus 500plusmn 151plusmn 067 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)D0 216plusmn 052plusmn 045 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)D0 230plusmn 098plusmn 043 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)Dlowast0 546plusmn 117plusmn 104 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)Dlowast0 392plusmn 246plusmn 083 BABAR [95]

Ds2(2573)plusmnB0 rarr Ds2(2573)(rarr D0K+)Dminus 034plusmn 017plusmn 005 BABAR [107]

B+ rarr Ds2(2573)(rarr D0K+)D0 008plusmn 14plusmn 005 BABAR [107]

Ds1(2700)plusmn B+ rarr Ds1(2700)+(rarr D0K+)D0

113plusmn 22+14minus28 Belle [108]

502plusmn 071plusmn 093 BABAR [107]

583plusmn 109 Our average

B0 rarr Ds1(2700)+(rarr D0K+)Dminus 714plusmn 096plusmn 069 BABAR [107]

32

Table 17 Mass dierence measurements for excited D mesons

Resonance Relative to ∆m [MeVc2] Measured by Reference

Dlowast1(2420)0 Dlowast+4102plusmn 21plusmn 09 Zeus [130]4117plusmn 07plusmn 04 CDF [114]

4115plusmn 08 Our average

D1(2420)plusmn Dlowast1(2420)0 4+2minus3 plusmn 3 CLEO [119]

Dlowast2(2460)0 D+ 5939plusmn 06plusmn 05 CDF [114]

Dlowast+ 4588plusmn 37+12minus13 Zeus [130]

Dlowast2(2460)plusmn Dlowast2(2460)0

31plusmn 19plusmn 09 Focus [75]minus2plusmn 4plusmn 4 CLEO [119]14plusmn 5plusmn 8 ARGUS [122]

30plusmn 19 Our average

Dlowasts0(2317)plusmn Dplusmns

3487plusmn 05plusmn 07 Belle [72]3500plusmn 12plusmn 10 CLEO [71]3513plusmn 21plusmn 19 Belle [125]

3492plusmn 07 Our average

Ds1(2460)plusmn

Dlowastplusmns

3441plusmn 13plusmn 11 Belle [72]3512plusmn 17plusmn 10 CLEO [71]3468plusmn 16plusmn 19 Belle [125]

3471plusmn 11 Our average

Dplusmns

4910plusmn 13plusmn 19 Belle [72]4914plusmn 09plusmn 15 Belle [72]

4913plusmn 14 Our average

Ds1(2536)plusmnDlowast(2010)plusmn

52483plusmn 001plusmn 004 BABAR [101]52530+044

minus041 plusmn 010 Zeus [130]5253plusmn 06plusmn 01 ALEPH [131]

52484plusmn 004 Our average

Dlowast(2007)0 5287plusmn 19plusmn 05 ALEPH [131]

Dlowasts2(2573)plusmn D0 704plusmn 3plusmn 1 ALEPH [131]

33

Table 18 Measurements of polarization amplitudes for excited D mesons

Resonance AD Measured by Reference

D1(2420)0

78+67minus27

+46minus18 ZEUS [113]

572plusmn 025 BABAR [29]59+30minus17

+24minus10 ZEUS [130]

38plusmn 06plusmn 08 BABAR [132]

561plusmn 024 Our average

D1(2420)plusmn 38plusmn 06plusmn 08 BABAR [132]

Dlowast2(2460)0 minus116plusmn 035 ZEUS [113]

D(2750)0 minus033plusmn 028 BABAR [29]

34

24 Rare and forbidden decays

This section provides a summary of rare and forbidden charm decays in tabular form The decaymodes can be categorized as avor-changing neutral currents lepton-avor-violating lepton-number-violating and both baryon- and lepton-number-violating decays Figures 9-11 plot theupper limits for D0 D+ D+

s and Λ+c decays Tables 19-22 give the corresponding numerical

results Some theoretical predictions are given in Refs [133134135136137138139140]In several cases the rare-decay nal states have been observed with the di-lepton pair being

the decay product of a hadronic resonance For these measurements the quoted limits are thoseexpected for the non-resonant di-lepton spectrum For the extrapolation to the full spectruma phase-space distribution of the non-resonant component has been assumed This applies tothe CLEO measurement of the decays D+

(s) rarr (K+π+)e+eminus [141] to the D0 measurements

of the decays D+(s) rarr π+micro+microminus [142] and to the BABAR measurements of the decays D+

(s) rarr(K+π+)e+eminus and D+

(s) rarr (K+π+)micro+microminus where the contribution from φ rarr l+lminus (l = e micro) has

been excluded In the case of the LHCb measurements of the decays D0 rarr π+πminusmicro+microminus [143]as well as the decays D+

(s) rarr π+micro+microminus [144] the contributions from φ rarr l+lminus as well as from

ρ ω rarr l+lminus (l = e micro) have been excluded

Table 19 Upper limits at 90 CL for D0 decays

Decay Limit times106 Experiment Referenceγγ 260 CLEO II [145]

38 BESIII [146]22 BaBar [147]085 Belle [148]

e+eminus 2200 CLEO [149]1700 Argus [150]1300 Mark3 [151]130 CLEO II [152]819 E789 [153]62 E791 [154]12 BaBar [155]0079 Belle [156]

micro+microminus 700 Argus [150]440 E653 [157]340 CLEO II [152]156 E789 [153]52 E791 [154]20 HERAb [158]13 BaBar [155]021 CDF [159]014 Belle [156]00062 LHCb [160]

π0e+eminus 450 CLEO II [152]π0micro+microminus 5400 CLEO II [152]

1800 E653 [157]

35

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceη e+eminus 1100 CLEO II [152]η micro+microminus 5300 CLEO II [152]π+πminuse+eminus 3700 E791 [161]ρ0e+eminus 4500 CLEO [149]

1240 E791 [161]1000 CLEO II [152]

π+πminusmicro+microminus 300 E791 [161]055 LHCb [143]

ρ0micro+microminus 8100 CLEO [149]4900 CLEO II [152]2300 E653 [157]220 E791 [161]

ω e+eminus 1800 CLEO II [152]ω micro+microminus 8300 CLEO II [152]K+Kminuse+eminus 3150 E791 [161]φ e+eminus 590 E791 [161]

520 CLEO II [152]K+Kminusmicro+microminus 330 E791 [161]φmicro+microminus 4100 CLEO II [152]

310 E791 [161]

K0e+eminus 17000 Mark3 [162]

1100 CLEO II [152]

K0micro+microminus 6700 CLEO II [152]

2600 E653 [157]Kminusπ+e+eminus 3850 E791 [161]

Klowast0

(892)e+eminus 1400 CLEO II [152]470 E791 [161]

Kminusπ+micro+microminus 3600 E791 [161]

Klowast0

(892)micro+microminus 11800 CLEO II [152]240 E791 [161]

π+πminusπ0micro+microminus 8100 E653 [157]microplusmne∓ 2700 CLEO [149]

1200 Mark3 [163]1000 Argus [150]190 CLEO II [152]172 E789 [153]81 E791 [154]081 BaBar [155]026 Belle [156]0016 LHCb [164]

π0eplusmnmicro∓ 860 CLEO II [152]η eplusmnmicro∓ 1000 CLEO II [152]

36

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceπ+πminuseplusmnmicro∓ 150 E791 [161]ρ0eplusmnmicro∓ 660 E791 [161]

490 CLEO II [152]ω eplusmnmicro∓ 1200 CLEO II [152]K+Kminuseplusmnmicro∓ 1800 E791 [161]φ eplusmnmicro∓ 470 E791 [161]

340 CLEO II [152]

K0eplusmnmicro∓ 1000 CLEO II [152]

Kminusπ+eplusmnmicro∓ 5500 E791 [161]Klowast0(892)eplusmnmicro∓ 1000 CLEO II [152]

830 E791 [161]π∓π∓eplusmneplusmn 1120 E791 [161]π∓π∓microplusmnmicroplusmn 290 E791 [161]K∓π∓eplusmneplusmn 2060 E791 [161]K∓π∓microplusmnmicroplusmn 3900 E791 [161]K∓K∓eplusmneplusmn 1520 E791 [161]K∓K∓microplusmnmicroplusmn 940 E791 [161]π∓π∓eplusmnmicroplusmn 790 E791 [161]K∓π∓eplusmnmicroplusmn 2180 E791 [161]K∓K∓eplusmnmicroplusmn 570 E791 [161]p eminus 100 CLEO [165]p e+ 110 CLEO [165]

37

γγ

ρ0micro

+microminus

π+πminusπ

0micro

+microminus

K+K

minuse

+eminus

ηe

+eminus

φmicro

+microminus

π0e

+eminus

φe

+eminus

ωmicro

+microminus

Kminusπ

+micro

+microminus

ρ0e

+eminus

K0micro

+microminus

Klowast0

(892

)e+eminus

π+πminusmicro

+microminus

micro+microminus

π+πminuse

+eminus

e+eminus

Klowast0

(892

)micro+microminus

K+K

minusmicro

+microminus

Kminusπ

+e

+eminus

π0micro

+microminus

K0e

+eminus

ωe

+eminus

ηmicro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

HFAG-charm

Belle

BESIII

CLEO II

BaBar

E791

CLEO

E653

LHCb

E789

HERAB

CDF

Argus

Mark3

June 16

K∓π∓microplusmnmicroplusmn

ωeplusmnmicro∓

Kminusπ

+eplusmnmicro∓

K∓K∓eplusmnmicroplusmn

π∓π∓eplusmnmicroplusmn

peminus

K∓π∓eplusmnmicroplusmn

π∓π∓eplusmneplusmn

ηeplusmnmicro∓

π∓π∓microplusmnmicroplusmn

K∓K∓eplusmneplusmn

K0eplusmnmicro∓

π+πminuseplusmnmicro∓

K∓K∓microplusmnmicroplusmn

ρ0eplusmnmicro∓

pe

+

φeplusmnmicro∓

microplusmne∓

K+K

minuseplusmnmicro∓

Klowast0

(892

)eplusmnmicro∓

π0eplusmnmicro∓

K∓π∓eplusmneplusmn

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

L BLHFAG-charm

E791

CLEO II

CLEO

Belle

E789

Mark3

Argus

LHCb

BaBar

June 16

Figure 9 Upper limits at 90 CL for D0 decays The top plot shows avor-changing neu-tral current decays and the bottom plot shows lepton-avor-changing (LF) lepton-number-changing (L) and both baryon- and lepton-number-changing (BL) decays38

Kminuse

+micro

+

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminusmicro

+micro

+

K+e

+eminus

π+e

+eminus

πminuse

+micro

+

Kminuse

+e

+

K+micro

+eminus

ρminusmicro

+micro

+

K+e

+microminus

K+eplusmnmicro∓

π+micro

+eminus

π+e

+microminus

πminusmicro

+micro

+

πminuse

+e

+

π+micro

+microminus

ρ+micro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E687

E653

E791

BaBar

Focus

CLEO

BESIII

LHCb

D0

June 16

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminuse

+micro

+

K+e

+eminus

π+e

+eminus

K+eplusmnmicro∓

Kminuse

+e

+

K+micro

+eminus

K+e

+microminus

Klowast+

(892

)micro+microminus

π+micro

+eminus

Kminusmicro

+micro

+

πminusmicro

+micro

+

πminuse

+e

+

πminuse

+micro

+

π+micro

+microminus

K+micro

+microminus

π+e

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E653

E791

CLEO

BaBar

Focus

LHCb

June 16

Figure 10 Upper limits at 90 CL for D+ (top) and D+s (bottom) decays Each plot shows

avor-changing neutral current decays lepton-avor-changing decays (LF) and lepton-number-changing (L) decays 39

pmicro

+microminus

pe

+microminus

σ+micro

+microminus

pe

+e

+

pe

+eminus

pe

+micro

+

pmicro

+micro

+

pmicro

+eminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

LHFAG-charm

BaBar E653

June 16

Figure 11 Upper limits at 90 CL for Λ+c decays Shown are avor-changing neutral current

decays lepton-avor-changing (LF) decays and lepton-number-changing (L) decays

40

Table 20 Upper limits at 90 CL for D+ decays

Decay Limit times106 Experiment Referenceπ+e+eminus 1100 E687 [166]

520 E791 [154]59 CLEO [141]11 BaBar [167]03 BESIII [168]

π+micro+microminus 2200 E653 [157]890 E687 [166]150 E791 [154]88 Focus [169]65 BaBar [167]39 D0 [142]0073 LHCb [144]

ρ+micro+microminus 5600 E653 [157]K+e+eminus 2000 E687 [166]

30 CLEO [141]12 BESIII [168]10 BaBar [167]

π+eplusmnmicro∓ 340 E791 [154]π+e+microminus 1100 E687 [166]

29 BaBar [167]π+micro+eminus 1300 E687 [166]

36 BaBar [167]K+eplusmnmicro∓ 680 E791 [154]K+e+microminus 1300 E687 [166]

12 BaBar [167]K+micro+eminus 1200 E687 [166]

28 BaBar [167]πminuse+e+ 1100 E687 [166]

960 E791 [154]19 BaBar [167]12 BESIII [168]11 CLEO [141]

πminusmicro+micro+ 870 E687 [166]170 E791 [154]48 Focus [169]20 BaBar [167]0022 LHCb [144]

πminuse+micro+ 1100 E687 [166]500 E791 [154]

ρminusmicro+micro+ 5600 E653 [157]Kminuse+e+ 1200 E687 [166]

35 CLEO [141]09 BaBar [167]

41

Table 20 continued from previous pageDecay Limit times106 Experiment Reference

06 BESIII [168]Kminusmicro+micro+ 3200 E653 [157]

1200 E687 [166]130 Focus [169]100 BaBar [167]

Kminuse+micro+ 1300 E687 [166]Klowastminus(892)micro+micro+ 8500 E653 [157]

Table 21 Upper limits at 90 CL for D+s decays

Decay Limit times106 Experiment Referenceπ+e+eminus 2700 E791 [154]

220 CLEO [141]130 BaBar [167]

π+micro+microminus 4300 E653 [157]1400 E791 [154]430 BaBar [167]260 Focus [169]041 LHCb [144]

K+e+eminus 16000 E791 [154]520 CLEO [141]37 BaBar [167]

K+micro+microminus 1400 E791 [154]360 Focus [169]210 BaBar [167]

Klowast+(892)micro+microminus 14000 E653 [157]π+eplusmnmicro∓ 6100 E791 [154]π+e+microminus 120 BaBar [167]π+micro+eminus 200 BaBar [167]K+eplusmnmicro∓ 6300 E791 [154]K+e+microminus 140 BaBar [167]K+micro+eminus 97 BaBar [167]πminuse+e+ 6900 E791 [154]

180 CLEO [141]41 BaBar [167]

πminusmicro+micro+ 4300 E653 [157]820 E791 [154]290 Focus [169]140 BaBar [167]012 LHCb [144]

πminuse+micro+ 7300 E791 [154]Kminuse+e+ 6300 E791 [154]

170 CLEO [141]

42

Table 21 continued from previous pageDecay Limit times106 Experiment Reference

52 BaBar [167]Kminusmicro+micro+ 5900 E653 [157]

1800 E791 [154]130 BaBar [167]

Kminuse+micro+ 6800 E791 [154]Klowastminus(892)micro+micro+ 14000 E653 [157]

Table 22 Upper limits at 90 CL for Λ+c decays

Decay Limit times106 Experiment Referencepe+eminus 55 BaBar [167]pmicro+microminus 3400 E653 [157]

440 BaBar [167]σ+micro+microminus 7000 E653 [157]pe+microminus 99 BaBar [167]pmicro+eminus 190 BaBar [167]p e+e+ 27 BaBar [167]p micro+micro+ 94 BaBar [167]

43

References

[1] N Cabibbo Phys Rev Lett 10 531533 (1963)

[2] M Kobayashi and T Maskawa Prog Theor Phys 49 652657 (1973)

[3] D Abbaneo et al (ALEPH CDF DELPHI L3 OPAL and SLD collaborations)arXivhep-ex0009052 (2000) CERN-EP-2000-096 arXivhep-ex0112028 (2001)CERN-EP-2001-050

[4] Y Amhis et al (Heavy Flavor Averaging Group) (2012) arXiv12071158 [hep-ex]

[5] K Olive et al (Particle Data Group) Chin Phys C38 090001 (2014)

[6] A L Kagan and M D Sokolo Phys Rev D80 076008 (2009) arXiv09073917 [hep-ph]

[7] Y Grossman A L Kagan and Y Nir Phys Rev D75 036008 (2007)arXivhep-ph0609178 [hep-ph]

[8] M Gersabeck M Alexander S Borghi V Gligorov and C Parkes J Phys G39 045005(2012) arXiv11116515 [hep-ex]

[9] J P Lees et al (BABAR collaboration) Phys Rev D87 012004 (2013) arXiv12093896[hep-ex]

[10] R Aaij et al (LHCb collaboration) Phys Rev Lett 112 041801 (2014) arXiv13107201[hep-ex]

[11] T A Aaltonen et al (CDF collaboration) Phys Rev D90 no 11 111103 (2014)arXiv14105435 [hep-ex]

[12] R Aaij et al (LHCb collaboration) JHEP 04 043 (2015) arXiv150106777 [hep-ex]

[13] M Staripound et al (Belle collaboration) Phys Lett B753 412418 (2016) arXiv150908266[hep-ex]

[14] B Aubert et al (BABAR collaboration) Phys Rev Lett 100 061803 (2008)arXiv07092715 [hep-ex]

[15] B Ko (Belle collaboration) PoS ICHEP2012 353 (2013) arXiv12121975

[16] T Aaltonen et al (CDF collaboration) Phys Rev Lett 109 111801 (2012)arXiv12072158 [hep-ex]

[17] R Aaij et al (LHCb collaboration) JHEP 07 041 (2014) arXiv14052797 [hep-ex]

[18] R Aaij et al (LHCb collaboration) Phys Rev Lett 116 no 19 191601 (2016)arXiv160203160 [hep-ex]

[19] T Becher and R J Hill Phys Lett B633 6169 (2006) arXivhep-ph0509090 [hep-ph]

[20] F J Gilman and R L Singleton Phys Rev D41 142 (1990)

[21] R J Hill eConf C060409 027 (2006) arXivhep-ph0606023 [hep-ph]

[22] D Becirevic and A B Kaidalov Phys Lett B478 417423 (2000) arXivhep-ph9904490[hep-ph]

44

[23] C G Boyd B Grinstein and R F Lebed Phys Rev Lett 74 46034606 (1995)arXivhep-ph9412324 [hep-ph]

[24] C G Boyd and M J Savage Phys Rev D56 303311 (1997) arXivhep-ph9702300[hep-ph]

[25] M C Arnesen B Grinstein I Z Rothstein and I W Stewart Phys Rev Lett 95 071802(2005)

[26] C Bourrely B Machet and E de Rafael Nucl Phys B189 157 (1981)

[27] D Becirevic A L Yaouanc A Oyanguren P Roudeau and F Sanlippo (2014)arXiv14071019 [hep-ph]

[28] J P Lees et al (BABAR collaboration) Phys Rev D88 052003 (2013) arXiv13045009[hep-ex]

[29] P del Amo Sanchez et al (BaBar Collaboration collaboration) PhysRev D82 111101(2010) arXiv10092076 [hep-ex]

[30] R Aaij et al (LHCb collaboration) JHEP 1309 145 (2013) arXiv13074556

[31] G Burdman and J Kambor Phys Rev D55 28172826 (1997) arXivhep-ph9602353[hep-ph]

[32] D Becirevic A Le Yaouanc L Oliver J-C Raynal P Roudeau and J Serrano Phys RevD87 no 5 054007 (2013) arXiv12065869 [hep-ph]

[33] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052022 (2015)arXiv14125502 [hep-ex]

[34] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 7 072012 (2015)arXiv150807560 [hep-ex]

[35] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 11 112008 (2015)arXiv151000308 [hep-ex]

[36] L Widhalm et al (Belle collaboration) Phys Rev Lett 97 061804 (2006)arXivhep-ex0604049 [hep-ex]

[37] B Aubert et al (BABAR collaboration) Phys Rev D76 052005 (2007) arXiv07040020[hep-ex]

[38] D Besson et al (CLEO collaboration) Phys Rev D80 032005 (2009) arXiv09062983[hep-ex]

[39] S Dobbs et al (CLEO collaboration) Phys Rev D77 112005 (2008) arXiv07121020[hep-ex]

[40] G Huang et al (CLEO collaboration) Phys Rev Lett 94 011802 (2005)arXivhep-ex0407035 [hep-ex]

[41] J Link et al (FOCUS collaboration) Phys Lett B607 233242 (2005)arXivhep-ex0410037 [hep-ex]

[42] J Adler et al (MARK-III collaboration) Phys Rev Lett 62 1821 (1989)

45

[43] K Kodama et al (Fermilab E653 collaboration) Phys Rev Lett 66 18191822 (1991)

[44] K Kodama et al (E653 collaboration) Phys Lett B336 605613 (1994)

[45] P L Frabetti et al (E687 collaboration) Phys Lett B364 127136 (1995)

[46] P L Frabetti et al (E687 collaboration) Phys Lett B315 203208 (1993)

[47] J C Anjos et al (Tagged Photon Spectrometer collaboration) Phys Rev Lett 6215871590 (1989)

[48] M Ablikim et al (BES collaboration) Phys Lett B597 3946 (2004)arXivhep-ex0406028 [hep-ex]

[49] M Ablikim et al (BES collaboration) (2006) arXivhep-ex0610019 [hep-ex]

[50] A Bean et al (CLEO collaboration) Phys Lett B317 647654 (1993)

[51] BESIII collaboration presented at ICHEP 2014 conference 2014httpindicoificuvesindicogetFilepyaccesscontribId=69ampsessionId=25ampresId=

0ampmaterialId=slidesampconfId=2025

[52] J G Korner and G A Schuler Z Phys C46 93 (1990)

[53] FLAG collaboration httpitpwikiunibechagimages44bFLAGpdf 2014httpitpwikiunibechflagimages44bFLAGpdf

[54] J Anjos et al (Fermilab E691 collaboration) Phys Rev Lett 65 26302633 (1990)

[55] K Kodama et al (Fermilab E653 collaboration) Phys Lett B274 246252 (1992)

[56] P Frabetti et al (Fermilab E687 collaboration) Phys Lett B307 262268 (1993)

[57] E Aitala et al (E791 collaboration) Phys Rev Lett 80 13931397 (1998)arXivhep-ph9710216 [hep-ph]

[58] E Aitala et al (E791 collaboration) Phys Lett B440 435441 (1998)arXivhep-ex9809026 [hep-ex]

[59] M Adamovich et al (BEATRICE collaboration) Eur Phys J C6 3541 (1999)

[60] J Link et al (FOCUS collaboration) Phys Lett B544 8996 (2002)arXivhep-ex0207049 [hep-ex]

[61] J Link et al (FOCUS collaboration) Phys Lett B607 6777 (2005)arXivhep-ex0410067 [hep-ex]

[62] P del Amo Sanchez et al (BABAR collaboration) Phys Rev D83 072001 (2011)arXiv10121810 [hep-ex]

[63] B Aubert et al (BABAR collaboration) Phys Rev D78 051101 (2008) arXiv08071599[hep-ex]

[64] H Mahlke eConf C0610161 014 (2006) arXivhep-ex0702014 [hep-ex]

[65] J Link et al (FOCUS collaboration) Phys Lett B535 4351 (2002)arXivhep-ex0203031 [hep-ex]

46

[66] K M Ecklund et al (CLEO collaboration) Phys Rev D80 052009 (2009)arXiv09073201 [hep-ex]

[67] R A Briere et al (CLEO collaboration) Phys Rev D81 112001 (2010) arXiv10041954[hep-ex]

[68] P Estabrooks R Carnegie A D Martin W Dunwoodie T Lasinski et al Nucl PhysB133 490 (1978)

[69] D Aston et al Nucl Phys B296 493 (1988)

[70] B Aubert et al (BABAR collaboration) Phys Rev Lett 90 242001 (2003)arXivhep-ex0304021 [hep-ex]

[71] D Besson et al (CLEO Collaboration collaboration) PhysRev D68 032002 (2003)arXivhep-ex0305100 [hep-ex]

[72] K Abe et al (Belle Collaboration collaboration) PhysRevLett 92 012002 (2004)arXivhep-ex0307052 [hep-ex]

[73] B Aubert et al (BaBar Collaboration collaboration) PhysRev D69 031101 (2004)arXivhep-ex0310050 [hep-ex]

[74] K Abe et al (Belle collaboration) Phys Rev D69 112002 (2004) arXivhep-ex0307021[hep-ex]

[75] J M Link et al (FOCUS Collaboration collaboration) PhysLett B586 1120 (2004)arXivhep-ex0312060 [hep-ex]

[76] S Godfrey and N Isgur Phys Rev D32 189231 (1985)

[77] S Godfrey and R Kokoski Phys Rev D43 16791687 (1991)

[78] N Isgur and M B Wise Phys Rev Lett 66 11301133 (1991)

[79] P Schweitzer S Bo and M Radici Phys Rev D66 114004 (2002)arXivhep-ph0207230 [hep-ph]

[80] F Jugeau A Le Yaouanc L Oliver and J-C Raynal Phys Rev D72 094010 (2005)arXivhep-ph0504206 [hep-ph]

[81] P Colangelo F De Fazio and R Ferrandes ModPhysLett A19 20832102 (2004)arXivhep-ph0407137 [hep-ph]

[82] R N Cahn and J D Jackson Phys Rev D68 037502 (2003) arXivhep-ph0305012[hep-ph]

[83] T Barnes F E Close and H J Lipkin PhysRev D68 054006 (2003)arXivhep-ph0305025 [hep-ph]

[84] H Lipkin PhysLett B580 5053 (2004) arXivhep-ph0306204 [hep-ph]

[85] W A Bardeen E J Eichten and C T Hill Phys Rev D68 054024 (2003)arXivhep-ph0305049 [hep-ph]

[86] B Aubert et al (BaBar Collaboration collaboration) PhysRev D80 092003 (2009)arXiv09080806 [hep-ex]

47

[87] R Aaij et al (LHCb Collaboration collaboration) JHEP 1210 151 (2012) arXiv12076016[hep-ex]

[88] R Aaij et al (LHCb collaboration) Phys Rev Lett 113 162001 (2014) arXiv14077574[hep-ex]

[89] R Aaij et al (LHCb collaboration) JHEP 02 133 (2016) arXiv160101495 [hep-ex]

[90] T Matsuki T Morii and K Sudoh EurPhysJ A31 701704 (2007)arXivhep-ph0610186 [hep-ph]

[91] N Isgur and M B Wise PhysLett B232 113117 (1989)

[92] M Neubert PhysRept 245 259396 (1994) arXivhep-ph9306320 [hep-ph]

[93] B Aubert et al (BaBar Collaboration collaboration) PhysRev D74 032007 (2006)arXivhep-ex0604030 [hep-ex]

[94] V M Abazov et al (D0 Collaboration collaboration) PhysRevLett 102 051801 (2009)arXiv07123789 [hep-ex]

[95] B Aubert et al (BABAR collaboration) Phys Rev D77 011102 (2008) arXiv07081565[hep-ex]

[96] P L Frabetti et al (E687 Collaboration collaboration) PhysRevLett 72 324327 (1994)

[97] J P Alexander et al (CLEO Collaboration collaboration) PhysLett B303 377384 (1993)

[98] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B297 425431 (1992)

[99] P Avery et al (CLEO Collaboration collaboration) PhysRev D41 774 (1990)

[100] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B230 162 (1989)

[101] J P Lees et al (BaBar Collaboration collaboration) PhysRev D83 072003 (2011)arXiv11032675 [hep-ex]

[102] R Aaij et al (LHCb collaboration) Phys Rev D90 no 7 072003 (2014) arXiv14077712[hep-ex]

[103] R Aaij et al (LHCb collaboration) PhysLett B698 1420 (2011) arXiv11020348[hep-ex]

[104] B Aubert et al (BaBar Collaboration collaboration) PhysRevLett 97 222001 (2006)arXivhep-ex0607082 [hep-ex]

[105] H Albrecht et al (ARGUS Collaboration collaboration) ZPhys C69 405408 (1996)

[106] Y Kubota et al (CLEO Collaboration collaboration) PhysRevLett 72 19721976 (1994)arXivhep-ph9403325 [hep-ph]

[107] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052002 (2015)arXiv14126751 [hep-ex]

[108] J Brodzicka et al (Belle collaboration) Phys Rev Lett 100 092001 (2008)arXiv07073491 [hep-ex]

48

[109] B Aubert et al (BABAR collaboration) Phys Rev D79 112004 (2009) arXiv09011291[hep-ex]

[110] R Aaij et al (LHCb collaboration) Phys Rev D92 no 3 032002 (2015)arXiv150501710 [hep-ex]

[111] R Aaij et al (LHCb collaboration) Phys Rev D92 no 1 012012 (2015)arXiv150501505 [hep-ex]

[112] A Kuzmin et al (Belle Collaboration collaboration) PhysRev D76 012006 (2007)arXivhep-ex0611054 [hep-ex]

[113] H Abramowicz et al (ZEUS Collaboration collaboration) NuclPhys B866 229254 (2013)arXiv12084468 [hep-ex]

[114] A Abulencia et al (CDF Collaboration collaboration) PhysRev D73 051104 (2006)arXivhep-ex0512069 [hep-ex]

[115] K Abe et al (Belle collaboration) Phys Rev Lett 94 221805 (2005)arXivhep-ex0410091 [hep-ex]

[116] P Avery et al (CLEO Collaboration collaboration) PhysLett B331 236244 (1994)arXivhep-ph9403359 [hep-ph]

[117] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B232 398 (1989)

[118] J C Anjos et al (Tagged Photon Spectrometer Collaboration collaboration) PhysRevLett62 1717 (1989)

[119] T Bergfeld et al (CLEO Collaboration collaboration) PhysLett B340 194204 (1994)

[120] R Aaij et al (LHCb collaboration) Phys Rev D91 no 9 092002 (2015)arXiv150302995 [hep-ex] [Erratum Phys RevD93no11119901(2016)]

[121] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B221 422 (1989)

[122] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B231 208 (1989)

[123] P Abreu et al (DELPHI Collaboration collaboration) PhysLett B426 231242 (1998)

[124] D Matvienko et al (Belle collaboration) Phys Rev D92 no 1 012013 (2015)arXiv150503362 [hep-ex]

[125] P Krokovny et al (Belle collaboration) Phys Rev Lett 91 262002 (2003)arXivhep-ex0308019 [hep-ex]

[126] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 181801 (2004)arXivhep-ex0408041 [hep-ex]

[127] S K Choi et al (Belle collaboration) Phys Rev D91 no 9 092011 (2015)arXiv150402637 [hep-ex] [Addendum Phys RevD92no3039905(2015)]

[128] A Drutskoy et al (Belle collaboration) Phys Rev Lett 94 061802 (2005)arXivhep-ex0409026 [hep-ex]

[129] B Aubert et al (BABAR collaboration) Phys Rev D74 031103 (2006)arXivhep-ex0605036 [hep-ex]

49

[130] S Chekanov et al (ZEUS Collaboration collaboration) EurPhysJ C60 2545 (2009)arXiv08071290 [hep-ex]

[131] A Heister et al (ALEPH Collaboration collaboration) PhysLett B526 3449 (2002)arXivhep-ex0112010 [hep-ex]

[132] B Aubert et al (BABAR collaboration) Phys Rev Lett 103 051803 (2009)arXiv08080333 [hep-ex]

[133] G Burdman E Golowich J L Hewett and S Pakvasa Phys Rev D66 014009 (2002)arXivhep-ph0112235 [hep-ph]

[134] S Fajfer A Prapotnik S Prelovsek P Singer and J Zupan Nucl Phys Proc Suppl 1159397 (2003) arXivhep-ph0208201 [hep-ph]

[135] S Fajfer N Kosnik and S Prelovsek Phys Rev D76 074010 (2007) arXiv07061133[hep-ph]

[136] E Golowich J Hewett S Pakvasa and A A Petrov Phys Rev D79 114030 (2009)arXiv09032830 [hep-ph]

[137] A Paul I I Bigi and S Recksiegel Phys Rev D82 094006 (2010) arXiv10083141[hep-ph]

[138] A Borisov (2011) arXiv11123269 [hep-ph]

[139] R-M Wang J-H Sheng J Zhu Y-Y Fan and Y Gao Int J Mod Phys A29 no 291450169 (2014)

[140] S de Boer and G Hiller Phys Rev D93 no 7 074001 (2016) arXiv151000311 [hep-ph]

[141] P Rubin et al (CLEO collaboration) Phys Rev D82 092007 (2010) arXiv10091606[hep-ex]

[142] V Abazov et al (D0 collaboration) Phys Rev Lett 100 101801 (2008) arXiv07082094[hep-ex]

[143] R Aaij et al (LHCb collaboration) Phys Lett B728 234243 (2014) arXiv13102535[hep-ex]

[144] R Aaij et al (LHCb collaboration) Phys Lett B724 203212 (2013) arXiv13046365[hep-ex]

[145] T Coan et al (CLEO collaboration) Phys Rev Lett 90 101801 (2003)arXivhep-ex0212045 [hep-ex]

[146] M Ablikim et al (BESIII collaboration) Phys Rev D91 no 11 112015 (2015)arXiv150503087 [hep-ex]

[147] J P Lees et al (BABAR collaboration) Phys Rev D85 091107 (2012) arXiv11106480[hep-ex]

[148] N K Nisar et al (Belle collaboration) Phys Rev D93 no 5 051102 (2016)arXiv151202992 [hep-ex]

[149] P Haas et al (CLEO collaboration) Phys Rev Lett 60 1614 (1988)

50

[150] H Albrecht et al (ARGUS collaboration) Phys Lett B209 380 (1988)

[151] J Adler et al (MARK-III collaboration) Phys Rev D37 2023 (1988) Erratum ibid D40(1989) 3788

[152] A Freyberger et al (CLEO collaboration) Phys Rev Lett 76 30653069 (1996)

[153] D Pripstein et al (E789 collaboration) Phys Rev D61 032005 (2000)arXivhep-ex9906022 [hep-ex]

[154] E Aitala et al (E791 collaboration) Phys Lett B462 401409 (1999)arXivhep-ex9906045 [hep-ex]

[155] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 191801 (2004)arXivhep-ex0408023 [hep-ex]

[156] M Petric et al (Belle collaboration) Phys Rev D81 091102 (2010) arXiv10032345[hep-ex]

[157] K Kodama et al (E653 collaboration) Phys Lett B345 8592 (1995)

[158] I Abt et al (HERA-B collaboration) Phys Lett B596 173183 (2004)arXivhep-ex0405059 [hep-ex]

[159] T Aaltonen et al (CDF collaboration) Phys Rev D82 091105 (2010) arXiv10085077[hep-ex]

[160] R Aaij et al (LHCb collaboration) Phys Lett B725 1524 (2013) arXiv13055059[hep-ex]

[161] E Aitala et al (E791 collaboration) Phys Rev Lett 86 39693972 (2001)arXivhep-ex0011077 [hep-ex]

[162] J Adler et al (MARK-III collaboration) Phys Rev D40 906 (1989)

[163] J Becker et al (MARK-III collaboration) Phys Lett B193 147 (1987)

[164] R Aaij et al (LHCb collaboration) Phys Lett B754 167175 (2016) arXiv151200322[hep-ex]

[165] P Rubin et al (CLEO collaboration) Phys Rev D79 097101 (2009) arXiv09041619[hep-ex]

[166] P Frabetti et al (E687 collaboration) Phys Lett B398 239244 (1997)

[167] J P Lees et al (BABAR collaboration) Phys Rev D84 072006 (2011) arXiv11074465[hep-ex]

[168] (BESIII collaboration) M-G Zhao D rareforbidden decays at BESIII in 7th International

Workshop on Charm Physics (Charm 2015) Detroit MI USA May 18-22 2015 2016arXiv160508952 [hep-ex]httpinspirehepnetrecord1466292filesarXiv160508952pdf

[169] J Link et al (FOCUS collaboration) Phys Lett B572 2131 (2003)arXivhep-ex0306049 [hep-ex]

51

  • Introduction
  • D decays
    • Interplay of direct and indirect CP violation
    • Semileptonic decays
      • Introduction
      • DP decays
      • Form factor parameterizations
      • Simple pole
      • z expansion
      • Three-pole formalism
      • Experimental techniques and results
      • Combined results for the DK channel
      • Combined results for the D channel
      • Vcs and Vcd determination
      • DV decays
      • Form factor measurements
        • Excited D(s) mesons
        • Rare and forbidden decays
          • References
Page 4: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

τ lepton-avor-violating decays are documented and combinations of upper limits arecomputed

The Lifetime and Oscillations and Semileptonic subgroups were formed from the mergerof four LEP working groups The Unitary Triangle B to Charm Decays and Rare De-cays subgroups were formed to provide averages for new results obtained from the B factoryexperiments (and now also from the Fermilab Tevatron and CERN LHC experiments) TheCharm and Tau subgroups were formed more recently in response to the wealth of new dataconcerning D and τ physics Subgroups typically include representatives from Belle BABARand LHCb plus when relevant CLEO CDF and D0

This article is an update of the last HFAG preprint which used results available at leastthrough early 2012 [4] Here we report world averages using results available at least throughsummer 2014 In some cases results made available in the latter part of 2014 have been in-cluded1 In general we use all publicly available results that have written documentationThese include preliminary results presented at conferences or workshops However we do notuse preliminary results that remain unpublished for an extended period of time or for whichno publication is planned Close contacts have been established between representatives fromthe experiments and members of subgroups that perform averaging to ensure that the data areprepared in a form suitable for combinations

In the case of obtaining a world average for which χ2dof gt 1 where dof is the numberof degrees of freedom in the average calculation we do not usually scale the resulting erroras is presently done by the Particle Data Group [5] Rather we examine the systematics ofeach measurement to better understand them Unless we nd possible systematic discrepanciesbetween the measurements we do not apply any additional correction to the calculated errorWe provide the condence level of the t as an indicator for the consistency of the measurementsincluded in the average In case some special treatment was necessary to calculate an averageor if an approximation used in an average calculation might not be suciently accurate (egassuming Gaussian errors when the likelihood function indicates non-Gaussian behavior) weinclude a warning message

Chapter describes the methodology used for calculating averages In the averagingprocedure common input parameters used in the various analyses are adjusted (rescaled) tocommon values and where possible known correlations are taken into account Chapters present world average values from each of the subgroups listed above A brief summary ofthe averages presented is given in Chapter A complete listing of the averages and plotsincluding updates since this document was prepared are also available on the HFAG web site

httpwwwslacstanfordeduxorghfag

1 Particularly important new results have been included whenever possible The precise cut-o date forincluding results in the averages varies between subgroups

4

2 D decays

5

21 Interplay of direct and indirect CP violation

In decays of D0 mesons CP asymmetry measurements have contributions from both directand indirect CP violation as discussed in Sec The contribution from indirect CP viola-tion depends on the decay-time distribution of the data sample [6] This section describes acombination of measurements that allows the extraction of the individual contributions of thetwo types of CP violation At the same time the level of agreement for a no-CP -violationhypothesis is tested The observables are

AΓ equivτ(D 0rarrh+hminus)minus τ(D0rarrh+hminus)

τ(D 0rarrh+hminus) + τ(D0rarrh+hminus) (1)

where h+hminus can be K+Kminus or π+πminus and

∆ACP equiv ACP(K+Kminus)minus ACP(π+πminus) (2)

where ACP are time-integrated CP asymmetries The underlying theoretical parameters are

adirCP equiv

|AD0rarrf |2 minus |AD 0rarrf |2

|AD0rarrf |2 + |AD 0rarrf |2

aindCP equiv 1

2

[(∣∣∣∣qp∣∣∣∣+

∣∣∣∣pq∣∣∣∣)x sinφminus

(∣∣∣∣qp∣∣∣∣minus ∣∣∣∣pq

∣∣∣∣) y cosφ

] (3)

where ADrarrf is the amplitude for D rarr f [7] We use the following relations between theobservables and the underlying parameters [8]

AΓ = minusaindCP minus adir

CPyCP

∆ACP = ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

+ adirCPyCP

∆〈t〉τ

(4)

asymp ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

(5)

The rst relation constrains mostly indirect CP violation and the direct CP violation contri-bution can dier for dierent nal states In the second relation 〈t〉τ denotes the mean decaytime in units of the D0 lifetime ∆X denotes the dierence in quantity X between K+Kminus andπ+πminus nal states and X denotes the average for quantity X We neglect the last term in thisrelation as all three factors are O(10minus2) or smaller and thus this term is negligible with respectto the other two terms Note that ∆〈t〉τ 〈t〉τ and it is expected that |adir

CP| lt |∆adirCP|

because adirCP(K+Kminus) and adir

CP(π+πminus) are expected to have opposite signs [7]A χ2 t is performed in the plane ∆adir

CP vs aindCP For the BABAR result the dierence of

the quoted values for ACP(K+Kminus) and ACP(π+πminus) is calculated adding all uncertainties inquadrature This may overestimate the systematic uncertainty for the dierence as it neglectscorrelated errors however the result is conservative and the eect is small as all measurementsare statistically limited For all measurements statistical and systematic uncertainties areadded in quadrature when calculating the χ2 We use the current world average value yCP =(0866plusmn 0155) (see Sec ) and the measurements listed in Table 1

6

Table 1 Inputs to the t for direct and indirect CP violation The rst uncertainty listed isstatistical and the second is systematic

Year Experiment Results ∆〈t〉τ 〈t〉τ Reference2012 BABAR AΓ = (009plusmn 026plusmn 006) - - [9]2013 LHCb prompt AΓ(KK) = (minus0035plusmn 0062plusmn 0012) - - [10]

AΓ(ππ) = (0033plusmn 0106plusmn 0014) - -2014 CDF AΓ = (minus012plusmn 012) - - [11]2015 LHCb SL AΓ = (minus0125plusmn 0073) - - [12]2015 Belle AΓ = (minus003plusmn 020plusmn 007) - - [13]2008 BABAR ACP(KK) = (000plusmn 034plusmn 013)

ACP(ππ) = (minus024plusmn 052plusmn 022) 000 100 [14]2012 Belle prel ∆ACP = (minus087plusmn 041plusmn 006) 000 100 [15]2012 CDF ∆ACP = (minus062plusmn 021plusmn 010) 025 258 [16]2014 LHCb SL ∆ACP = (014plusmn 016plusmn 008) 001 107 [17]2016 LHCb prompt ∆ACP = (minus010plusmn 008plusmn 003) 012 210 [18]

In this t AΓ(KK) and AΓ(ππ) are assumed to be identical This assumption is sup-ported by all measurements to date A signicant relative shift due to nal-state dependentAΓ values between ∆ACP measurements with dierent mean decay times is excluded by thesemeasurements

The combination plot (see Fig 1) shows the measurements listed in Table 1 for ∆ACP andAΓ where the bands represent plusmn1σ intervals The point of no CP violation (00) is shownas a lled circle and two-dimensional 68 CL 95 CL and 997 CL regions are plotted asellipses The best t value is indicated by a cross showing the one-dimensional errors

From the t the change in χ2 from the minimum value for the no-CPV point (00) is55 which corresponds to a CL of 65 times 10minus2 for two degrees of freedom Thus the data areconsistent with the no-CP -violation hypothesis at 65 CL This p-value corresponds to 18σThe central values and plusmn1σ uncertainties for the individual parameters are

aindCP = (0056plusmn 0040)

∆adirCP = (minus0137plusmn 0070) (6)

Compared to the previous average the tension in the dierence between direct CP violationin the two nal states reduced while the common indirect CP violation moved away from theno CP violation point by about one standard deviation

7

0015 0010 0005 0000 0005 0010

aindCP

0015

0010

0005

0000

0005

0010

0015

∆adirCP

Contours contain 68 95 99 CL

CD

F

LHC

b S

L

LHC

b p

rom

pt

BaBarBelleCDF KK+ππLHCb SL KK+ππ

LHCb prompt KKLHCb prompt ππ

HFAG-charmWinter 16

no CPV

BaBar

Belle

CDF

LHCb

Figure 1 Plot of all data and the t result Individual measurements are plotted as bandsshowing their plusmn1σ range The no-CPV point (00) is shown as a lled circle and the best tvalue is indicated by a cross showing the one-dimensional uncertainties Two-dimensional 68CL 95 CL and 997 CL regions are plotted as ellipses

8

22 Semileptonic decays

221 Introduction

Semileptonic decays of D mesons involve the interaction of a leptonic current with a hadroniccurrent The latter is nonperturbative and cannot be calculated from rst principles thus it isusually parameterized in terms of form factors The transition matrix element is written

M = minusi GFradic2Vcq L

microHmicro (7)

where GF is the Fermi constant and Vcq is a CKM matrix element The leptonic current Lmicro isevaluated directly from the lepton spinors and has a simple structure this allows one to extractinformation about the form factors (in Hmicro) from data on semileptonic decays [19] Converselybecause there are no strong nal-state interactions between the leptonic and hadronic systemssemileptonic decays for which the form factors can be calculated allow one to determine Vcq [2]

222 DrarrP`ν` decays

When the nal state hadron is a pseudoscalar the hadronic current is given by

Hmicro = 〈P (p)|qγmicroc|D(pprime)〉 = f+(q2)

[(pprime + p)micro minus

m2D minusm2

P

q2qmicro

]+ f0(q2)

m2D minusm2

P

q2qmicro (8)

where mD and pprime are the mass and four momentum of the parent D meson mP and p are thoseof the daughter meson f+(q2) and f0(q2) are form factors and q = pprime minus p Kinematics requirethat f+(0) = f0(0) The contraction qmicroL

micro results in terms proportional to m` [20] and thus for` = e the terms proportionals to qmicro in Eq (8) are negligible For light leptons only the f+(q2)vector form factor is relevant and the dierential partial width is

dΓ(D rarr P`ν`)

dq2 d cos θ`=

G2F |Vcq|2

32π3plowast 3|f+(q2)|2 sin θ2

` (9)

where plowast is the magnitude of the momentum of the nal state hadron in the D rest frame andθ` is the angle of the lepton in the `ν rest frame with respect to the direction of the pseudoscalarmeson in the D rest frame

223 Form factor parameterizations

The form factor is traditionally parameterized with an explicit pole and a sum of eective poles

f+(q2) =f+(0)

(1minus α)

[(1

1minus q2m2pole

)+

Nsumk=1

ρk1minus q2(γkm2

pole)

] (10)

where ρk and γk are expansion parameters and α is a parameter that normalizes the formfactor at q2 = 0 f+(0) The parameter mpole is the mass of the lowest-lying cq resonance withthe vector quantum numbers this is expected to provide the largest contribution to the formfactor for the crarr q transition The sum over N gives the contribution of higher mass statesFor example for D rarr π transitions the dominant resonance is expected to be Dlowast(2010) andthus mpole = mDlowast(2010) For D rarr K transitions the dominant contribution is expected from

Dlowasts(2112) with mpole = mDlowasts (2112)

9

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Comparison between CLEO-c and BABAR results for the quantities q2H20 (q2) and

q2h0(q2)H0(q2)

Table 11 Results for rV and r2 from various experiments

Experiment Ref rV r2

D+ rarr Klowast0l+ν

E691 [54] 20plusmn 06plusmn 03 00plusmn 05plusmn 02E653 [55] 200plusmn 033plusmn 016 082plusmn 022plusmn 011E687 [56] 174plusmn 027plusmn 028 078plusmn 018plusmn 011

E791 (e) [57] 190plusmn 011plusmn 009 071plusmn 008plusmn 009E791 (micro) [58] 184plusmn011plusmn009 075plusmn008plusmn009Beatrice [59] 145plusmn 023plusmn 007 100plusmn 015plusmn 003FOCUS [60] 1504plusmn0057plusmn0039 0875plusmn0049plusmn0064

D0 rarr K0πminusmicro+ν

FOCUS [61] 1706plusmn0677plusmn0342 0912plusmn0370plusmn0104BABAR [62] 1493plusmn 0014plusmn 0021 0775plusmn 0011plusmn 0011

D+s rarr φ e+νBABAR [63] 1849plusmn0060plusmn0095 0763plusmn0071plusmn0065

D0 D+ rarr ρ eνCLEO [64] 140plusmn025plusmn003 057plusmn018plusmn006

23

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

HFLAV())+-amp

Figure 7 A comparison of r2 (lled inverted triangles) and rV (open triangles) values fromvarious experiments The rst seven measurements are for D+ rarr Kminusπ+l+νl decays Alsoshown as a line with 1-σ limits is the average of these The last two points are D+

s and D0

decays

24

23 Excited D(s) mesons

Excited charm meson states have received increased attention since the rst observation ofstates that could not be accommodated by QCD predictions [70 71 72 73] Tables 12 13and 14 summarize recent measurements of the masses and widths of excited D and Ds mesonsrespectively If a preferred assignment of spin and parity was measured it is listed in the columnJP where the label natural denotes JP = 0minus 1+ 2minus and unnatural JP = 0+ 1minus 2+ Ifpossible an average mass and width was calculated which is listed in the gray shaded rowThe calculation of the averages assumes no correlation between individual measurements Asummary of the averaged masses and widths is shown in Figure 8

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

0+ 1+ 2+ 1minus 1 3minus

unnatu

ral

Dlowast s0

(2317)plusmn

Ds1

(2460)plusmn

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn D

sJ(3

040)plusmn

HFAG-charmAugust 2016

(a)

Mas

s[M

eVc

2]

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

0+ 1+ 2+ 0minus 1minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ralDlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn

D(2

550)0

D(2

580)0

D(2

600)0

D(2

600)plusmn

Dlowast (

2640)plusmn

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(b)

Mas

s[M

eVc

2]

0

50

100

150

200

250

300

350

400

450

500

550

1+ 2+ 1minus 1 3minus

unnatu

ral

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn

DsJ

(3040)plusmn

HFAG-charmAugust 2016

(c)

Wid

th[M

eV]

50100150200250300350400450500550600650700

0+ 1+ 2+ 0minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ral

Dlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn D(2

550)0

D(2

580)0

D(2

600)0

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(d)

Wid

th[M

eV]

Figure 8 Averaged masses for Ds mesons are shown in subgure (a) and for D mesons insubgure (b) The average widths for Ds mesons are shown in subgure (c) and for D mesonsin subgure (d) The vertical shaded regions distinguish between dierent spin parity states

The masses and widths of narrow (Γ lt 50 MeV) orbitally excited D mesons (denotedDlowastlowast) both neutral and charged are well established Measurements of broad states (Γ sim200400 MeV) are less abundant as identifying the signal is more challenging There is aslight discrepancy between the Dlowast0(2400)0 masses measured by the Belle [74] and FOCUS [75]experiments No data exist yet for the D1(2430)plusmn state Dalitz plot analyses of B rarr D(lowast)ππ

25

decays strongly favor the assignments 0+ and 1+ for the spin-parity quantum numbers of theDlowast0(2400)0Dlowast0(2400)plusmn and D1(2430)0 states respectively The measured masses and widthsas well as the JP values are in agreement with theoretical predictions based on potentialmodels [76777879]

Tables 15 and 16 summarizes the branching fractions of B mesons decays to excited D andDs states respectively It can be noted that the branching fractions for B mesons decaying to anarrow Dlowastlowast state and a pion are similar for charged and neutral B initial states the branchingfractions to a broad Dlowastlowast state and π+ are much larger for B+ than for B0 This may be dueto the fact that color-suppressed amplitudes contribute only to the B+ decay and not to theB0 decay (for a theoretical discussion see Ref [8081]) Measurements of individual branchingfractions of D mesons are dicult due to the unknown fragmentation of cc rarr Dlowastlowast or due tothe unknown B rarr DlowastlowastX branching fractions

The discoveries of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn have triggered increased interest in prop-erties of and searches for excited Ds mesons (here generically denoted D

lowastlowasts ) While the masses

and widths of Ds1(2536)plusmn and Ds2(2573)plusmn states are in relatively good agreement with po-tential model predictions the masses of Dlowasts0(2317)plusmn and Ds1(2460)plusmn states are signicantlylower than expected (see Ref [82] for a discussion of cs models) Moreover the mass splittingbetween these two states greatly exceeds that between the Ds1(2536)plusmn and Ds2(2573)plusmn Theseunexpected properties have led to interpretations of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn as exoticfour-quark states [8384]

While there are few measurements of the JP values of Dlowasts0(2317)plusmn andDs1(2460)plusmn the avail-able data favor 0+ and 1+ respectively A molecule-like (DK) interpretation of the Dlowasts0(2317)plusmn

and Ds1(2460)plusmn [8384] that can account for their low masses and isospin-breaking decay modesis tested by searching for charged and neutral isospin partners of these states thus far suchsearches have yielded negative results Therefore the subset of models that predict equal pro-duction rates for dierent charged states is excluded The molecular picture can also be testedby measuring the rates for the radiative processes Dlowasts0(2317)plusmnDs1(2460)plusmn rarr D

(lowast)s γ and com-

paring to theoretical predictions The predicted rates however are below the sensitivity ofcurrent experiments

Another model successful in explaining the total widths and the Dlowasts0(2317)plusmn Ds1(2460)plusmn

mass splitting is based on the assumption that these states are chiral partners of the groundstates D+

s and Dlowasts [85] While some measured branching fraction ratios agree with predictedvalues further experimental tests with better sensitivity are needed to conrm or refute thisscenario A summary of the mass dierence measurements is given in Table 17

Measurements by BABAR [86] and LHCb [87] rst indicated the existence of a strange-charm DlowastsJ(2860)plusmn meson An LHCb study of B0

s rarr D0Kminusπ+ decays in which they searchedfor excited Ds mesons [88] showed with 10σ signicance that this state is comprised of twodierent particles one of spin 1 and one of spin 3 This represents the rst measurement of aheavy avored spin-3 particle and the rst observation B mesons decays to spin 3 particlesA subsequent study of DsJ mesons by the LHCb collaboration [89] supports the natural parityassignment for this state (JP = 3minus) This study also shows weak evidence for a further structureat a mass around 3040 MeVc2 with unnatural parity which was rst hinted at by a Babaranalysis [86]

Recent evidence shows that the 1D family of charm resonances can be explored in the Dalitzplot analyses of B-meson decays in the same way as seen for the charm-strange resonances TheLHCb collaboration performed an analysis of B0 rarr D0π+πminus decays in which they measured

26

the spin-parity assignment of the stateDlowast3(2760)plusmn which was observed previously by BABAR [29]and LHCb [30] to be JP = 3minus The measurement suggests a spectroscopic assignment of 3D3This is the second observation of a spin-3 charm meson

Other observed excited Ds states include Ds1(2700)plusmn and Ds2(2573)plusmn The properties ofboth (mass width JP ) have been measured and determined in several analyses A theoreticaldiscussion [90] investigates the possibility that theDs1(2700)plusmn could represent radial excitationsof the Dlowastplusmns Similarly the Ds1(2860)plusmn and DsJ(3040)plusmn could be excitations of Dlowasts0(2317)plusmn andDs1(2460)plusmn or Ds1(2536)plusmn respectively

Table 18 summarizes measurements of the polarization amplitude AD (sometimes also re-ferred as helicity parameter) which describes the initial polarization of the D meson In Dlowastlowast

meson decay the helicity distribution varies like 1 + AD cos2 θH where θH is the angle in theDlowast rest frame between the two pions emitted by decay Dlowastlowast rarr Dlowastπ and the Dlowast rarr Dπ Theparameter is sensitive to possible S-wave contributions in the decay In the case of an unpolar-ized D meson decay decaying purely via D-wave the polarization amplitude is predicted to giveAD = 3 Studies of the D1(2420)0 meson by the ZEUS and BABAR collaborations suggest thatthere is an S-wave admixture in the decay which is contrary to Heavy Quark Eective Theorycalculations [9192]

27

Table 12 Recent measurements of mass and width for dierent excited Ds mesons Thecolumn JP list the most signicant assignment of spin and parity If possible an average massor width is calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowasts0(2317)plusmn 0+

D+s π

0 23196plusmn 02plusmn 14 BABAR [93]D+s π

0 23173plusmn 04plusmn 08 BABAR [73]

23180plusmn 08 Our average

Ds1(2460)plusmn 1+

D+s π

0γD+s γD

+s π

+πminus 24601plusmn 02plusmn 08 BABAR [93]D+s π

0γ 2458plusmn 10plusmn 10 BABAR [73]

24596plusmn 07 Our average

Ds1(2536)plusmn 1+

Dlowast+K0S 25357plusmn 06plusmn 05 DOslash [94]

Dlowast+K0S D

lowast0K+ 253478plusmn 031plusmn 040 BABAR [95]D+s π

+πminus 25346plusmn 03plusmn 07 BABAR [93]Dlowast+K0

S Dlowast0K+ 25350plusmn 06plusmn 10 E687 [96]

Dlowast0K+ 25353plusmn 02plusmn 05 CLEO [97]Dlowast+K0

S 25348plusmn 06plusmn 06 CLEO [97]Dlowast0K+ 25352plusmn 05plusmn 15 ARGUS [98]Dlowast+K0

S 25356plusmn 07plusmn 04 CLEO [99]Dlowast+K0

S 25359plusmn 06plusmn 20 ARGUS [100]Dlowast+K0

S 092plusmn 003plusmn 004 BABAR [101]

253510plusmn 026 092plusmn 005 Our average

Dlowasts2(2573)plusmn 2+

D0K+ Dlowast+K0S 256839plusmn 029plusmn 026 169plusmn 05plusmn 06 LHCb [102]

D+K0S D

0K+ 25694plusmn 16plusmn 05 121plusmn 45plusmn 16 LHCb [103]D+K0

S D0K+ 25722plusmn 03plusmn 10 271plusmn 06plusmn 56 BABAR [104]

D0K+ 257425plusmn 33plusmn 16 104plusmn 83plusmn 30 ARGUS [105]D0K+ 25732+17

minus16 plusmn 09 16+5minus4 plusmn 3 CLEO [106]

256908plusmn 035 169plusmn 08 Our average

Dlowasts1(2700)plusmn 1minus

Dlowast+K0S D

lowast0K+ 27323plusmn 43plusmn 58 136plusmn 19plusmn 24 LHCb [89]D0K+ 2699+14

minus7 127+24minus19 BABAR [107]

Dlowast+K0S D

lowast0K+ 27092plusmn 19plusmn 45 1158plusmn 73plusmn 121 LHCb [87]DKDlowastK 2710plusmn 2+12

minus7 149plusmn 7+39minus52 BABAR [86]

D0K+ 2708plusmn 9+11minus10 108plusmn 2+36

minus31 Belle [108]

27120plusmn 15 1215plusmn 102 Our average

Dlowasts1(2860)plusmn 1 D0K+ 2859plusmn 12plusmn 24 159plusmn 23plusmn 77 LHCb [88]

Dlowasts3(2860)plusmn 3minusDlowast+K0

S Dlowast0K+ 28671plusmn 43plusmn 19 50plusmn 11plusmn 13 LHCb [89]

D0K+ 28605plusmn 26plusmn 65 53plusmn 7plusmn 7 LHCb [88]

28650plusmn 39 522plusmn 86 Our average

DsJ(3040)plusmn Unnatural DlowastK 3044plusmn 8+30minus5 239plusmn 35+46

minus42 BABAR (m amp Γ) + LHCb(JP ) [86]+ [89]

28

Table 13 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast0(2400)0 0+

D+πminus 2297plusmn 8plusmn 20 273plusmn 12plusmn 48 BABAR [109]D+πminus 2308plusmn 17plusmn 32 276plusmn 21plusmn 63 Belle [74]D+πminus 2407plusmn 21plusmn 35 240plusmn 55plusmn 59 Focus [75]

23182plusmn 169 2674plusmn 356 Our average

Dlowast0(2400)plusmn 0+

D0π+ 2349plusmn 6plusmn 1plusmn 4 217plusmn 13plusmn 5plusmn 12 LHCb [110]D0π+ 2360plusmn 15plusmn 12plusmn 28 255plusmn 26plusmn 20plusmn 47 LHCb [111]D0π+ 2403plusmn 14plusmn 35 283plusmn 24plusmn 34 Focus(m ampΓ) + Belle(JP ) [75] + [112]

23506plusmn 59 2337plusmn 155 Our average

D1(2420)0 1+

Dlowast+πminus 24196plusmn 01plusmn 07 352plusmn 04plusmn 09 LHCb [30]Dlowast+πminus 24231plusmn 15+04

minus10 388plusmn 5+19minus54 Zeus [113]

Dlowast+πminus 24201plusmn 01plusmn 08 314plusmn 05plusmn 13 BABAR [29]Dlowast+πminus 200plusmn 17plusmn 13 CDF [114]D0π+πminus 2426plusmn 3plusmn 1 24plusmn 7plusmn 8 Belle [115]Dlowast+πminus 24214plusmn 15plusmn 09 237plusmn 27plusmn 40 Belle [74]Dlowast+πminus 2421+1

minus2 plusmn 2 20+6minus5

+3minus3 CLEO [116]

Dlowast+πminus 2422plusmn 2plusmn 2 15plusmn 8plusmn 4 E687 [96]Dlowast+πminus 2428plusmn 3plusmn 2 23+8

minus6+10minus4 CLEO [99]

Dlowast+πminus 2414plusmn 2plusmn 5 13plusmn 6+10minus5 ARGUS [117]

Dlowast+πminus 2428plusmn 8plusmn 5 58plusmn 14plusmn 10 TPS [118]

24205plusmn 05 317plusmn 07 Our average

D1(2420)plusmn 1+

Dlowast0π+ 24219plusmn 47+34minus12 Zeus [113]

D+πminusπ+ 2421plusmn 2plusmn 1 21plusmn 5plusmn 8 Belle [115]Dlowast0π+ 2425plusmn 2plusmn 2 26+8

minus7 plusmn 4 CLEO [119]Dlowast0π+ 2443plusmn 7plusmn 5 41plusmn 19plusmn 8 TPS [118]

24232plusmn 16 252plusmn 60 Our average

D1(2430)0 1+ Dlowast+πminus 2427plusmn 26plusmn 25 384+107minus75 plusmn 74 Belle [74]

Dlowast2(2460)0 2+

Dlowast+πminus 24640plusmn 14plusmn 05plusmn 02 438plusmn 29plusmn 17plusmn 06 LHCb [120]Dlowast+πminus 24604plusmn 04plusmn 12 432plusmn 12plusmn 30 LHCb [30]D+πminus 24604plusmn 01plusmn 01 456plusmn 04plusmn 11 LHCb [30]

Dlowast+πminus D+πminus 24625plusmn 24+13minus11 466plusmn 81+59

minus38 Zeus [113]D+πminus 24622plusmn 01plusmn 08 505plusmn 06plusmn 07 BABAR [29]D+πminus 24604plusmn 12plusmn 22 418plusmn 25plusmn 29 BABAR [109]D+πminus 492plusmn 23plusmn 13 CDF [114]D+πminus 24616plusmn 21plusmn 33 456plusmn 44plusmn 67 Belle [74]D+πminus 24645plusmn 11plusmn 19 387plusmn 53plusmn 29 Focus [75]D+πminus 2465plusmn 3plusmn 3 28+8

minus7 plusmn 6 CLEO [116]D+πminus 2453plusmn 3plusmn 2 25plusmn 10plusmn 5 E687 [96]Dlowast+πminus 2461plusmn 3plusmn 1 20+9

minus12+9minus10 CLEO [99]

D+πminus 2455plusmn 3plusmn 5 15+13minus10

+5minus10 ARGUS [121]

D+πminus 2459plusmn 3plusmn 2 20plusmn 10plusmn 5 TPS [118]

246049plusmn 017 4752plusmn 065 Our average

29

Table 14 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast2(2460)plusmn 2+

D0π+ 24686plusmn 06plusmn 00plusmn 03 473plusmn 15plusmn 03plusmn 06 LHCb [110]D0π+ 24656plusmn 18plusmn 05plusmn 12 460plusmn 34plusmn 14plusmn 29 LHCb [111]D0π+ 24631plusmn 02plusmn 06 486plusmn 13plusmn 19 LHCb [30]

Dlowast0π+ D0π+ 24606plusmn 44+36minus08 Zeus [113]

D0π+ 24654plusmn 02plusmn 11 BABAR [29]D0π+ 24657plusmn 18+14

minus48 497plusmn 38plusmn 64 Belle [112]D0π+ 24676plusmn 15plusmn 08 341plusmn 65plusmn 42 Focus [75]D0π+ 2463plusmn 3plusmn 3 27+11

minus8 plusmn 5 CLEO [119]D0π+ 2453plusmn 3plusmn 2 23plusmn 9plusmn 5 E687 [96]D0π+ 2469plusmn 4plusmn 6 ARGUS [122]

246555plusmn 040 467plusmn 12 Our average

D(2550)0 0minus Dlowast+πminus 25394plusmn 45plusmn 68 130plusmn 12plusmn 13 BABAR [29]

D(2580)0 Unnatural Dlowast+πminus 25795plusmn 34plusmn 55 1175plusmn 178plusmn 460 LHCb [30]

D(2600)0 Natural D+πminus 26087plusmn 24plusmn 25 93plusmn 6plusmn 13 BABAR [29]

D(2600)plusmn Natural D0π+ 26213plusmn 37plusmn 42 BABAR [29]

Dlowast(2640)plusmn 1minus Dlowast+π+πminus 2637plusmn 2plusmn 6 Delphi [123]

Dlowast(2650)0 Natural Dlowast+πminus 26492plusmn 35plusmn 35 1402plusmn 171plusmn 186 LHCb [30]

D(2740)0 Unnatural Dlowast+πminus 27370plusmn 35plusmn 112 732plusmn 134plusmn 250 LHCb [30]

D(2750)0 Dlowast+πminus 27524plusmn 17plusmn 27 71plusmn 6plusmn 11 BABAR [29]

Dlowast1(2760)0 1+

D+πminus 2781plusmn 18plusmn 11plusmn 6 177plusmn 32plusmn 20plusmn 7 LHCb [120]Dlowast+πminus 27611plusmn 51plusmn 65 744plusmn 34plusmn 370 LHCb [30]D+πminus 27601plusmn 11plusmn 37 744plusmn 34plusmn 191 LHCb [30]D+πminus 27633plusmn 23plusmn 23 609plusmn 51plusmn 36 BABAR [29]

27621plusmn 24 651plusmn 58 Our average

Dlowast3(2760)plusmn 3minus

D0π+ 2798plusmn 7plusmn 1plusmn 7 105plusmn 18plusmn 6plusmn 23 LHCb [110]D0π+ 27717plusmn 17plusmn 38 667plusmn 66plusmn 105 LHCb [30]D0π+ 27697plusmn 38plusmn 15 BABAR [29]

27739plusmn 33 723plusmn 115 Our average

30

Table 15 Product of B meson branching fraction and (daughter) excited D meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowast0(2400)0

Bminus rarr Dlowast0(2400)0(rarr D+π+)πminus61plusmn 06plusmn 18 Belle [74]68plusmn 03plusmn 20 BABAR [109]

64plusmn 14 Our average

Bminus rarr Dlowast0(2400)0(rarr D+π+)Kminus 0061plusmn 0019plusmn 0005plusmn 0014plusmn 0004 LHCb [120]

Dlowast0(2400)plusmnB0 rarr Dlowast0(2400)+(rarr D0π+)πminus

077plusmn 005plusmn 003plusmn 003plusmn 004 LHCb [110]060plusmn 013plusmn 027 Belle [112]

076plusmn 007 Our average

B0 rarr Dlowast0(2400)+(rarr D0π+)Kminus 0177plusmn 0026plusmn 0019plusmn 0067plusmn 020 LHCb [111]

D1(2420)0

Bminus rarr D1(2420)0(rarr Dlowast+πminus)πminus 68plusmn 07plusmn 13 Belle [74]

Bminus rarr D1(2420)0(rarr D0π+πminus)πminus 185plusmn 029plusmn 027plusmn 041 Belle [115]

B0 rarr D1(2420)0(rarr Dlowast+πminus)ω 07plusmn 02+01minus00 plusmn 01 Belle [124]

D1(2420)plusmn B0 rarr D1(2420)+(rarr D+πminusπ+)πminus 089plusmn 015plusmn 022 Belle [115]

D1(2430)0Bminus rarr D1(2430)0(rarr Dlowast+πminus)πminus 50plusmn 04plusmn 108 Belle [74]

B0 rarr D1(2430)0(rarr Dlowast+πminus)ω 25plusmn 04+07minus02

+04minus01 Belle [124]

Dlowast2(2460)0

Bminus rarr Dlowast2(2460)0(rarr D+πminus)πminus34plusmn 03plusmn 07 Belle [74]35plusmn 02plusmn 05 BABAR [109]

34plusmn 03 Our average

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)πminus 18plusmn 03plusmn 04 Belle [74]

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)ω 04plusmn 01+00minus01 plusmn 01 Belle [124]

Bminus rarr Dlowast2(2460)0(rarr D+π+)Kminus 0232plusmn 0011plusmn 0006plusmn 0010plusmn 0016 LHCb [120]

Dlowast2(2460)plusmnB0 rarr Dlowast2(2460)+(rarr D0π+)πminus

244plusmn 007plusmn 010plusmn 004plusmn 012 LHCb [110]215plusmn 017plusmn 031 Belle [112]

238plusmn 016 Our average

B0 rarr Dlowast2(2460)+(rarr D0π+)Kminus 0212plusmn 0010plusmn 0011plusmn 0011plusmn 025 LHCb [111]

Dlowast1(2760)0 Bminus rarr Dlowast1(2760)0(rarr D+π+)Kminus 0036plusmn 0009plusmn 0003plusmn 0007plusmn 0002 LHCb [120]

Dlowast3(2760)plusmn B0 rarr Dlowast3(2760)0(rarr D0π+)πminus 0103plusmn 0016plusmn 0007plusmn 0008plusmn 0005 LHCb [110]

31

Table 16 Product of B meson branching fraction and (daughter) excited Ds meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowasts0(2317)plusmnB0 rarr Dlowasts0(2317)+(rarr D+

s π0)Dminus

86+33minus26 plusmn 26 Belle [125]

180plusmn 40+67minus50 BABAR [126]

101+13minus12 plusmn 10plusmn 04 Belle [127]

102plusmn 15 Our average

B+ rarr Dlowasts0(2317)+(rarr D+s π

0)D0 80+13minus12 plusmn 10plusmn 04 Belle [127]

B0 rarr Dlowasts0(2317)+(rarr D+s π

0)Kminus 053+015minus013 plusmn 016 Belle [128]

Ds1(2460)plusmn

B0 rarr Ds1(2460)+(rarr Dlowast+s π0)Dminus227+73

minus62 plusmn 68 Belle [125]280plusmn 80+112

minus78 BABAR [126]

247plusmn 76 Our average

B0 rarr Ds1(2460)+(rarr Dlowast+s γ)Dminus82+22minus19 plusmn 25 Belle [125]

80plusmn 20+32minus23 BABAR [126]

81plusmn 23 Our average

Ds1(2460)+ rarr Dlowast+s π0 (56plusmn 13plusmn 9) BABAR [129]

Ds1(2460)+ rarr Dlowast+s γ (16plusmn 4plusmn 3) BABAR [129]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dminus 171plusmn 048plusmn 032 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast+K0)Dminus 261plusmn 103plusmn 031 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dlowastminus 332plusmn 088plusmn 066 BABAR [95]

Ds1(2536)plusmnB0 rarr Ds1(2536)+(rarr Dlowast+K0)Dlowastminus 500plusmn 151plusmn 067 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)D0 216plusmn 052plusmn 045 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)D0 230plusmn 098plusmn 043 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)Dlowast0 546plusmn 117plusmn 104 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)Dlowast0 392plusmn 246plusmn 083 BABAR [95]

Ds2(2573)plusmnB0 rarr Ds2(2573)(rarr D0K+)Dminus 034plusmn 017plusmn 005 BABAR [107]

B+ rarr Ds2(2573)(rarr D0K+)D0 008plusmn 14plusmn 005 BABAR [107]

Ds1(2700)plusmn B+ rarr Ds1(2700)+(rarr D0K+)D0

113plusmn 22+14minus28 Belle [108]

502plusmn 071plusmn 093 BABAR [107]

583plusmn 109 Our average

B0 rarr Ds1(2700)+(rarr D0K+)Dminus 714plusmn 096plusmn 069 BABAR [107]

32

Table 17 Mass dierence measurements for excited D mesons

Resonance Relative to ∆m [MeVc2] Measured by Reference

Dlowast1(2420)0 Dlowast+4102plusmn 21plusmn 09 Zeus [130]4117plusmn 07plusmn 04 CDF [114]

4115plusmn 08 Our average

D1(2420)plusmn Dlowast1(2420)0 4+2minus3 plusmn 3 CLEO [119]

Dlowast2(2460)0 D+ 5939plusmn 06plusmn 05 CDF [114]

Dlowast+ 4588plusmn 37+12minus13 Zeus [130]

Dlowast2(2460)plusmn Dlowast2(2460)0

31plusmn 19plusmn 09 Focus [75]minus2plusmn 4plusmn 4 CLEO [119]14plusmn 5plusmn 8 ARGUS [122]

30plusmn 19 Our average

Dlowasts0(2317)plusmn Dplusmns

3487plusmn 05plusmn 07 Belle [72]3500plusmn 12plusmn 10 CLEO [71]3513plusmn 21plusmn 19 Belle [125]

3492plusmn 07 Our average

Ds1(2460)plusmn

Dlowastplusmns

3441plusmn 13plusmn 11 Belle [72]3512plusmn 17plusmn 10 CLEO [71]3468plusmn 16plusmn 19 Belle [125]

3471plusmn 11 Our average

Dplusmns

4910plusmn 13plusmn 19 Belle [72]4914plusmn 09plusmn 15 Belle [72]

4913plusmn 14 Our average

Ds1(2536)plusmnDlowast(2010)plusmn

52483plusmn 001plusmn 004 BABAR [101]52530+044

minus041 plusmn 010 Zeus [130]5253plusmn 06plusmn 01 ALEPH [131]

52484plusmn 004 Our average

Dlowast(2007)0 5287plusmn 19plusmn 05 ALEPH [131]

Dlowasts2(2573)plusmn D0 704plusmn 3plusmn 1 ALEPH [131]

33

Table 18 Measurements of polarization amplitudes for excited D mesons

Resonance AD Measured by Reference

D1(2420)0

78+67minus27

+46minus18 ZEUS [113]

572plusmn 025 BABAR [29]59+30minus17

+24minus10 ZEUS [130]

38plusmn 06plusmn 08 BABAR [132]

561plusmn 024 Our average

D1(2420)plusmn 38plusmn 06plusmn 08 BABAR [132]

Dlowast2(2460)0 minus116plusmn 035 ZEUS [113]

D(2750)0 minus033plusmn 028 BABAR [29]

34

24 Rare and forbidden decays

This section provides a summary of rare and forbidden charm decays in tabular form The decaymodes can be categorized as avor-changing neutral currents lepton-avor-violating lepton-number-violating and both baryon- and lepton-number-violating decays Figures 9-11 plot theupper limits for D0 D+ D+

s and Λ+c decays Tables 19-22 give the corresponding numerical

results Some theoretical predictions are given in Refs [133134135136137138139140]In several cases the rare-decay nal states have been observed with the di-lepton pair being

the decay product of a hadronic resonance For these measurements the quoted limits are thoseexpected for the non-resonant di-lepton spectrum For the extrapolation to the full spectruma phase-space distribution of the non-resonant component has been assumed This applies tothe CLEO measurement of the decays D+

(s) rarr (K+π+)e+eminus [141] to the D0 measurements

of the decays D+(s) rarr π+micro+microminus [142] and to the BABAR measurements of the decays D+

(s) rarr(K+π+)e+eminus and D+

(s) rarr (K+π+)micro+microminus where the contribution from φ rarr l+lminus (l = e micro) has

been excluded In the case of the LHCb measurements of the decays D0 rarr π+πminusmicro+microminus [143]as well as the decays D+

(s) rarr π+micro+microminus [144] the contributions from φ rarr l+lminus as well as from

ρ ω rarr l+lminus (l = e micro) have been excluded

Table 19 Upper limits at 90 CL for D0 decays

Decay Limit times106 Experiment Referenceγγ 260 CLEO II [145]

38 BESIII [146]22 BaBar [147]085 Belle [148]

e+eminus 2200 CLEO [149]1700 Argus [150]1300 Mark3 [151]130 CLEO II [152]819 E789 [153]62 E791 [154]12 BaBar [155]0079 Belle [156]

micro+microminus 700 Argus [150]440 E653 [157]340 CLEO II [152]156 E789 [153]52 E791 [154]20 HERAb [158]13 BaBar [155]021 CDF [159]014 Belle [156]00062 LHCb [160]

π0e+eminus 450 CLEO II [152]π0micro+microminus 5400 CLEO II [152]

1800 E653 [157]

35

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceη e+eminus 1100 CLEO II [152]η micro+microminus 5300 CLEO II [152]π+πminuse+eminus 3700 E791 [161]ρ0e+eminus 4500 CLEO [149]

1240 E791 [161]1000 CLEO II [152]

π+πminusmicro+microminus 300 E791 [161]055 LHCb [143]

ρ0micro+microminus 8100 CLEO [149]4900 CLEO II [152]2300 E653 [157]220 E791 [161]

ω e+eminus 1800 CLEO II [152]ω micro+microminus 8300 CLEO II [152]K+Kminuse+eminus 3150 E791 [161]φ e+eminus 590 E791 [161]

520 CLEO II [152]K+Kminusmicro+microminus 330 E791 [161]φmicro+microminus 4100 CLEO II [152]

310 E791 [161]

K0e+eminus 17000 Mark3 [162]

1100 CLEO II [152]

K0micro+microminus 6700 CLEO II [152]

2600 E653 [157]Kminusπ+e+eminus 3850 E791 [161]

Klowast0

(892)e+eminus 1400 CLEO II [152]470 E791 [161]

Kminusπ+micro+microminus 3600 E791 [161]

Klowast0

(892)micro+microminus 11800 CLEO II [152]240 E791 [161]

π+πminusπ0micro+microminus 8100 E653 [157]microplusmne∓ 2700 CLEO [149]

1200 Mark3 [163]1000 Argus [150]190 CLEO II [152]172 E789 [153]81 E791 [154]081 BaBar [155]026 Belle [156]0016 LHCb [164]

π0eplusmnmicro∓ 860 CLEO II [152]η eplusmnmicro∓ 1000 CLEO II [152]

36

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceπ+πminuseplusmnmicro∓ 150 E791 [161]ρ0eplusmnmicro∓ 660 E791 [161]

490 CLEO II [152]ω eplusmnmicro∓ 1200 CLEO II [152]K+Kminuseplusmnmicro∓ 1800 E791 [161]φ eplusmnmicro∓ 470 E791 [161]

340 CLEO II [152]

K0eplusmnmicro∓ 1000 CLEO II [152]

Kminusπ+eplusmnmicro∓ 5500 E791 [161]Klowast0(892)eplusmnmicro∓ 1000 CLEO II [152]

830 E791 [161]π∓π∓eplusmneplusmn 1120 E791 [161]π∓π∓microplusmnmicroplusmn 290 E791 [161]K∓π∓eplusmneplusmn 2060 E791 [161]K∓π∓microplusmnmicroplusmn 3900 E791 [161]K∓K∓eplusmneplusmn 1520 E791 [161]K∓K∓microplusmnmicroplusmn 940 E791 [161]π∓π∓eplusmnmicroplusmn 790 E791 [161]K∓π∓eplusmnmicroplusmn 2180 E791 [161]K∓K∓eplusmnmicroplusmn 570 E791 [161]p eminus 100 CLEO [165]p e+ 110 CLEO [165]

37

γγ

ρ0micro

+microminus

π+πminusπ

0micro

+microminus

K+K

minuse

+eminus

ηe

+eminus

φmicro

+microminus

π0e

+eminus

φe

+eminus

ωmicro

+microminus

Kminusπ

+micro

+microminus

ρ0e

+eminus

K0micro

+microminus

Klowast0

(892

)e+eminus

π+πminusmicro

+microminus

micro+microminus

π+πminuse

+eminus

e+eminus

Klowast0

(892

)micro+microminus

K+K

minusmicro

+microminus

Kminusπ

+e

+eminus

π0micro

+microminus

K0e

+eminus

ωe

+eminus

ηmicro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

HFAG-charm

Belle

BESIII

CLEO II

BaBar

E791

CLEO

E653

LHCb

E789

HERAB

CDF

Argus

Mark3

June 16

K∓π∓microplusmnmicroplusmn

ωeplusmnmicro∓

Kminusπ

+eplusmnmicro∓

K∓K∓eplusmnmicroplusmn

π∓π∓eplusmnmicroplusmn

peminus

K∓π∓eplusmnmicroplusmn

π∓π∓eplusmneplusmn

ηeplusmnmicro∓

π∓π∓microplusmnmicroplusmn

K∓K∓eplusmneplusmn

K0eplusmnmicro∓

π+πminuseplusmnmicro∓

K∓K∓microplusmnmicroplusmn

ρ0eplusmnmicro∓

pe

+

φeplusmnmicro∓

microplusmne∓

K+K

minuseplusmnmicro∓

Klowast0

(892

)eplusmnmicro∓

π0eplusmnmicro∓

K∓π∓eplusmneplusmn

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

L BLHFAG-charm

E791

CLEO II

CLEO

Belle

E789

Mark3

Argus

LHCb

BaBar

June 16

Figure 9 Upper limits at 90 CL for D0 decays The top plot shows avor-changing neu-tral current decays and the bottom plot shows lepton-avor-changing (LF) lepton-number-changing (L) and both baryon- and lepton-number-changing (BL) decays38

Kminuse

+micro

+

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminusmicro

+micro

+

K+e

+eminus

π+e

+eminus

πminuse

+micro

+

Kminuse

+e

+

K+micro

+eminus

ρminusmicro

+micro

+

K+e

+microminus

K+eplusmnmicro∓

π+micro

+eminus

π+e

+microminus

πminusmicro

+micro

+

πminuse

+e

+

π+micro

+microminus

ρ+micro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E687

E653

E791

BaBar

Focus

CLEO

BESIII

LHCb

D0

June 16

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminuse

+micro

+

K+e

+eminus

π+e

+eminus

K+eplusmnmicro∓

Kminuse

+e

+

K+micro

+eminus

K+e

+microminus

Klowast+

(892

)micro+microminus

π+micro

+eminus

Kminusmicro

+micro

+

πminusmicro

+micro

+

πminuse

+e

+

πminuse

+micro

+

π+micro

+microminus

K+micro

+microminus

π+e

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E653

E791

CLEO

BaBar

Focus

LHCb

June 16

Figure 10 Upper limits at 90 CL for D+ (top) and D+s (bottom) decays Each plot shows

avor-changing neutral current decays lepton-avor-changing decays (LF) and lepton-number-changing (L) decays 39

pmicro

+microminus

pe

+microminus

σ+micro

+microminus

pe

+e

+

pe

+eminus

pe

+micro

+

pmicro

+micro

+

pmicro

+eminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

LHFAG-charm

BaBar E653

June 16

Figure 11 Upper limits at 90 CL for Λ+c decays Shown are avor-changing neutral current

decays lepton-avor-changing (LF) decays and lepton-number-changing (L) decays

40

Table 20 Upper limits at 90 CL for D+ decays

Decay Limit times106 Experiment Referenceπ+e+eminus 1100 E687 [166]

520 E791 [154]59 CLEO [141]11 BaBar [167]03 BESIII [168]

π+micro+microminus 2200 E653 [157]890 E687 [166]150 E791 [154]88 Focus [169]65 BaBar [167]39 D0 [142]0073 LHCb [144]

ρ+micro+microminus 5600 E653 [157]K+e+eminus 2000 E687 [166]

30 CLEO [141]12 BESIII [168]10 BaBar [167]

π+eplusmnmicro∓ 340 E791 [154]π+e+microminus 1100 E687 [166]

29 BaBar [167]π+micro+eminus 1300 E687 [166]

36 BaBar [167]K+eplusmnmicro∓ 680 E791 [154]K+e+microminus 1300 E687 [166]

12 BaBar [167]K+micro+eminus 1200 E687 [166]

28 BaBar [167]πminuse+e+ 1100 E687 [166]

960 E791 [154]19 BaBar [167]12 BESIII [168]11 CLEO [141]

πminusmicro+micro+ 870 E687 [166]170 E791 [154]48 Focus [169]20 BaBar [167]0022 LHCb [144]

πminuse+micro+ 1100 E687 [166]500 E791 [154]

ρminusmicro+micro+ 5600 E653 [157]Kminuse+e+ 1200 E687 [166]

35 CLEO [141]09 BaBar [167]

41

Table 20 continued from previous pageDecay Limit times106 Experiment Reference

06 BESIII [168]Kminusmicro+micro+ 3200 E653 [157]

1200 E687 [166]130 Focus [169]100 BaBar [167]

Kminuse+micro+ 1300 E687 [166]Klowastminus(892)micro+micro+ 8500 E653 [157]

Table 21 Upper limits at 90 CL for D+s decays

Decay Limit times106 Experiment Referenceπ+e+eminus 2700 E791 [154]

220 CLEO [141]130 BaBar [167]

π+micro+microminus 4300 E653 [157]1400 E791 [154]430 BaBar [167]260 Focus [169]041 LHCb [144]

K+e+eminus 16000 E791 [154]520 CLEO [141]37 BaBar [167]

K+micro+microminus 1400 E791 [154]360 Focus [169]210 BaBar [167]

Klowast+(892)micro+microminus 14000 E653 [157]π+eplusmnmicro∓ 6100 E791 [154]π+e+microminus 120 BaBar [167]π+micro+eminus 200 BaBar [167]K+eplusmnmicro∓ 6300 E791 [154]K+e+microminus 140 BaBar [167]K+micro+eminus 97 BaBar [167]πminuse+e+ 6900 E791 [154]

180 CLEO [141]41 BaBar [167]

πminusmicro+micro+ 4300 E653 [157]820 E791 [154]290 Focus [169]140 BaBar [167]012 LHCb [144]

πminuse+micro+ 7300 E791 [154]Kminuse+e+ 6300 E791 [154]

170 CLEO [141]

42

Table 21 continued from previous pageDecay Limit times106 Experiment Reference

52 BaBar [167]Kminusmicro+micro+ 5900 E653 [157]

1800 E791 [154]130 BaBar [167]

Kminuse+micro+ 6800 E791 [154]Klowastminus(892)micro+micro+ 14000 E653 [157]

Table 22 Upper limits at 90 CL for Λ+c decays

Decay Limit times106 Experiment Referencepe+eminus 55 BaBar [167]pmicro+microminus 3400 E653 [157]

440 BaBar [167]σ+micro+microminus 7000 E653 [157]pe+microminus 99 BaBar [167]pmicro+eminus 190 BaBar [167]p e+e+ 27 BaBar [167]p micro+micro+ 94 BaBar [167]

43

References

[1] N Cabibbo Phys Rev Lett 10 531533 (1963)

[2] M Kobayashi and T Maskawa Prog Theor Phys 49 652657 (1973)

[3] D Abbaneo et al (ALEPH CDF DELPHI L3 OPAL and SLD collaborations)arXivhep-ex0009052 (2000) CERN-EP-2000-096 arXivhep-ex0112028 (2001)CERN-EP-2001-050

[4] Y Amhis et al (Heavy Flavor Averaging Group) (2012) arXiv12071158 [hep-ex]

[5] K Olive et al (Particle Data Group) Chin Phys C38 090001 (2014)

[6] A L Kagan and M D Sokolo Phys Rev D80 076008 (2009) arXiv09073917 [hep-ph]

[7] Y Grossman A L Kagan and Y Nir Phys Rev D75 036008 (2007)arXivhep-ph0609178 [hep-ph]

[8] M Gersabeck M Alexander S Borghi V Gligorov and C Parkes J Phys G39 045005(2012) arXiv11116515 [hep-ex]

[9] J P Lees et al (BABAR collaboration) Phys Rev D87 012004 (2013) arXiv12093896[hep-ex]

[10] R Aaij et al (LHCb collaboration) Phys Rev Lett 112 041801 (2014) arXiv13107201[hep-ex]

[11] T A Aaltonen et al (CDF collaboration) Phys Rev D90 no 11 111103 (2014)arXiv14105435 [hep-ex]

[12] R Aaij et al (LHCb collaboration) JHEP 04 043 (2015) arXiv150106777 [hep-ex]

[13] M Staripound et al (Belle collaboration) Phys Lett B753 412418 (2016) arXiv150908266[hep-ex]

[14] B Aubert et al (BABAR collaboration) Phys Rev Lett 100 061803 (2008)arXiv07092715 [hep-ex]

[15] B Ko (Belle collaboration) PoS ICHEP2012 353 (2013) arXiv12121975

[16] T Aaltonen et al (CDF collaboration) Phys Rev Lett 109 111801 (2012)arXiv12072158 [hep-ex]

[17] R Aaij et al (LHCb collaboration) JHEP 07 041 (2014) arXiv14052797 [hep-ex]

[18] R Aaij et al (LHCb collaboration) Phys Rev Lett 116 no 19 191601 (2016)arXiv160203160 [hep-ex]

[19] T Becher and R J Hill Phys Lett B633 6169 (2006) arXivhep-ph0509090 [hep-ph]

[20] F J Gilman and R L Singleton Phys Rev D41 142 (1990)

[21] R J Hill eConf C060409 027 (2006) arXivhep-ph0606023 [hep-ph]

[22] D Becirevic and A B Kaidalov Phys Lett B478 417423 (2000) arXivhep-ph9904490[hep-ph]

44

[23] C G Boyd B Grinstein and R F Lebed Phys Rev Lett 74 46034606 (1995)arXivhep-ph9412324 [hep-ph]

[24] C G Boyd and M J Savage Phys Rev D56 303311 (1997) arXivhep-ph9702300[hep-ph]

[25] M C Arnesen B Grinstein I Z Rothstein and I W Stewart Phys Rev Lett 95 071802(2005)

[26] C Bourrely B Machet and E de Rafael Nucl Phys B189 157 (1981)

[27] D Becirevic A L Yaouanc A Oyanguren P Roudeau and F Sanlippo (2014)arXiv14071019 [hep-ph]

[28] J P Lees et al (BABAR collaboration) Phys Rev D88 052003 (2013) arXiv13045009[hep-ex]

[29] P del Amo Sanchez et al (BaBar Collaboration collaboration) PhysRev D82 111101(2010) arXiv10092076 [hep-ex]

[30] R Aaij et al (LHCb collaboration) JHEP 1309 145 (2013) arXiv13074556

[31] G Burdman and J Kambor Phys Rev D55 28172826 (1997) arXivhep-ph9602353[hep-ph]

[32] D Becirevic A Le Yaouanc L Oliver J-C Raynal P Roudeau and J Serrano Phys RevD87 no 5 054007 (2013) arXiv12065869 [hep-ph]

[33] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052022 (2015)arXiv14125502 [hep-ex]

[34] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 7 072012 (2015)arXiv150807560 [hep-ex]

[35] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 11 112008 (2015)arXiv151000308 [hep-ex]

[36] L Widhalm et al (Belle collaboration) Phys Rev Lett 97 061804 (2006)arXivhep-ex0604049 [hep-ex]

[37] B Aubert et al (BABAR collaboration) Phys Rev D76 052005 (2007) arXiv07040020[hep-ex]

[38] D Besson et al (CLEO collaboration) Phys Rev D80 032005 (2009) arXiv09062983[hep-ex]

[39] S Dobbs et al (CLEO collaboration) Phys Rev D77 112005 (2008) arXiv07121020[hep-ex]

[40] G Huang et al (CLEO collaboration) Phys Rev Lett 94 011802 (2005)arXivhep-ex0407035 [hep-ex]

[41] J Link et al (FOCUS collaboration) Phys Lett B607 233242 (2005)arXivhep-ex0410037 [hep-ex]

[42] J Adler et al (MARK-III collaboration) Phys Rev Lett 62 1821 (1989)

45

[43] K Kodama et al (Fermilab E653 collaboration) Phys Rev Lett 66 18191822 (1991)

[44] K Kodama et al (E653 collaboration) Phys Lett B336 605613 (1994)

[45] P L Frabetti et al (E687 collaboration) Phys Lett B364 127136 (1995)

[46] P L Frabetti et al (E687 collaboration) Phys Lett B315 203208 (1993)

[47] J C Anjos et al (Tagged Photon Spectrometer collaboration) Phys Rev Lett 6215871590 (1989)

[48] M Ablikim et al (BES collaboration) Phys Lett B597 3946 (2004)arXivhep-ex0406028 [hep-ex]

[49] M Ablikim et al (BES collaboration) (2006) arXivhep-ex0610019 [hep-ex]

[50] A Bean et al (CLEO collaboration) Phys Lett B317 647654 (1993)

[51] BESIII collaboration presented at ICHEP 2014 conference 2014httpindicoificuvesindicogetFilepyaccesscontribId=69ampsessionId=25ampresId=

0ampmaterialId=slidesampconfId=2025

[52] J G Korner and G A Schuler Z Phys C46 93 (1990)

[53] FLAG collaboration httpitpwikiunibechagimages44bFLAGpdf 2014httpitpwikiunibechflagimages44bFLAGpdf

[54] J Anjos et al (Fermilab E691 collaboration) Phys Rev Lett 65 26302633 (1990)

[55] K Kodama et al (Fermilab E653 collaboration) Phys Lett B274 246252 (1992)

[56] P Frabetti et al (Fermilab E687 collaboration) Phys Lett B307 262268 (1993)

[57] E Aitala et al (E791 collaboration) Phys Rev Lett 80 13931397 (1998)arXivhep-ph9710216 [hep-ph]

[58] E Aitala et al (E791 collaboration) Phys Lett B440 435441 (1998)arXivhep-ex9809026 [hep-ex]

[59] M Adamovich et al (BEATRICE collaboration) Eur Phys J C6 3541 (1999)

[60] J Link et al (FOCUS collaboration) Phys Lett B544 8996 (2002)arXivhep-ex0207049 [hep-ex]

[61] J Link et al (FOCUS collaboration) Phys Lett B607 6777 (2005)arXivhep-ex0410067 [hep-ex]

[62] P del Amo Sanchez et al (BABAR collaboration) Phys Rev D83 072001 (2011)arXiv10121810 [hep-ex]

[63] B Aubert et al (BABAR collaboration) Phys Rev D78 051101 (2008) arXiv08071599[hep-ex]

[64] H Mahlke eConf C0610161 014 (2006) arXivhep-ex0702014 [hep-ex]

[65] J Link et al (FOCUS collaboration) Phys Lett B535 4351 (2002)arXivhep-ex0203031 [hep-ex]

46

[66] K M Ecklund et al (CLEO collaboration) Phys Rev D80 052009 (2009)arXiv09073201 [hep-ex]

[67] R A Briere et al (CLEO collaboration) Phys Rev D81 112001 (2010) arXiv10041954[hep-ex]

[68] P Estabrooks R Carnegie A D Martin W Dunwoodie T Lasinski et al Nucl PhysB133 490 (1978)

[69] D Aston et al Nucl Phys B296 493 (1988)

[70] B Aubert et al (BABAR collaboration) Phys Rev Lett 90 242001 (2003)arXivhep-ex0304021 [hep-ex]

[71] D Besson et al (CLEO Collaboration collaboration) PhysRev D68 032002 (2003)arXivhep-ex0305100 [hep-ex]

[72] K Abe et al (Belle Collaboration collaboration) PhysRevLett 92 012002 (2004)arXivhep-ex0307052 [hep-ex]

[73] B Aubert et al (BaBar Collaboration collaboration) PhysRev D69 031101 (2004)arXivhep-ex0310050 [hep-ex]

[74] K Abe et al (Belle collaboration) Phys Rev D69 112002 (2004) arXivhep-ex0307021[hep-ex]

[75] J M Link et al (FOCUS Collaboration collaboration) PhysLett B586 1120 (2004)arXivhep-ex0312060 [hep-ex]

[76] S Godfrey and N Isgur Phys Rev D32 189231 (1985)

[77] S Godfrey and R Kokoski Phys Rev D43 16791687 (1991)

[78] N Isgur and M B Wise Phys Rev Lett 66 11301133 (1991)

[79] P Schweitzer S Bo and M Radici Phys Rev D66 114004 (2002)arXivhep-ph0207230 [hep-ph]

[80] F Jugeau A Le Yaouanc L Oliver and J-C Raynal Phys Rev D72 094010 (2005)arXivhep-ph0504206 [hep-ph]

[81] P Colangelo F De Fazio and R Ferrandes ModPhysLett A19 20832102 (2004)arXivhep-ph0407137 [hep-ph]

[82] R N Cahn and J D Jackson Phys Rev D68 037502 (2003) arXivhep-ph0305012[hep-ph]

[83] T Barnes F E Close and H J Lipkin PhysRev D68 054006 (2003)arXivhep-ph0305025 [hep-ph]

[84] H Lipkin PhysLett B580 5053 (2004) arXivhep-ph0306204 [hep-ph]

[85] W A Bardeen E J Eichten and C T Hill Phys Rev D68 054024 (2003)arXivhep-ph0305049 [hep-ph]

[86] B Aubert et al (BaBar Collaboration collaboration) PhysRev D80 092003 (2009)arXiv09080806 [hep-ex]

47

[87] R Aaij et al (LHCb Collaboration collaboration) JHEP 1210 151 (2012) arXiv12076016[hep-ex]

[88] R Aaij et al (LHCb collaboration) Phys Rev Lett 113 162001 (2014) arXiv14077574[hep-ex]

[89] R Aaij et al (LHCb collaboration) JHEP 02 133 (2016) arXiv160101495 [hep-ex]

[90] T Matsuki T Morii and K Sudoh EurPhysJ A31 701704 (2007)arXivhep-ph0610186 [hep-ph]

[91] N Isgur and M B Wise PhysLett B232 113117 (1989)

[92] M Neubert PhysRept 245 259396 (1994) arXivhep-ph9306320 [hep-ph]

[93] B Aubert et al (BaBar Collaboration collaboration) PhysRev D74 032007 (2006)arXivhep-ex0604030 [hep-ex]

[94] V M Abazov et al (D0 Collaboration collaboration) PhysRevLett 102 051801 (2009)arXiv07123789 [hep-ex]

[95] B Aubert et al (BABAR collaboration) Phys Rev D77 011102 (2008) arXiv07081565[hep-ex]

[96] P L Frabetti et al (E687 Collaboration collaboration) PhysRevLett 72 324327 (1994)

[97] J P Alexander et al (CLEO Collaboration collaboration) PhysLett B303 377384 (1993)

[98] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B297 425431 (1992)

[99] P Avery et al (CLEO Collaboration collaboration) PhysRev D41 774 (1990)

[100] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B230 162 (1989)

[101] J P Lees et al (BaBar Collaboration collaboration) PhysRev D83 072003 (2011)arXiv11032675 [hep-ex]

[102] R Aaij et al (LHCb collaboration) Phys Rev D90 no 7 072003 (2014) arXiv14077712[hep-ex]

[103] R Aaij et al (LHCb collaboration) PhysLett B698 1420 (2011) arXiv11020348[hep-ex]

[104] B Aubert et al (BaBar Collaboration collaboration) PhysRevLett 97 222001 (2006)arXivhep-ex0607082 [hep-ex]

[105] H Albrecht et al (ARGUS Collaboration collaboration) ZPhys C69 405408 (1996)

[106] Y Kubota et al (CLEO Collaboration collaboration) PhysRevLett 72 19721976 (1994)arXivhep-ph9403325 [hep-ph]

[107] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052002 (2015)arXiv14126751 [hep-ex]

[108] J Brodzicka et al (Belle collaboration) Phys Rev Lett 100 092001 (2008)arXiv07073491 [hep-ex]

48

[109] B Aubert et al (BABAR collaboration) Phys Rev D79 112004 (2009) arXiv09011291[hep-ex]

[110] R Aaij et al (LHCb collaboration) Phys Rev D92 no 3 032002 (2015)arXiv150501710 [hep-ex]

[111] R Aaij et al (LHCb collaboration) Phys Rev D92 no 1 012012 (2015)arXiv150501505 [hep-ex]

[112] A Kuzmin et al (Belle Collaboration collaboration) PhysRev D76 012006 (2007)arXivhep-ex0611054 [hep-ex]

[113] H Abramowicz et al (ZEUS Collaboration collaboration) NuclPhys B866 229254 (2013)arXiv12084468 [hep-ex]

[114] A Abulencia et al (CDF Collaboration collaboration) PhysRev D73 051104 (2006)arXivhep-ex0512069 [hep-ex]

[115] K Abe et al (Belle collaboration) Phys Rev Lett 94 221805 (2005)arXivhep-ex0410091 [hep-ex]

[116] P Avery et al (CLEO Collaboration collaboration) PhysLett B331 236244 (1994)arXivhep-ph9403359 [hep-ph]

[117] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B232 398 (1989)

[118] J C Anjos et al (Tagged Photon Spectrometer Collaboration collaboration) PhysRevLett62 1717 (1989)

[119] T Bergfeld et al (CLEO Collaboration collaboration) PhysLett B340 194204 (1994)

[120] R Aaij et al (LHCb collaboration) Phys Rev D91 no 9 092002 (2015)arXiv150302995 [hep-ex] [Erratum Phys RevD93no11119901(2016)]

[121] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B221 422 (1989)

[122] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B231 208 (1989)

[123] P Abreu et al (DELPHI Collaboration collaboration) PhysLett B426 231242 (1998)

[124] D Matvienko et al (Belle collaboration) Phys Rev D92 no 1 012013 (2015)arXiv150503362 [hep-ex]

[125] P Krokovny et al (Belle collaboration) Phys Rev Lett 91 262002 (2003)arXivhep-ex0308019 [hep-ex]

[126] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 181801 (2004)arXivhep-ex0408041 [hep-ex]

[127] S K Choi et al (Belle collaboration) Phys Rev D91 no 9 092011 (2015)arXiv150402637 [hep-ex] [Addendum Phys RevD92no3039905(2015)]

[128] A Drutskoy et al (Belle collaboration) Phys Rev Lett 94 061802 (2005)arXivhep-ex0409026 [hep-ex]

[129] B Aubert et al (BABAR collaboration) Phys Rev D74 031103 (2006)arXivhep-ex0605036 [hep-ex]

49

[130] S Chekanov et al (ZEUS Collaboration collaboration) EurPhysJ C60 2545 (2009)arXiv08071290 [hep-ex]

[131] A Heister et al (ALEPH Collaboration collaboration) PhysLett B526 3449 (2002)arXivhep-ex0112010 [hep-ex]

[132] B Aubert et al (BABAR collaboration) Phys Rev Lett 103 051803 (2009)arXiv08080333 [hep-ex]

[133] G Burdman E Golowich J L Hewett and S Pakvasa Phys Rev D66 014009 (2002)arXivhep-ph0112235 [hep-ph]

[134] S Fajfer A Prapotnik S Prelovsek P Singer and J Zupan Nucl Phys Proc Suppl 1159397 (2003) arXivhep-ph0208201 [hep-ph]

[135] S Fajfer N Kosnik and S Prelovsek Phys Rev D76 074010 (2007) arXiv07061133[hep-ph]

[136] E Golowich J Hewett S Pakvasa and A A Petrov Phys Rev D79 114030 (2009)arXiv09032830 [hep-ph]

[137] A Paul I I Bigi and S Recksiegel Phys Rev D82 094006 (2010) arXiv10083141[hep-ph]

[138] A Borisov (2011) arXiv11123269 [hep-ph]

[139] R-M Wang J-H Sheng J Zhu Y-Y Fan and Y Gao Int J Mod Phys A29 no 291450169 (2014)

[140] S de Boer and G Hiller Phys Rev D93 no 7 074001 (2016) arXiv151000311 [hep-ph]

[141] P Rubin et al (CLEO collaboration) Phys Rev D82 092007 (2010) arXiv10091606[hep-ex]

[142] V Abazov et al (D0 collaboration) Phys Rev Lett 100 101801 (2008) arXiv07082094[hep-ex]

[143] R Aaij et al (LHCb collaboration) Phys Lett B728 234243 (2014) arXiv13102535[hep-ex]

[144] R Aaij et al (LHCb collaboration) Phys Lett B724 203212 (2013) arXiv13046365[hep-ex]

[145] T Coan et al (CLEO collaboration) Phys Rev Lett 90 101801 (2003)arXivhep-ex0212045 [hep-ex]

[146] M Ablikim et al (BESIII collaboration) Phys Rev D91 no 11 112015 (2015)arXiv150503087 [hep-ex]

[147] J P Lees et al (BABAR collaboration) Phys Rev D85 091107 (2012) arXiv11106480[hep-ex]

[148] N K Nisar et al (Belle collaboration) Phys Rev D93 no 5 051102 (2016)arXiv151202992 [hep-ex]

[149] P Haas et al (CLEO collaboration) Phys Rev Lett 60 1614 (1988)

50

[150] H Albrecht et al (ARGUS collaboration) Phys Lett B209 380 (1988)

[151] J Adler et al (MARK-III collaboration) Phys Rev D37 2023 (1988) Erratum ibid D40(1989) 3788

[152] A Freyberger et al (CLEO collaboration) Phys Rev Lett 76 30653069 (1996)

[153] D Pripstein et al (E789 collaboration) Phys Rev D61 032005 (2000)arXivhep-ex9906022 [hep-ex]

[154] E Aitala et al (E791 collaboration) Phys Lett B462 401409 (1999)arXivhep-ex9906045 [hep-ex]

[155] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 191801 (2004)arXivhep-ex0408023 [hep-ex]

[156] M Petric et al (Belle collaboration) Phys Rev D81 091102 (2010) arXiv10032345[hep-ex]

[157] K Kodama et al (E653 collaboration) Phys Lett B345 8592 (1995)

[158] I Abt et al (HERA-B collaboration) Phys Lett B596 173183 (2004)arXivhep-ex0405059 [hep-ex]

[159] T Aaltonen et al (CDF collaboration) Phys Rev D82 091105 (2010) arXiv10085077[hep-ex]

[160] R Aaij et al (LHCb collaboration) Phys Lett B725 1524 (2013) arXiv13055059[hep-ex]

[161] E Aitala et al (E791 collaboration) Phys Rev Lett 86 39693972 (2001)arXivhep-ex0011077 [hep-ex]

[162] J Adler et al (MARK-III collaboration) Phys Rev D40 906 (1989)

[163] J Becker et al (MARK-III collaboration) Phys Lett B193 147 (1987)

[164] R Aaij et al (LHCb collaboration) Phys Lett B754 167175 (2016) arXiv151200322[hep-ex]

[165] P Rubin et al (CLEO collaboration) Phys Rev D79 097101 (2009) arXiv09041619[hep-ex]

[166] P Frabetti et al (E687 collaboration) Phys Lett B398 239244 (1997)

[167] J P Lees et al (BABAR collaboration) Phys Rev D84 072006 (2011) arXiv11074465[hep-ex]

[168] (BESIII collaboration) M-G Zhao D rareforbidden decays at BESIII in 7th International

Workshop on Charm Physics (Charm 2015) Detroit MI USA May 18-22 2015 2016arXiv160508952 [hep-ex]httpinspirehepnetrecord1466292filesarXiv160508952pdf

[169] J Link et al (FOCUS collaboration) Phys Lett B572 2131 (2003)arXivhep-ex0306049 [hep-ex]

51

  • Introduction
  • D decays
    • Interplay of direct and indirect CP violation
    • Semileptonic decays
      • Introduction
      • DP decays
      • Form factor parameterizations
      • Simple pole
      • z expansion
      • Three-pole formalism
      • Experimental techniques and results
      • Combined results for the DK channel
      • Combined results for the D channel
      • Vcs and Vcd determination
      • DV decays
      • Form factor measurements
        • Excited D(s) mesons
        • Rare and forbidden decays
          • References
Page 5: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

2 D decays

5

21 Interplay of direct and indirect CP violation

In decays of D0 mesons CP asymmetry measurements have contributions from both directand indirect CP violation as discussed in Sec The contribution from indirect CP viola-tion depends on the decay-time distribution of the data sample [6] This section describes acombination of measurements that allows the extraction of the individual contributions of thetwo types of CP violation At the same time the level of agreement for a no-CP -violationhypothesis is tested The observables are

AΓ equivτ(D 0rarrh+hminus)minus τ(D0rarrh+hminus)

τ(D 0rarrh+hminus) + τ(D0rarrh+hminus) (1)

where h+hminus can be K+Kminus or π+πminus and

∆ACP equiv ACP(K+Kminus)minus ACP(π+πminus) (2)

where ACP are time-integrated CP asymmetries The underlying theoretical parameters are

adirCP equiv

|AD0rarrf |2 minus |AD 0rarrf |2

|AD0rarrf |2 + |AD 0rarrf |2

aindCP equiv 1

2

[(∣∣∣∣qp∣∣∣∣+

∣∣∣∣pq∣∣∣∣)x sinφminus

(∣∣∣∣qp∣∣∣∣minus ∣∣∣∣pq

∣∣∣∣) y cosφ

] (3)

where ADrarrf is the amplitude for D rarr f [7] We use the following relations between theobservables and the underlying parameters [8]

AΓ = minusaindCP minus adir

CPyCP

∆ACP = ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

+ adirCPyCP

∆〈t〉τ

(4)

asymp ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

(5)

The rst relation constrains mostly indirect CP violation and the direct CP violation contri-bution can dier for dierent nal states In the second relation 〈t〉τ denotes the mean decaytime in units of the D0 lifetime ∆X denotes the dierence in quantity X between K+Kminus andπ+πminus nal states and X denotes the average for quantity X We neglect the last term in thisrelation as all three factors are O(10minus2) or smaller and thus this term is negligible with respectto the other two terms Note that ∆〈t〉τ 〈t〉τ and it is expected that |adir

CP| lt |∆adirCP|

because adirCP(K+Kminus) and adir

CP(π+πminus) are expected to have opposite signs [7]A χ2 t is performed in the plane ∆adir

CP vs aindCP For the BABAR result the dierence of

the quoted values for ACP(K+Kminus) and ACP(π+πminus) is calculated adding all uncertainties inquadrature This may overestimate the systematic uncertainty for the dierence as it neglectscorrelated errors however the result is conservative and the eect is small as all measurementsare statistically limited For all measurements statistical and systematic uncertainties areadded in quadrature when calculating the χ2 We use the current world average value yCP =(0866plusmn 0155) (see Sec ) and the measurements listed in Table 1

6

Table 1 Inputs to the t for direct and indirect CP violation The rst uncertainty listed isstatistical and the second is systematic

Year Experiment Results ∆〈t〉τ 〈t〉τ Reference2012 BABAR AΓ = (009plusmn 026plusmn 006) - - [9]2013 LHCb prompt AΓ(KK) = (minus0035plusmn 0062plusmn 0012) - - [10]

AΓ(ππ) = (0033plusmn 0106plusmn 0014) - -2014 CDF AΓ = (minus012plusmn 012) - - [11]2015 LHCb SL AΓ = (minus0125plusmn 0073) - - [12]2015 Belle AΓ = (minus003plusmn 020plusmn 007) - - [13]2008 BABAR ACP(KK) = (000plusmn 034plusmn 013)

ACP(ππ) = (minus024plusmn 052plusmn 022) 000 100 [14]2012 Belle prel ∆ACP = (minus087plusmn 041plusmn 006) 000 100 [15]2012 CDF ∆ACP = (minus062plusmn 021plusmn 010) 025 258 [16]2014 LHCb SL ∆ACP = (014plusmn 016plusmn 008) 001 107 [17]2016 LHCb prompt ∆ACP = (minus010plusmn 008plusmn 003) 012 210 [18]

In this t AΓ(KK) and AΓ(ππ) are assumed to be identical This assumption is sup-ported by all measurements to date A signicant relative shift due to nal-state dependentAΓ values between ∆ACP measurements with dierent mean decay times is excluded by thesemeasurements

The combination plot (see Fig 1) shows the measurements listed in Table 1 for ∆ACP andAΓ where the bands represent plusmn1σ intervals The point of no CP violation (00) is shownas a lled circle and two-dimensional 68 CL 95 CL and 997 CL regions are plotted asellipses The best t value is indicated by a cross showing the one-dimensional errors

From the t the change in χ2 from the minimum value for the no-CPV point (00) is55 which corresponds to a CL of 65 times 10minus2 for two degrees of freedom Thus the data areconsistent with the no-CP -violation hypothesis at 65 CL This p-value corresponds to 18σThe central values and plusmn1σ uncertainties for the individual parameters are

aindCP = (0056plusmn 0040)

∆adirCP = (minus0137plusmn 0070) (6)

Compared to the previous average the tension in the dierence between direct CP violationin the two nal states reduced while the common indirect CP violation moved away from theno CP violation point by about one standard deviation

7

0015 0010 0005 0000 0005 0010

aindCP

0015

0010

0005

0000

0005

0010

0015

∆adirCP

Contours contain 68 95 99 CL

CD

F

LHC

b S

L

LHC

b p

rom

pt

BaBarBelleCDF KK+ππLHCb SL KK+ππ

LHCb prompt KKLHCb prompt ππ

HFAG-charmWinter 16

no CPV

BaBar

Belle

CDF

LHCb

Figure 1 Plot of all data and the t result Individual measurements are plotted as bandsshowing their plusmn1σ range The no-CPV point (00) is shown as a lled circle and the best tvalue is indicated by a cross showing the one-dimensional uncertainties Two-dimensional 68CL 95 CL and 997 CL regions are plotted as ellipses

8

22 Semileptonic decays

221 Introduction

Semileptonic decays of D mesons involve the interaction of a leptonic current with a hadroniccurrent The latter is nonperturbative and cannot be calculated from rst principles thus it isusually parameterized in terms of form factors The transition matrix element is written

M = minusi GFradic2Vcq L

microHmicro (7)

where GF is the Fermi constant and Vcq is a CKM matrix element The leptonic current Lmicro isevaluated directly from the lepton spinors and has a simple structure this allows one to extractinformation about the form factors (in Hmicro) from data on semileptonic decays [19] Converselybecause there are no strong nal-state interactions between the leptonic and hadronic systemssemileptonic decays for which the form factors can be calculated allow one to determine Vcq [2]

222 DrarrP`ν` decays

When the nal state hadron is a pseudoscalar the hadronic current is given by

Hmicro = 〈P (p)|qγmicroc|D(pprime)〉 = f+(q2)

[(pprime + p)micro minus

m2D minusm2

P

q2qmicro

]+ f0(q2)

m2D minusm2

P

q2qmicro (8)

where mD and pprime are the mass and four momentum of the parent D meson mP and p are thoseof the daughter meson f+(q2) and f0(q2) are form factors and q = pprime minus p Kinematics requirethat f+(0) = f0(0) The contraction qmicroL

micro results in terms proportional to m` [20] and thus for` = e the terms proportionals to qmicro in Eq (8) are negligible For light leptons only the f+(q2)vector form factor is relevant and the dierential partial width is

dΓ(D rarr P`ν`)

dq2 d cos θ`=

G2F |Vcq|2

32π3plowast 3|f+(q2)|2 sin θ2

` (9)

where plowast is the magnitude of the momentum of the nal state hadron in the D rest frame andθ` is the angle of the lepton in the `ν rest frame with respect to the direction of the pseudoscalarmeson in the D rest frame

223 Form factor parameterizations

The form factor is traditionally parameterized with an explicit pole and a sum of eective poles

f+(q2) =f+(0)

(1minus α)

[(1

1minus q2m2pole

)+

Nsumk=1

ρk1minus q2(γkm2

pole)

] (10)

where ρk and γk are expansion parameters and α is a parameter that normalizes the formfactor at q2 = 0 f+(0) The parameter mpole is the mass of the lowest-lying cq resonance withthe vector quantum numbers this is expected to provide the largest contribution to the formfactor for the crarr q transition The sum over N gives the contribution of higher mass statesFor example for D rarr π transitions the dominant resonance is expected to be Dlowast(2010) andthus mpole = mDlowast(2010) For D rarr K transitions the dominant contribution is expected from

Dlowasts(2112) with mpole = mDlowasts (2112)

9

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Comparison between CLEO-c and BABAR results for the quantities q2H20 (q2) and

q2h0(q2)H0(q2)

Table 11 Results for rV and r2 from various experiments

Experiment Ref rV r2

D+ rarr Klowast0l+ν

E691 [54] 20plusmn 06plusmn 03 00plusmn 05plusmn 02E653 [55] 200plusmn 033plusmn 016 082plusmn 022plusmn 011E687 [56] 174plusmn 027plusmn 028 078plusmn 018plusmn 011

E791 (e) [57] 190plusmn 011plusmn 009 071plusmn 008plusmn 009E791 (micro) [58] 184plusmn011plusmn009 075plusmn008plusmn009Beatrice [59] 145plusmn 023plusmn 007 100plusmn 015plusmn 003FOCUS [60] 1504plusmn0057plusmn0039 0875plusmn0049plusmn0064

D0 rarr K0πminusmicro+ν

FOCUS [61] 1706plusmn0677plusmn0342 0912plusmn0370plusmn0104BABAR [62] 1493plusmn 0014plusmn 0021 0775plusmn 0011plusmn 0011

D+s rarr φ e+νBABAR [63] 1849plusmn0060plusmn0095 0763plusmn0071plusmn0065

D0 D+ rarr ρ eνCLEO [64] 140plusmn025plusmn003 057plusmn018plusmn006

23

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

HFLAV())+-amp

Figure 7 A comparison of r2 (lled inverted triangles) and rV (open triangles) values fromvarious experiments The rst seven measurements are for D+ rarr Kminusπ+l+νl decays Alsoshown as a line with 1-σ limits is the average of these The last two points are D+

s and D0

decays

24

23 Excited D(s) mesons

Excited charm meson states have received increased attention since the rst observation ofstates that could not be accommodated by QCD predictions [70 71 72 73] Tables 12 13and 14 summarize recent measurements of the masses and widths of excited D and Ds mesonsrespectively If a preferred assignment of spin and parity was measured it is listed in the columnJP where the label natural denotes JP = 0minus 1+ 2minus and unnatural JP = 0+ 1minus 2+ Ifpossible an average mass and width was calculated which is listed in the gray shaded rowThe calculation of the averages assumes no correlation between individual measurements Asummary of the averaged masses and widths is shown in Figure 8

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

0+ 1+ 2+ 1minus 1 3minus

unnatu

ral

Dlowast s0

(2317)plusmn

Ds1

(2460)plusmn

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn D

sJ(3

040)plusmn

HFAG-charmAugust 2016

(a)

Mas

s[M

eVc

2]

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

0+ 1+ 2+ 0minus 1minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ralDlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn

D(2

550)0

D(2

580)0

D(2

600)0

D(2

600)plusmn

Dlowast (

2640)plusmn

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(b)

Mas

s[M

eVc

2]

0

50

100

150

200

250

300

350

400

450

500

550

1+ 2+ 1minus 1 3minus

unnatu

ral

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn

DsJ

(3040)plusmn

HFAG-charmAugust 2016

(c)

Wid

th[M

eV]

50100150200250300350400450500550600650700

0+ 1+ 2+ 0minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ral

Dlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn D(2

550)0

D(2

580)0

D(2

600)0

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(d)

Wid

th[M

eV]

Figure 8 Averaged masses for Ds mesons are shown in subgure (a) and for D mesons insubgure (b) The average widths for Ds mesons are shown in subgure (c) and for D mesonsin subgure (d) The vertical shaded regions distinguish between dierent spin parity states

The masses and widths of narrow (Γ lt 50 MeV) orbitally excited D mesons (denotedDlowastlowast) both neutral and charged are well established Measurements of broad states (Γ sim200400 MeV) are less abundant as identifying the signal is more challenging There is aslight discrepancy between the Dlowast0(2400)0 masses measured by the Belle [74] and FOCUS [75]experiments No data exist yet for the D1(2430)plusmn state Dalitz plot analyses of B rarr D(lowast)ππ

25

decays strongly favor the assignments 0+ and 1+ for the spin-parity quantum numbers of theDlowast0(2400)0Dlowast0(2400)plusmn and D1(2430)0 states respectively The measured masses and widthsas well as the JP values are in agreement with theoretical predictions based on potentialmodels [76777879]

Tables 15 and 16 summarizes the branching fractions of B mesons decays to excited D andDs states respectively It can be noted that the branching fractions for B mesons decaying to anarrow Dlowastlowast state and a pion are similar for charged and neutral B initial states the branchingfractions to a broad Dlowastlowast state and π+ are much larger for B+ than for B0 This may be dueto the fact that color-suppressed amplitudes contribute only to the B+ decay and not to theB0 decay (for a theoretical discussion see Ref [8081]) Measurements of individual branchingfractions of D mesons are dicult due to the unknown fragmentation of cc rarr Dlowastlowast or due tothe unknown B rarr DlowastlowastX branching fractions

The discoveries of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn have triggered increased interest in prop-erties of and searches for excited Ds mesons (here generically denoted D

lowastlowasts ) While the masses

and widths of Ds1(2536)plusmn and Ds2(2573)plusmn states are in relatively good agreement with po-tential model predictions the masses of Dlowasts0(2317)plusmn and Ds1(2460)plusmn states are signicantlylower than expected (see Ref [82] for a discussion of cs models) Moreover the mass splittingbetween these two states greatly exceeds that between the Ds1(2536)plusmn and Ds2(2573)plusmn Theseunexpected properties have led to interpretations of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn as exoticfour-quark states [8384]

While there are few measurements of the JP values of Dlowasts0(2317)plusmn andDs1(2460)plusmn the avail-able data favor 0+ and 1+ respectively A molecule-like (DK) interpretation of the Dlowasts0(2317)plusmn

and Ds1(2460)plusmn [8384] that can account for their low masses and isospin-breaking decay modesis tested by searching for charged and neutral isospin partners of these states thus far suchsearches have yielded negative results Therefore the subset of models that predict equal pro-duction rates for dierent charged states is excluded The molecular picture can also be testedby measuring the rates for the radiative processes Dlowasts0(2317)plusmnDs1(2460)plusmn rarr D

(lowast)s γ and com-

paring to theoretical predictions The predicted rates however are below the sensitivity ofcurrent experiments

Another model successful in explaining the total widths and the Dlowasts0(2317)plusmn Ds1(2460)plusmn

mass splitting is based on the assumption that these states are chiral partners of the groundstates D+

s and Dlowasts [85] While some measured branching fraction ratios agree with predictedvalues further experimental tests with better sensitivity are needed to conrm or refute thisscenario A summary of the mass dierence measurements is given in Table 17

Measurements by BABAR [86] and LHCb [87] rst indicated the existence of a strange-charm DlowastsJ(2860)plusmn meson An LHCb study of B0

s rarr D0Kminusπ+ decays in which they searchedfor excited Ds mesons [88] showed with 10σ signicance that this state is comprised of twodierent particles one of spin 1 and one of spin 3 This represents the rst measurement of aheavy avored spin-3 particle and the rst observation B mesons decays to spin 3 particlesA subsequent study of DsJ mesons by the LHCb collaboration [89] supports the natural parityassignment for this state (JP = 3minus) This study also shows weak evidence for a further structureat a mass around 3040 MeVc2 with unnatural parity which was rst hinted at by a Babaranalysis [86]

Recent evidence shows that the 1D family of charm resonances can be explored in the Dalitzplot analyses of B-meson decays in the same way as seen for the charm-strange resonances TheLHCb collaboration performed an analysis of B0 rarr D0π+πminus decays in which they measured

26

the spin-parity assignment of the stateDlowast3(2760)plusmn which was observed previously by BABAR [29]and LHCb [30] to be JP = 3minus The measurement suggests a spectroscopic assignment of 3D3This is the second observation of a spin-3 charm meson

Other observed excited Ds states include Ds1(2700)plusmn and Ds2(2573)plusmn The properties ofboth (mass width JP ) have been measured and determined in several analyses A theoreticaldiscussion [90] investigates the possibility that theDs1(2700)plusmn could represent radial excitationsof the Dlowastplusmns Similarly the Ds1(2860)plusmn and DsJ(3040)plusmn could be excitations of Dlowasts0(2317)plusmn andDs1(2460)plusmn or Ds1(2536)plusmn respectively

Table 18 summarizes measurements of the polarization amplitude AD (sometimes also re-ferred as helicity parameter) which describes the initial polarization of the D meson In Dlowastlowast

meson decay the helicity distribution varies like 1 + AD cos2 θH where θH is the angle in theDlowast rest frame between the two pions emitted by decay Dlowastlowast rarr Dlowastπ and the Dlowast rarr Dπ Theparameter is sensitive to possible S-wave contributions in the decay In the case of an unpolar-ized D meson decay decaying purely via D-wave the polarization amplitude is predicted to giveAD = 3 Studies of the D1(2420)0 meson by the ZEUS and BABAR collaborations suggest thatthere is an S-wave admixture in the decay which is contrary to Heavy Quark Eective Theorycalculations [9192]

27

Table 12 Recent measurements of mass and width for dierent excited Ds mesons Thecolumn JP list the most signicant assignment of spin and parity If possible an average massor width is calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowasts0(2317)plusmn 0+

D+s π

0 23196plusmn 02plusmn 14 BABAR [93]D+s π

0 23173plusmn 04plusmn 08 BABAR [73]

23180plusmn 08 Our average

Ds1(2460)plusmn 1+

D+s π

0γD+s γD

+s π

+πminus 24601plusmn 02plusmn 08 BABAR [93]D+s π

0γ 2458plusmn 10plusmn 10 BABAR [73]

24596plusmn 07 Our average

Ds1(2536)plusmn 1+

Dlowast+K0S 25357plusmn 06plusmn 05 DOslash [94]

Dlowast+K0S D

lowast0K+ 253478plusmn 031plusmn 040 BABAR [95]D+s π

+πminus 25346plusmn 03plusmn 07 BABAR [93]Dlowast+K0

S Dlowast0K+ 25350plusmn 06plusmn 10 E687 [96]

Dlowast0K+ 25353plusmn 02plusmn 05 CLEO [97]Dlowast+K0

S 25348plusmn 06plusmn 06 CLEO [97]Dlowast0K+ 25352plusmn 05plusmn 15 ARGUS [98]Dlowast+K0

S 25356plusmn 07plusmn 04 CLEO [99]Dlowast+K0

S 25359plusmn 06plusmn 20 ARGUS [100]Dlowast+K0

S 092plusmn 003plusmn 004 BABAR [101]

253510plusmn 026 092plusmn 005 Our average

Dlowasts2(2573)plusmn 2+

D0K+ Dlowast+K0S 256839plusmn 029plusmn 026 169plusmn 05plusmn 06 LHCb [102]

D+K0S D

0K+ 25694plusmn 16plusmn 05 121plusmn 45plusmn 16 LHCb [103]D+K0

S D0K+ 25722plusmn 03plusmn 10 271plusmn 06plusmn 56 BABAR [104]

D0K+ 257425plusmn 33plusmn 16 104plusmn 83plusmn 30 ARGUS [105]D0K+ 25732+17

minus16 plusmn 09 16+5minus4 plusmn 3 CLEO [106]

256908plusmn 035 169plusmn 08 Our average

Dlowasts1(2700)plusmn 1minus

Dlowast+K0S D

lowast0K+ 27323plusmn 43plusmn 58 136plusmn 19plusmn 24 LHCb [89]D0K+ 2699+14

minus7 127+24minus19 BABAR [107]

Dlowast+K0S D

lowast0K+ 27092plusmn 19plusmn 45 1158plusmn 73plusmn 121 LHCb [87]DKDlowastK 2710plusmn 2+12

minus7 149plusmn 7+39minus52 BABAR [86]

D0K+ 2708plusmn 9+11minus10 108plusmn 2+36

minus31 Belle [108]

27120plusmn 15 1215plusmn 102 Our average

Dlowasts1(2860)plusmn 1 D0K+ 2859plusmn 12plusmn 24 159plusmn 23plusmn 77 LHCb [88]

Dlowasts3(2860)plusmn 3minusDlowast+K0

S Dlowast0K+ 28671plusmn 43plusmn 19 50plusmn 11plusmn 13 LHCb [89]

D0K+ 28605plusmn 26plusmn 65 53plusmn 7plusmn 7 LHCb [88]

28650plusmn 39 522plusmn 86 Our average

DsJ(3040)plusmn Unnatural DlowastK 3044plusmn 8+30minus5 239plusmn 35+46

minus42 BABAR (m amp Γ) + LHCb(JP ) [86]+ [89]

28

Table 13 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast0(2400)0 0+

D+πminus 2297plusmn 8plusmn 20 273plusmn 12plusmn 48 BABAR [109]D+πminus 2308plusmn 17plusmn 32 276plusmn 21plusmn 63 Belle [74]D+πminus 2407plusmn 21plusmn 35 240plusmn 55plusmn 59 Focus [75]

23182plusmn 169 2674plusmn 356 Our average

Dlowast0(2400)plusmn 0+

D0π+ 2349plusmn 6plusmn 1plusmn 4 217plusmn 13plusmn 5plusmn 12 LHCb [110]D0π+ 2360plusmn 15plusmn 12plusmn 28 255plusmn 26plusmn 20plusmn 47 LHCb [111]D0π+ 2403plusmn 14plusmn 35 283plusmn 24plusmn 34 Focus(m ampΓ) + Belle(JP ) [75] + [112]

23506plusmn 59 2337plusmn 155 Our average

D1(2420)0 1+

Dlowast+πminus 24196plusmn 01plusmn 07 352plusmn 04plusmn 09 LHCb [30]Dlowast+πminus 24231plusmn 15+04

minus10 388plusmn 5+19minus54 Zeus [113]

Dlowast+πminus 24201plusmn 01plusmn 08 314plusmn 05plusmn 13 BABAR [29]Dlowast+πminus 200plusmn 17plusmn 13 CDF [114]D0π+πminus 2426plusmn 3plusmn 1 24plusmn 7plusmn 8 Belle [115]Dlowast+πminus 24214plusmn 15plusmn 09 237plusmn 27plusmn 40 Belle [74]Dlowast+πminus 2421+1

minus2 plusmn 2 20+6minus5

+3minus3 CLEO [116]

Dlowast+πminus 2422plusmn 2plusmn 2 15plusmn 8plusmn 4 E687 [96]Dlowast+πminus 2428plusmn 3plusmn 2 23+8

minus6+10minus4 CLEO [99]

Dlowast+πminus 2414plusmn 2plusmn 5 13plusmn 6+10minus5 ARGUS [117]

Dlowast+πminus 2428plusmn 8plusmn 5 58plusmn 14plusmn 10 TPS [118]

24205plusmn 05 317plusmn 07 Our average

D1(2420)plusmn 1+

Dlowast0π+ 24219plusmn 47+34minus12 Zeus [113]

D+πminusπ+ 2421plusmn 2plusmn 1 21plusmn 5plusmn 8 Belle [115]Dlowast0π+ 2425plusmn 2plusmn 2 26+8

minus7 plusmn 4 CLEO [119]Dlowast0π+ 2443plusmn 7plusmn 5 41plusmn 19plusmn 8 TPS [118]

24232plusmn 16 252plusmn 60 Our average

D1(2430)0 1+ Dlowast+πminus 2427plusmn 26plusmn 25 384+107minus75 plusmn 74 Belle [74]

Dlowast2(2460)0 2+

Dlowast+πminus 24640plusmn 14plusmn 05plusmn 02 438plusmn 29plusmn 17plusmn 06 LHCb [120]Dlowast+πminus 24604plusmn 04plusmn 12 432plusmn 12plusmn 30 LHCb [30]D+πminus 24604plusmn 01plusmn 01 456plusmn 04plusmn 11 LHCb [30]

Dlowast+πminus D+πminus 24625plusmn 24+13minus11 466plusmn 81+59

minus38 Zeus [113]D+πminus 24622plusmn 01plusmn 08 505plusmn 06plusmn 07 BABAR [29]D+πminus 24604plusmn 12plusmn 22 418plusmn 25plusmn 29 BABAR [109]D+πminus 492plusmn 23plusmn 13 CDF [114]D+πminus 24616plusmn 21plusmn 33 456plusmn 44plusmn 67 Belle [74]D+πminus 24645plusmn 11plusmn 19 387plusmn 53plusmn 29 Focus [75]D+πminus 2465plusmn 3plusmn 3 28+8

minus7 plusmn 6 CLEO [116]D+πminus 2453plusmn 3plusmn 2 25plusmn 10plusmn 5 E687 [96]Dlowast+πminus 2461plusmn 3plusmn 1 20+9

minus12+9minus10 CLEO [99]

D+πminus 2455plusmn 3plusmn 5 15+13minus10

+5minus10 ARGUS [121]

D+πminus 2459plusmn 3plusmn 2 20plusmn 10plusmn 5 TPS [118]

246049plusmn 017 4752plusmn 065 Our average

29

Table 14 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast2(2460)plusmn 2+

D0π+ 24686plusmn 06plusmn 00plusmn 03 473plusmn 15plusmn 03plusmn 06 LHCb [110]D0π+ 24656plusmn 18plusmn 05plusmn 12 460plusmn 34plusmn 14plusmn 29 LHCb [111]D0π+ 24631plusmn 02plusmn 06 486plusmn 13plusmn 19 LHCb [30]

Dlowast0π+ D0π+ 24606plusmn 44+36minus08 Zeus [113]

D0π+ 24654plusmn 02plusmn 11 BABAR [29]D0π+ 24657plusmn 18+14

minus48 497plusmn 38plusmn 64 Belle [112]D0π+ 24676plusmn 15plusmn 08 341plusmn 65plusmn 42 Focus [75]D0π+ 2463plusmn 3plusmn 3 27+11

minus8 plusmn 5 CLEO [119]D0π+ 2453plusmn 3plusmn 2 23plusmn 9plusmn 5 E687 [96]D0π+ 2469plusmn 4plusmn 6 ARGUS [122]

246555plusmn 040 467plusmn 12 Our average

D(2550)0 0minus Dlowast+πminus 25394plusmn 45plusmn 68 130plusmn 12plusmn 13 BABAR [29]

D(2580)0 Unnatural Dlowast+πminus 25795plusmn 34plusmn 55 1175plusmn 178plusmn 460 LHCb [30]

D(2600)0 Natural D+πminus 26087plusmn 24plusmn 25 93plusmn 6plusmn 13 BABAR [29]

D(2600)plusmn Natural D0π+ 26213plusmn 37plusmn 42 BABAR [29]

Dlowast(2640)plusmn 1minus Dlowast+π+πminus 2637plusmn 2plusmn 6 Delphi [123]

Dlowast(2650)0 Natural Dlowast+πminus 26492plusmn 35plusmn 35 1402plusmn 171plusmn 186 LHCb [30]

D(2740)0 Unnatural Dlowast+πminus 27370plusmn 35plusmn 112 732plusmn 134plusmn 250 LHCb [30]

D(2750)0 Dlowast+πminus 27524plusmn 17plusmn 27 71plusmn 6plusmn 11 BABAR [29]

Dlowast1(2760)0 1+

D+πminus 2781plusmn 18plusmn 11plusmn 6 177plusmn 32plusmn 20plusmn 7 LHCb [120]Dlowast+πminus 27611plusmn 51plusmn 65 744plusmn 34plusmn 370 LHCb [30]D+πminus 27601plusmn 11plusmn 37 744plusmn 34plusmn 191 LHCb [30]D+πminus 27633plusmn 23plusmn 23 609plusmn 51plusmn 36 BABAR [29]

27621plusmn 24 651plusmn 58 Our average

Dlowast3(2760)plusmn 3minus

D0π+ 2798plusmn 7plusmn 1plusmn 7 105plusmn 18plusmn 6plusmn 23 LHCb [110]D0π+ 27717plusmn 17plusmn 38 667plusmn 66plusmn 105 LHCb [30]D0π+ 27697plusmn 38plusmn 15 BABAR [29]

27739plusmn 33 723plusmn 115 Our average

30

Table 15 Product of B meson branching fraction and (daughter) excited D meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowast0(2400)0

Bminus rarr Dlowast0(2400)0(rarr D+π+)πminus61plusmn 06plusmn 18 Belle [74]68plusmn 03plusmn 20 BABAR [109]

64plusmn 14 Our average

Bminus rarr Dlowast0(2400)0(rarr D+π+)Kminus 0061plusmn 0019plusmn 0005plusmn 0014plusmn 0004 LHCb [120]

Dlowast0(2400)plusmnB0 rarr Dlowast0(2400)+(rarr D0π+)πminus

077plusmn 005plusmn 003plusmn 003plusmn 004 LHCb [110]060plusmn 013plusmn 027 Belle [112]

076plusmn 007 Our average

B0 rarr Dlowast0(2400)+(rarr D0π+)Kminus 0177plusmn 0026plusmn 0019plusmn 0067plusmn 020 LHCb [111]

D1(2420)0

Bminus rarr D1(2420)0(rarr Dlowast+πminus)πminus 68plusmn 07plusmn 13 Belle [74]

Bminus rarr D1(2420)0(rarr D0π+πminus)πminus 185plusmn 029plusmn 027plusmn 041 Belle [115]

B0 rarr D1(2420)0(rarr Dlowast+πminus)ω 07plusmn 02+01minus00 plusmn 01 Belle [124]

D1(2420)plusmn B0 rarr D1(2420)+(rarr D+πminusπ+)πminus 089plusmn 015plusmn 022 Belle [115]

D1(2430)0Bminus rarr D1(2430)0(rarr Dlowast+πminus)πminus 50plusmn 04plusmn 108 Belle [74]

B0 rarr D1(2430)0(rarr Dlowast+πminus)ω 25plusmn 04+07minus02

+04minus01 Belle [124]

Dlowast2(2460)0

Bminus rarr Dlowast2(2460)0(rarr D+πminus)πminus34plusmn 03plusmn 07 Belle [74]35plusmn 02plusmn 05 BABAR [109]

34plusmn 03 Our average

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)πminus 18plusmn 03plusmn 04 Belle [74]

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)ω 04plusmn 01+00minus01 plusmn 01 Belle [124]

Bminus rarr Dlowast2(2460)0(rarr D+π+)Kminus 0232plusmn 0011plusmn 0006plusmn 0010plusmn 0016 LHCb [120]

Dlowast2(2460)plusmnB0 rarr Dlowast2(2460)+(rarr D0π+)πminus

244plusmn 007plusmn 010plusmn 004plusmn 012 LHCb [110]215plusmn 017plusmn 031 Belle [112]

238plusmn 016 Our average

B0 rarr Dlowast2(2460)+(rarr D0π+)Kminus 0212plusmn 0010plusmn 0011plusmn 0011plusmn 025 LHCb [111]

Dlowast1(2760)0 Bminus rarr Dlowast1(2760)0(rarr D+π+)Kminus 0036plusmn 0009plusmn 0003plusmn 0007plusmn 0002 LHCb [120]

Dlowast3(2760)plusmn B0 rarr Dlowast3(2760)0(rarr D0π+)πminus 0103plusmn 0016plusmn 0007plusmn 0008plusmn 0005 LHCb [110]

31

Table 16 Product of B meson branching fraction and (daughter) excited Ds meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowasts0(2317)plusmnB0 rarr Dlowasts0(2317)+(rarr D+

s π0)Dminus

86+33minus26 plusmn 26 Belle [125]

180plusmn 40+67minus50 BABAR [126]

101+13minus12 plusmn 10plusmn 04 Belle [127]

102plusmn 15 Our average

B+ rarr Dlowasts0(2317)+(rarr D+s π

0)D0 80+13minus12 plusmn 10plusmn 04 Belle [127]

B0 rarr Dlowasts0(2317)+(rarr D+s π

0)Kminus 053+015minus013 plusmn 016 Belle [128]

Ds1(2460)plusmn

B0 rarr Ds1(2460)+(rarr Dlowast+s π0)Dminus227+73

minus62 plusmn 68 Belle [125]280plusmn 80+112

minus78 BABAR [126]

247plusmn 76 Our average

B0 rarr Ds1(2460)+(rarr Dlowast+s γ)Dminus82+22minus19 plusmn 25 Belle [125]

80plusmn 20+32minus23 BABAR [126]

81plusmn 23 Our average

Ds1(2460)+ rarr Dlowast+s π0 (56plusmn 13plusmn 9) BABAR [129]

Ds1(2460)+ rarr Dlowast+s γ (16plusmn 4plusmn 3) BABAR [129]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dminus 171plusmn 048plusmn 032 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast+K0)Dminus 261plusmn 103plusmn 031 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dlowastminus 332plusmn 088plusmn 066 BABAR [95]

Ds1(2536)plusmnB0 rarr Ds1(2536)+(rarr Dlowast+K0)Dlowastminus 500plusmn 151plusmn 067 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)D0 216plusmn 052plusmn 045 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)D0 230plusmn 098plusmn 043 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)Dlowast0 546plusmn 117plusmn 104 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)Dlowast0 392plusmn 246plusmn 083 BABAR [95]

Ds2(2573)plusmnB0 rarr Ds2(2573)(rarr D0K+)Dminus 034plusmn 017plusmn 005 BABAR [107]

B+ rarr Ds2(2573)(rarr D0K+)D0 008plusmn 14plusmn 005 BABAR [107]

Ds1(2700)plusmn B+ rarr Ds1(2700)+(rarr D0K+)D0

113plusmn 22+14minus28 Belle [108]

502plusmn 071plusmn 093 BABAR [107]

583plusmn 109 Our average

B0 rarr Ds1(2700)+(rarr D0K+)Dminus 714plusmn 096plusmn 069 BABAR [107]

32

Table 17 Mass dierence measurements for excited D mesons

Resonance Relative to ∆m [MeVc2] Measured by Reference

Dlowast1(2420)0 Dlowast+4102plusmn 21plusmn 09 Zeus [130]4117plusmn 07plusmn 04 CDF [114]

4115plusmn 08 Our average

D1(2420)plusmn Dlowast1(2420)0 4+2minus3 plusmn 3 CLEO [119]

Dlowast2(2460)0 D+ 5939plusmn 06plusmn 05 CDF [114]

Dlowast+ 4588plusmn 37+12minus13 Zeus [130]

Dlowast2(2460)plusmn Dlowast2(2460)0

31plusmn 19plusmn 09 Focus [75]minus2plusmn 4plusmn 4 CLEO [119]14plusmn 5plusmn 8 ARGUS [122]

30plusmn 19 Our average

Dlowasts0(2317)plusmn Dplusmns

3487plusmn 05plusmn 07 Belle [72]3500plusmn 12plusmn 10 CLEO [71]3513plusmn 21plusmn 19 Belle [125]

3492plusmn 07 Our average

Ds1(2460)plusmn

Dlowastplusmns

3441plusmn 13plusmn 11 Belle [72]3512plusmn 17plusmn 10 CLEO [71]3468plusmn 16plusmn 19 Belle [125]

3471plusmn 11 Our average

Dplusmns

4910plusmn 13plusmn 19 Belle [72]4914plusmn 09plusmn 15 Belle [72]

4913plusmn 14 Our average

Ds1(2536)plusmnDlowast(2010)plusmn

52483plusmn 001plusmn 004 BABAR [101]52530+044

minus041 plusmn 010 Zeus [130]5253plusmn 06plusmn 01 ALEPH [131]

52484plusmn 004 Our average

Dlowast(2007)0 5287plusmn 19plusmn 05 ALEPH [131]

Dlowasts2(2573)plusmn D0 704plusmn 3plusmn 1 ALEPH [131]

33

Table 18 Measurements of polarization amplitudes for excited D mesons

Resonance AD Measured by Reference

D1(2420)0

78+67minus27

+46minus18 ZEUS [113]

572plusmn 025 BABAR [29]59+30minus17

+24minus10 ZEUS [130]

38plusmn 06plusmn 08 BABAR [132]

561plusmn 024 Our average

D1(2420)plusmn 38plusmn 06plusmn 08 BABAR [132]

Dlowast2(2460)0 minus116plusmn 035 ZEUS [113]

D(2750)0 minus033plusmn 028 BABAR [29]

34

24 Rare and forbidden decays

This section provides a summary of rare and forbidden charm decays in tabular form The decaymodes can be categorized as avor-changing neutral currents lepton-avor-violating lepton-number-violating and both baryon- and lepton-number-violating decays Figures 9-11 plot theupper limits for D0 D+ D+

s and Λ+c decays Tables 19-22 give the corresponding numerical

results Some theoretical predictions are given in Refs [133134135136137138139140]In several cases the rare-decay nal states have been observed with the di-lepton pair being

the decay product of a hadronic resonance For these measurements the quoted limits are thoseexpected for the non-resonant di-lepton spectrum For the extrapolation to the full spectruma phase-space distribution of the non-resonant component has been assumed This applies tothe CLEO measurement of the decays D+

(s) rarr (K+π+)e+eminus [141] to the D0 measurements

of the decays D+(s) rarr π+micro+microminus [142] and to the BABAR measurements of the decays D+

(s) rarr(K+π+)e+eminus and D+

(s) rarr (K+π+)micro+microminus where the contribution from φ rarr l+lminus (l = e micro) has

been excluded In the case of the LHCb measurements of the decays D0 rarr π+πminusmicro+microminus [143]as well as the decays D+

(s) rarr π+micro+microminus [144] the contributions from φ rarr l+lminus as well as from

ρ ω rarr l+lminus (l = e micro) have been excluded

Table 19 Upper limits at 90 CL for D0 decays

Decay Limit times106 Experiment Referenceγγ 260 CLEO II [145]

38 BESIII [146]22 BaBar [147]085 Belle [148]

e+eminus 2200 CLEO [149]1700 Argus [150]1300 Mark3 [151]130 CLEO II [152]819 E789 [153]62 E791 [154]12 BaBar [155]0079 Belle [156]

micro+microminus 700 Argus [150]440 E653 [157]340 CLEO II [152]156 E789 [153]52 E791 [154]20 HERAb [158]13 BaBar [155]021 CDF [159]014 Belle [156]00062 LHCb [160]

π0e+eminus 450 CLEO II [152]π0micro+microminus 5400 CLEO II [152]

1800 E653 [157]

35

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceη e+eminus 1100 CLEO II [152]η micro+microminus 5300 CLEO II [152]π+πminuse+eminus 3700 E791 [161]ρ0e+eminus 4500 CLEO [149]

1240 E791 [161]1000 CLEO II [152]

π+πminusmicro+microminus 300 E791 [161]055 LHCb [143]

ρ0micro+microminus 8100 CLEO [149]4900 CLEO II [152]2300 E653 [157]220 E791 [161]

ω e+eminus 1800 CLEO II [152]ω micro+microminus 8300 CLEO II [152]K+Kminuse+eminus 3150 E791 [161]φ e+eminus 590 E791 [161]

520 CLEO II [152]K+Kminusmicro+microminus 330 E791 [161]φmicro+microminus 4100 CLEO II [152]

310 E791 [161]

K0e+eminus 17000 Mark3 [162]

1100 CLEO II [152]

K0micro+microminus 6700 CLEO II [152]

2600 E653 [157]Kminusπ+e+eminus 3850 E791 [161]

Klowast0

(892)e+eminus 1400 CLEO II [152]470 E791 [161]

Kminusπ+micro+microminus 3600 E791 [161]

Klowast0

(892)micro+microminus 11800 CLEO II [152]240 E791 [161]

π+πminusπ0micro+microminus 8100 E653 [157]microplusmne∓ 2700 CLEO [149]

1200 Mark3 [163]1000 Argus [150]190 CLEO II [152]172 E789 [153]81 E791 [154]081 BaBar [155]026 Belle [156]0016 LHCb [164]

π0eplusmnmicro∓ 860 CLEO II [152]η eplusmnmicro∓ 1000 CLEO II [152]

36

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceπ+πminuseplusmnmicro∓ 150 E791 [161]ρ0eplusmnmicro∓ 660 E791 [161]

490 CLEO II [152]ω eplusmnmicro∓ 1200 CLEO II [152]K+Kminuseplusmnmicro∓ 1800 E791 [161]φ eplusmnmicro∓ 470 E791 [161]

340 CLEO II [152]

K0eplusmnmicro∓ 1000 CLEO II [152]

Kminusπ+eplusmnmicro∓ 5500 E791 [161]Klowast0(892)eplusmnmicro∓ 1000 CLEO II [152]

830 E791 [161]π∓π∓eplusmneplusmn 1120 E791 [161]π∓π∓microplusmnmicroplusmn 290 E791 [161]K∓π∓eplusmneplusmn 2060 E791 [161]K∓π∓microplusmnmicroplusmn 3900 E791 [161]K∓K∓eplusmneplusmn 1520 E791 [161]K∓K∓microplusmnmicroplusmn 940 E791 [161]π∓π∓eplusmnmicroplusmn 790 E791 [161]K∓π∓eplusmnmicroplusmn 2180 E791 [161]K∓K∓eplusmnmicroplusmn 570 E791 [161]p eminus 100 CLEO [165]p e+ 110 CLEO [165]

37

γγ

ρ0micro

+microminus

π+πminusπ

0micro

+microminus

K+K

minuse

+eminus

ηe

+eminus

φmicro

+microminus

π0e

+eminus

φe

+eminus

ωmicro

+microminus

Kminusπ

+micro

+microminus

ρ0e

+eminus

K0micro

+microminus

Klowast0

(892

)e+eminus

π+πminusmicro

+microminus

micro+microminus

π+πminuse

+eminus

e+eminus

Klowast0

(892

)micro+microminus

K+K

minusmicro

+microminus

Kminusπ

+e

+eminus

π0micro

+microminus

K0e

+eminus

ωe

+eminus

ηmicro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

HFAG-charm

Belle

BESIII

CLEO II

BaBar

E791

CLEO

E653

LHCb

E789

HERAB

CDF

Argus

Mark3

June 16

K∓π∓microplusmnmicroplusmn

ωeplusmnmicro∓

Kminusπ

+eplusmnmicro∓

K∓K∓eplusmnmicroplusmn

π∓π∓eplusmnmicroplusmn

peminus

K∓π∓eplusmnmicroplusmn

π∓π∓eplusmneplusmn

ηeplusmnmicro∓

π∓π∓microplusmnmicroplusmn

K∓K∓eplusmneplusmn

K0eplusmnmicro∓

π+πminuseplusmnmicro∓

K∓K∓microplusmnmicroplusmn

ρ0eplusmnmicro∓

pe

+

φeplusmnmicro∓

microplusmne∓

K+K

minuseplusmnmicro∓

Klowast0

(892

)eplusmnmicro∓

π0eplusmnmicro∓

K∓π∓eplusmneplusmn

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

L BLHFAG-charm

E791

CLEO II

CLEO

Belle

E789

Mark3

Argus

LHCb

BaBar

June 16

Figure 9 Upper limits at 90 CL for D0 decays The top plot shows avor-changing neu-tral current decays and the bottom plot shows lepton-avor-changing (LF) lepton-number-changing (L) and both baryon- and lepton-number-changing (BL) decays38

Kminuse

+micro

+

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminusmicro

+micro

+

K+e

+eminus

π+e

+eminus

πminuse

+micro

+

Kminuse

+e

+

K+micro

+eminus

ρminusmicro

+micro

+

K+e

+microminus

K+eplusmnmicro∓

π+micro

+eminus

π+e

+microminus

πminusmicro

+micro

+

πminuse

+e

+

π+micro

+microminus

ρ+micro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E687

E653

E791

BaBar

Focus

CLEO

BESIII

LHCb

D0

June 16

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminuse

+micro

+

K+e

+eminus

π+e

+eminus

K+eplusmnmicro∓

Kminuse

+e

+

K+micro

+eminus

K+e

+microminus

Klowast+

(892

)micro+microminus

π+micro

+eminus

Kminusmicro

+micro

+

πminusmicro

+micro

+

πminuse

+e

+

πminuse

+micro

+

π+micro

+microminus

K+micro

+microminus

π+e

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E653

E791

CLEO

BaBar

Focus

LHCb

June 16

Figure 10 Upper limits at 90 CL for D+ (top) and D+s (bottom) decays Each plot shows

avor-changing neutral current decays lepton-avor-changing decays (LF) and lepton-number-changing (L) decays 39

pmicro

+microminus

pe

+microminus

σ+micro

+microminus

pe

+e

+

pe

+eminus

pe

+micro

+

pmicro

+micro

+

pmicro

+eminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

LHFAG-charm

BaBar E653

June 16

Figure 11 Upper limits at 90 CL for Λ+c decays Shown are avor-changing neutral current

decays lepton-avor-changing (LF) decays and lepton-number-changing (L) decays

40

Table 20 Upper limits at 90 CL for D+ decays

Decay Limit times106 Experiment Referenceπ+e+eminus 1100 E687 [166]

520 E791 [154]59 CLEO [141]11 BaBar [167]03 BESIII [168]

π+micro+microminus 2200 E653 [157]890 E687 [166]150 E791 [154]88 Focus [169]65 BaBar [167]39 D0 [142]0073 LHCb [144]

ρ+micro+microminus 5600 E653 [157]K+e+eminus 2000 E687 [166]

30 CLEO [141]12 BESIII [168]10 BaBar [167]

π+eplusmnmicro∓ 340 E791 [154]π+e+microminus 1100 E687 [166]

29 BaBar [167]π+micro+eminus 1300 E687 [166]

36 BaBar [167]K+eplusmnmicro∓ 680 E791 [154]K+e+microminus 1300 E687 [166]

12 BaBar [167]K+micro+eminus 1200 E687 [166]

28 BaBar [167]πminuse+e+ 1100 E687 [166]

960 E791 [154]19 BaBar [167]12 BESIII [168]11 CLEO [141]

πminusmicro+micro+ 870 E687 [166]170 E791 [154]48 Focus [169]20 BaBar [167]0022 LHCb [144]

πminuse+micro+ 1100 E687 [166]500 E791 [154]

ρminusmicro+micro+ 5600 E653 [157]Kminuse+e+ 1200 E687 [166]

35 CLEO [141]09 BaBar [167]

41

Table 20 continued from previous pageDecay Limit times106 Experiment Reference

06 BESIII [168]Kminusmicro+micro+ 3200 E653 [157]

1200 E687 [166]130 Focus [169]100 BaBar [167]

Kminuse+micro+ 1300 E687 [166]Klowastminus(892)micro+micro+ 8500 E653 [157]

Table 21 Upper limits at 90 CL for D+s decays

Decay Limit times106 Experiment Referenceπ+e+eminus 2700 E791 [154]

220 CLEO [141]130 BaBar [167]

π+micro+microminus 4300 E653 [157]1400 E791 [154]430 BaBar [167]260 Focus [169]041 LHCb [144]

K+e+eminus 16000 E791 [154]520 CLEO [141]37 BaBar [167]

K+micro+microminus 1400 E791 [154]360 Focus [169]210 BaBar [167]

Klowast+(892)micro+microminus 14000 E653 [157]π+eplusmnmicro∓ 6100 E791 [154]π+e+microminus 120 BaBar [167]π+micro+eminus 200 BaBar [167]K+eplusmnmicro∓ 6300 E791 [154]K+e+microminus 140 BaBar [167]K+micro+eminus 97 BaBar [167]πminuse+e+ 6900 E791 [154]

180 CLEO [141]41 BaBar [167]

πminusmicro+micro+ 4300 E653 [157]820 E791 [154]290 Focus [169]140 BaBar [167]012 LHCb [144]

πminuse+micro+ 7300 E791 [154]Kminuse+e+ 6300 E791 [154]

170 CLEO [141]

42

Table 21 continued from previous pageDecay Limit times106 Experiment Reference

52 BaBar [167]Kminusmicro+micro+ 5900 E653 [157]

1800 E791 [154]130 BaBar [167]

Kminuse+micro+ 6800 E791 [154]Klowastminus(892)micro+micro+ 14000 E653 [157]

Table 22 Upper limits at 90 CL for Λ+c decays

Decay Limit times106 Experiment Referencepe+eminus 55 BaBar [167]pmicro+microminus 3400 E653 [157]

440 BaBar [167]σ+micro+microminus 7000 E653 [157]pe+microminus 99 BaBar [167]pmicro+eminus 190 BaBar [167]p e+e+ 27 BaBar [167]p micro+micro+ 94 BaBar [167]

43

References

[1] N Cabibbo Phys Rev Lett 10 531533 (1963)

[2] M Kobayashi and T Maskawa Prog Theor Phys 49 652657 (1973)

[3] D Abbaneo et al (ALEPH CDF DELPHI L3 OPAL and SLD collaborations)arXivhep-ex0009052 (2000) CERN-EP-2000-096 arXivhep-ex0112028 (2001)CERN-EP-2001-050

[4] Y Amhis et al (Heavy Flavor Averaging Group) (2012) arXiv12071158 [hep-ex]

[5] K Olive et al (Particle Data Group) Chin Phys C38 090001 (2014)

[6] A L Kagan and M D Sokolo Phys Rev D80 076008 (2009) arXiv09073917 [hep-ph]

[7] Y Grossman A L Kagan and Y Nir Phys Rev D75 036008 (2007)arXivhep-ph0609178 [hep-ph]

[8] M Gersabeck M Alexander S Borghi V Gligorov and C Parkes J Phys G39 045005(2012) arXiv11116515 [hep-ex]

[9] J P Lees et al (BABAR collaboration) Phys Rev D87 012004 (2013) arXiv12093896[hep-ex]

[10] R Aaij et al (LHCb collaboration) Phys Rev Lett 112 041801 (2014) arXiv13107201[hep-ex]

[11] T A Aaltonen et al (CDF collaboration) Phys Rev D90 no 11 111103 (2014)arXiv14105435 [hep-ex]

[12] R Aaij et al (LHCb collaboration) JHEP 04 043 (2015) arXiv150106777 [hep-ex]

[13] M Staripound et al (Belle collaboration) Phys Lett B753 412418 (2016) arXiv150908266[hep-ex]

[14] B Aubert et al (BABAR collaboration) Phys Rev Lett 100 061803 (2008)arXiv07092715 [hep-ex]

[15] B Ko (Belle collaboration) PoS ICHEP2012 353 (2013) arXiv12121975

[16] T Aaltonen et al (CDF collaboration) Phys Rev Lett 109 111801 (2012)arXiv12072158 [hep-ex]

[17] R Aaij et al (LHCb collaboration) JHEP 07 041 (2014) arXiv14052797 [hep-ex]

[18] R Aaij et al (LHCb collaboration) Phys Rev Lett 116 no 19 191601 (2016)arXiv160203160 [hep-ex]

[19] T Becher and R J Hill Phys Lett B633 6169 (2006) arXivhep-ph0509090 [hep-ph]

[20] F J Gilman and R L Singleton Phys Rev D41 142 (1990)

[21] R J Hill eConf C060409 027 (2006) arXivhep-ph0606023 [hep-ph]

[22] D Becirevic and A B Kaidalov Phys Lett B478 417423 (2000) arXivhep-ph9904490[hep-ph]

44

[23] C G Boyd B Grinstein and R F Lebed Phys Rev Lett 74 46034606 (1995)arXivhep-ph9412324 [hep-ph]

[24] C G Boyd and M J Savage Phys Rev D56 303311 (1997) arXivhep-ph9702300[hep-ph]

[25] M C Arnesen B Grinstein I Z Rothstein and I W Stewart Phys Rev Lett 95 071802(2005)

[26] C Bourrely B Machet and E de Rafael Nucl Phys B189 157 (1981)

[27] D Becirevic A L Yaouanc A Oyanguren P Roudeau and F Sanlippo (2014)arXiv14071019 [hep-ph]

[28] J P Lees et al (BABAR collaboration) Phys Rev D88 052003 (2013) arXiv13045009[hep-ex]

[29] P del Amo Sanchez et al (BaBar Collaboration collaboration) PhysRev D82 111101(2010) arXiv10092076 [hep-ex]

[30] R Aaij et al (LHCb collaboration) JHEP 1309 145 (2013) arXiv13074556

[31] G Burdman and J Kambor Phys Rev D55 28172826 (1997) arXivhep-ph9602353[hep-ph]

[32] D Becirevic A Le Yaouanc L Oliver J-C Raynal P Roudeau and J Serrano Phys RevD87 no 5 054007 (2013) arXiv12065869 [hep-ph]

[33] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052022 (2015)arXiv14125502 [hep-ex]

[34] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 7 072012 (2015)arXiv150807560 [hep-ex]

[35] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 11 112008 (2015)arXiv151000308 [hep-ex]

[36] L Widhalm et al (Belle collaboration) Phys Rev Lett 97 061804 (2006)arXivhep-ex0604049 [hep-ex]

[37] B Aubert et al (BABAR collaboration) Phys Rev D76 052005 (2007) arXiv07040020[hep-ex]

[38] D Besson et al (CLEO collaboration) Phys Rev D80 032005 (2009) arXiv09062983[hep-ex]

[39] S Dobbs et al (CLEO collaboration) Phys Rev D77 112005 (2008) arXiv07121020[hep-ex]

[40] G Huang et al (CLEO collaboration) Phys Rev Lett 94 011802 (2005)arXivhep-ex0407035 [hep-ex]

[41] J Link et al (FOCUS collaboration) Phys Lett B607 233242 (2005)arXivhep-ex0410037 [hep-ex]

[42] J Adler et al (MARK-III collaboration) Phys Rev Lett 62 1821 (1989)

45

[43] K Kodama et al (Fermilab E653 collaboration) Phys Rev Lett 66 18191822 (1991)

[44] K Kodama et al (E653 collaboration) Phys Lett B336 605613 (1994)

[45] P L Frabetti et al (E687 collaboration) Phys Lett B364 127136 (1995)

[46] P L Frabetti et al (E687 collaboration) Phys Lett B315 203208 (1993)

[47] J C Anjos et al (Tagged Photon Spectrometer collaboration) Phys Rev Lett 6215871590 (1989)

[48] M Ablikim et al (BES collaboration) Phys Lett B597 3946 (2004)arXivhep-ex0406028 [hep-ex]

[49] M Ablikim et al (BES collaboration) (2006) arXivhep-ex0610019 [hep-ex]

[50] A Bean et al (CLEO collaboration) Phys Lett B317 647654 (1993)

[51] BESIII collaboration presented at ICHEP 2014 conference 2014httpindicoificuvesindicogetFilepyaccesscontribId=69ampsessionId=25ampresId=

0ampmaterialId=slidesampconfId=2025

[52] J G Korner and G A Schuler Z Phys C46 93 (1990)

[53] FLAG collaboration httpitpwikiunibechagimages44bFLAGpdf 2014httpitpwikiunibechflagimages44bFLAGpdf

[54] J Anjos et al (Fermilab E691 collaboration) Phys Rev Lett 65 26302633 (1990)

[55] K Kodama et al (Fermilab E653 collaboration) Phys Lett B274 246252 (1992)

[56] P Frabetti et al (Fermilab E687 collaboration) Phys Lett B307 262268 (1993)

[57] E Aitala et al (E791 collaboration) Phys Rev Lett 80 13931397 (1998)arXivhep-ph9710216 [hep-ph]

[58] E Aitala et al (E791 collaboration) Phys Lett B440 435441 (1998)arXivhep-ex9809026 [hep-ex]

[59] M Adamovich et al (BEATRICE collaboration) Eur Phys J C6 3541 (1999)

[60] J Link et al (FOCUS collaboration) Phys Lett B544 8996 (2002)arXivhep-ex0207049 [hep-ex]

[61] J Link et al (FOCUS collaboration) Phys Lett B607 6777 (2005)arXivhep-ex0410067 [hep-ex]

[62] P del Amo Sanchez et al (BABAR collaboration) Phys Rev D83 072001 (2011)arXiv10121810 [hep-ex]

[63] B Aubert et al (BABAR collaboration) Phys Rev D78 051101 (2008) arXiv08071599[hep-ex]

[64] H Mahlke eConf C0610161 014 (2006) arXivhep-ex0702014 [hep-ex]

[65] J Link et al (FOCUS collaboration) Phys Lett B535 4351 (2002)arXivhep-ex0203031 [hep-ex]

46

[66] K M Ecklund et al (CLEO collaboration) Phys Rev D80 052009 (2009)arXiv09073201 [hep-ex]

[67] R A Briere et al (CLEO collaboration) Phys Rev D81 112001 (2010) arXiv10041954[hep-ex]

[68] P Estabrooks R Carnegie A D Martin W Dunwoodie T Lasinski et al Nucl PhysB133 490 (1978)

[69] D Aston et al Nucl Phys B296 493 (1988)

[70] B Aubert et al (BABAR collaboration) Phys Rev Lett 90 242001 (2003)arXivhep-ex0304021 [hep-ex]

[71] D Besson et al (CLEO Collaboration collaboration) PhysRev D68 032002 (2003)arXivhep-ex0305100 [hep-ex]

[72] K Abe et al (Belle Collaboration collaboration) PhysRevLett 92 012002 (2004)arXivhep-ex0307052 [hep-ex]

[73] B Aubert et al (BaBar Collaboration collaboration) PhysRev D69 031101 (2004)arXivhep-ex0310050 [hep-ex]

[74] K Abe et al (Belle collaboration) Phys Rev D69 112002 (2004) arXivhep-ex0307021[hep-ex]

[75] J M Link et al (FOCUS Collaboration collaboration) PhysLett B586 1120 (2004)arXivhep-ex0312060 [hep-ex]

[76] S Godfrey and N Isgur Phys Rev D32 189231 (1985)

[77] S Godfrey and R Kokoski Phys Rev D43 16791687 (1991)

[78] N Isgur and M B Wise Phys Rev Lett 66 11301133 (1991)

[79] P Schweitzer S Bo and M Radici Phys Rev D66 114004 (2002)arXivhep-ph0207230 [hep-ph]

[80] F Jugeau A Le Yaouanc L Oliver and J-C Raynal Phys Rev D72 094010 (2005)arXivhep-ph0504206 [hep-ph]

[81] P Colangelo F De Fazio and R Ferrandes ModPhysLett A19 20832102 (2004)arXivhep-ph0407137 [hep-ph]

[82] R N Cahn and J D Jackson Phys Rev D68 037502 (2003) arXivhep-ph0305012[hep-ph]

[83] T Barnes F E Close and H J Lipkin PhysRev D68 054006 (2003)arXivhep-ph0305025 [hep-ph]

[84] H Lipkin PhysLett B580 5053 (2004) arXivhep-ph0306204 [hep-ph]

[85] W A Bardeen E J Eichten and C T Hill Phys Rev D68 054024 (2003)arXivhep-ph0305049 [hep-ph]

[86] B Aubert et al (BaBar Collaboration collaboration) PhysRev D80 092003 (2009)arXiv09080806 [hep-ex]

47

[87] R Aaij et al (LHCb Collaboration collaboration) JHEP 1210 151 (2012) arXiv12076016[hep-ex]

[88] R Aaij et al (LHCb collaboration) Phys Rev Lett 113 162001 (2014) arXiv14077574[hep-ex]

[89] R Aaij et al (LHCb collaboration) JHEP 02 133 (2016) arXiv160101495 [hep-ex]

[90] T Matsuki T Morii and K Sudoh EurPhysJ A31 701704 (2007)arXivhep-ph0610186 [hep-ph]

[91] N Isgur and M B Wise PhysLett B232 113117 (1989)

[92] M Neubert PhysRept 245 259396 (1994) arXivhep-ph9306320 [hep-ph]

[93] B Aubert et al (BaBar Collaboration collaboration) PhysRev D74 032007 (2006)arXivhep-ex0604030 [hep-ex]

[94] V M Abazov et al (D0 Collaboration collaboration) PhysRevLett 102 051801 (2009)arXiv07123789 [hep-ex]

[95] B Aubert et al (BABAR collaboration) Phys Rev D77 011102 (2008) arXiv07081565[hep-ex]

[96] P L Frabetti et al (E687 Collaboration collaboration) PhysRevLett 72 324327 (1994)

[97] J P Alexander et al (CLEO Collaboration collaboration) PhysLett B303 377384 (1993)

[98] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B297 425431 (1992)

[99] P Avery et al (CLEO Collaboration collaboration) PhysRev D41 774 (1990)

[100] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B230 162 (1989)

[101] J P Lees et al (BaBar Collaboration collaboration) PhysRev D83 072003 (2011)arXiv11032675 [hep-ex]

[102] R Aaij et al (LHCb collaboration) Phys Rev D90 no 7 072003 (2014) arXiv14077712[hep-ex]

[103] R Aaij et al (LHCb collaboration) PhysLett B698 1420 (2011) arXiv11020348[hep-ex]

[104] B Aubert et al (BaBar Collaboration collaboration) PhysRevLett 97 222001 (2006)arXivhep-ex0607082 [hep-ex]

[105] H Albrecht et al (ARGUS Collaboration collaboration) ZPhys C69 405408 (1996)

[106] Y Kubota et al (CLEO Collaboration collaboration) PhysRevLett 72 19721976 (1994)arXivhep-ph9403325 [hep-ph]

[107] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052002 (2015)arXiv14126751 [hep-ex]

[108] J Brodzicka et al (Belle collaboration) Phys Rev Lett 100 092001 (2008)arXiv07073491 [hep-ex]

48

[109] B Aubert et al (BABAR collaboration) Phys Rev D79 112004 (2009) arXiv09011291[hep-ex]

[110] R Aaij et al (LHCb collaboration) Phys Rev D92 no 3 032002 (2015)arXiv150501710 [hep-ex]

[111] R Aaij et al (LHCb collaboration) Phys Rev D92 no 1 012012 (2015)arXiv150501505 [hep-ex]

[112] A Kuzmin et al (Belle Collaboration collaboration) PhysRev D76 012006 (2007)arXivhep-ex0611054 [hep-ex]

[113] H Abramowicz et al (ZEUS Collaboration collaboration) NuclPhys B866 229254 (2013)arXiv12084468 [hep-ex]

[114] A Abulencia et al (CDF Collaboration collaboration) PhysRev D73 051104 (2006)arXivhep-ex0512069 [hep-ex]

[115] K Abe et al (Belle collaboration) Phys Rev Lett 94 221805 (2005)arXivhep-ex0410091 [hep-ex]

[116] P Avery et al (CLEO Collaboration collaboration) PhysLett B331 236244 (1994)arXivhep-ph9403359 [hep-ph]

[117] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B232 398 (1989)

[118] J C Anjos et al (Tagged Photon Spectrometer Collaboration collaboration) PhysRevLett62 1717 (1989)

[119] T Bergfeld et al (CLEO Collaboration collaboration) PhysLett B340 194204 (1994)

[120] R Aaij et al (LHCb collaboration) Phys Rev D91 no 9 092002 (2015)arXiv150302995 [hep-ex] [Erratum Phys RevD93no11119901(2016)]

[121] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B221 422 (1989)

[122] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B231 208 (1989)

[123] P Abreu et al (DELPHI Collaboration collaboration) PhysLett B426 231242 (1998)

[124] D Matvienko et al (Belle collaboration) Phys Rev D92 no 1 012013 (2015)arXiv150503362 [hep-ex]

[125] P Krokovny et al (Belle collaboration) Phys Rev Lett 91 262002 (2003)arXivhep-ex0308019 [hep-ex]

[126] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 181801 (2004)arXivhep-ex0408041 [hep-ex]

[127] S K Choi et al (Belle collaboration) Phys Rev D91 no 9 092011 (2015)arXiv150402637 [hep-ex] [Addendum Phys RevD92no3039905(2015)]

[128] A Drutskoy et al (Belle collaboration) Phys Rev Lett 94 061802 (2005)arXivhep-ex0409026 [hep-ex]

[129] B Aubert et al (BABAR collaboration) Phys Rev D74 031103 (2006)arXivhep-ex0605036 [hep-ex]

49

[130] S Chekanov et al (ZEUS Collaboration collaboration) EurPhysJ C60 2545 (2009)arXiv08071290 [hep-ex]

[131] A Heister et al (ALEPH Collaboration collaboration) PhysLett B526 3449 (2002)arXivhep-ex0112010 [hep-ex]

[132] B Aubert et al (BABAR collaboration) Phys Rev Lett 103 051803 (2009)arXiv08080333 [hep-ex]

[133] G Burdman E Golowich J L Hewett and S Pakvasa Phys Rev D66 014009 (2002)arXivhep-ph0112235 [hep-ph]

[134] S Fajfer A Prapotnik S Prelovsek P Singer and J Zupan Nucl Phys Proc Suppl 1159397 (2003) arXivhep-ph0208201 [hep-ph]

[135] S Fajfer N Kosnik and S Prelovsek Phys Rev D76 074010 (2007) arXiv07061133[hep-ph]

[136] E Golowich J Hewett S Pakvasa and A A Petrov Phys Rev D79 114030 (2009)arXiv09032830 [hep-ph]

[137] A Paul I I Bigi and S Recksiegel Phys Rev D82 094006 (2010) arXiv10083141[hep-ph]

[138] A Borisov (2011) arXiv11123269 [hep-ph]

[139] R-M Wang J-H Sheng J Zhu Y-Y Fan and Y Gao Int J Mod Phys A29 no 291450169 (2014)

[140] S de Boer and G Hiller Phys Rev D93 no 7 074001 (2016) arXiv151000311 [hep-ph]

[141] P Rubin et al (CLEO collaboration) Phys Rev D82 092007 (2010) arXiv10091606[hep-ex]

[142] V Abazov et al (D0 collaboration) Phys Rev Lett 100 101801 (2008) arXiv07082094[hep-ex]

[143] R Aaij et al (LHCb collaboration) Phys Lett B728 234243 (2014) arXiv13102535[hep-ex]

[144] R Aaij et al (LHCb collaboration) Phys Lett B724 203212 (2013) arXiv13046365[hep-ex]

[145] T Coan et al (CLEO collaboration) Phys Rev Lett 90 101801 (2003)arXivhep-ex0212045 [hep-ex]

[146] M Ablikim et al (BESIII collaboration) Phys Rev D91 no 11 112015 (2015)arXiv150503087 [hep-ex]

[147] J P Lees et al (BABAR collaboration) Phys Rev D85 091107 (2012) arXiv11106480[hep-ex]

[148] N K Nisar et al (Belle collaboration) Phys Rev D93 no 5 051102 (2016)arXiv151202992 [hep-ex]

[149] P Haas et al (CLEO collaboration) Phys Rev Lett 60 1614 (1988)

50

[150] H Albrecht et al (ARGUS collaboration) Phys Lett B209 380 (1988)

[151] J Adler et al (MARK-III collaboration) Phys Rev D37 2023 (1988) Erratum ibid D40(1989) 3788

[152] A Freyberger et al (CLEO collaboration) Phys Rev Lett 76 30653069 (1996)

[153] D Pripstein et al (E789 collaboration) Phys Rev D61 032005 (2000)arXivhep-ex9906022 [hep-ex]

[154] E Aitala et al (E791 collaboration) Phys Lett B462 401409 (1999)arXivhep-ex9906045 [hep-ex]

[155] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 191801 (2004)arXivhep-ex0408023 [hep-ex]

[156] M Petric et al (Belle collaboration) Phys Rev D81 091102 (2010) arXiv10032345[hep-ex]

[157] K Kodama et al (E653 collaboration) Phys Lett B345 8592 (1995)

[158] I Abt et al (HERA-B collaboration) Phys Lett B596 173183 (2004)arXivhep-ex0405059 [hep-ex]

[159] T Aaltonen et al (CDF collaboration) Phys Rev D82 091105 (2010) arXiv10085077[hep-ex]

[160] R Aaij et al (LHCb collaboration) Phys Lett B725 1524 (2013) arXiv13055059[hep-ex]

[161] E Aitala et al (E791 collaboration) Phys Rev Lett 86 39693972 (2001)arXivhep-ex0011077 [hep-ex]

[162] J Adler et al (MARK-III collaboration) Phys Rev D40 906 (1989)

[163] J Becker et al (MARK-III collaboration) Phys Lett B193 147 (1987)

[164] R Aaij et al (LHCb collaboration) Phys Lett B754 167175 (2016) arXiv151200322[hep-ex]

[165] P Rubin et al (CLEO collaboration) Phys Rev D79 097101 (2009) arXiv09041619[hep-ex]

[166] P Frabetti et al (E687 collaboration) Phys Lett B398 239244 (1997)

[167] J P Lees et al (BABAR collaboration) Phys Rev D84 072006 (2011) arXiv11074465[hep-ex]

[168] (BESIII collaboration) M-G Zhao D rareforbidden decays at BESIII in 7th International

Workshop on Charm Physics (Charm 2015) Detroit MI USA May 18-22 2015 2016arXiv160508952 [hep-ex]httpinspirehepnetrecord1466292filesarXiv160508952pdf

[169] J Link et al (FOCUS collaboration) Phys Lett B572 2131 (2003)arXivhep-ex0306049 [hep-ex]

51

  • Introduction
  • D decays
    • Interplay of direct and indirect CP violation
    • Semileptonic decays
      • Introduction
      • DP decays
      • Form factor parameterizations
      • Simple pole
      • z expansion
      • Three-pole formalism
      • Experimental techniques and results
      • Combined results for the DK channel
      • Combined results for the D channel
      • Vcs and Vcd determination
      • DV decays
      • Form factor measurements
        • Excited D(s) mesons
        • Rare and forbidden decays
          • References
Page 6: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

21 Interplay of direct and indirect CP violation

In decays of D0 mesons CP asymmetry measurements have contributions from both directand indirect CP violation as discussed in Sec The contribution from indirect CP viola-tion depends on the decay-time distribution of the data sample [6] This section describes acombination of measurements that allows the extraction of the individual contributions of thetwo types of CP violation At the same time the level of agreement for a no-CP -violationhypothesis is tested The observables are

AΓ equivτ(D 0rarrh+hminus)minus τ(D0rarrh+hminus)

τ(D 0rarrh+hminus) + τ(D0rarrh+hminus) (1)

where h+hminus can be K+Kminus or π+πminus and

∆ACP equiv ACP(K+Kminus)minus ACP(π+πminus) (2)

where ACP are time-integrated CP asymmetries The underlying theoretical parameters are

adirCP equiv

|AD0rarrf |2 minus |AD 0rarrf |2

|AD0rarrf |2 + |AD 0rarrf |2

aindCP equiv 1

2

[(∣∣∣∣qp∣∣∣∣+

∣∣∣∣pq∣∣∣∣)x sinφminus

(∣∣∣∣qp∣∣∣∣minus ∣∣∣∣pq

∣∣∣∣) y cosφ

] (3)

where ADrarrf is the amplitude for D rarr f [7] We use the following relations between theobservables and the underlying parameters [8]

AΓ = minusaindCP minus adir

CPyCP

∆ACP = ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

+ adirCPyCP

∆〈t〉τ

(4)

asymp ∆adirCP

(1 + yCP

〈t〉τ

)+ aind

CP

∆〈t〉τ

(5)

The rst relation constrains mostly indirect CP violation and the direct CP violation contri-bution can dier for dierent nal states In the second relation 〈t〉τ denotes the mean decaytime in units of the D0 lifetime ∆X denotes the dierence in quantity X between K+Kminus andπ+πminus nal states and X denotes the average for quantity X We neglect the last term in thisrelation as all three factors are O(10minus2) or smaller and thus this term is negligible with respectto the other two terms Note that ∆〈t〉τ 〈t〉τ and it is expected that |adir

CP| lt |∆adirCP|

because adirCP(K+Kminus) and adir

CP(π+πminus) are expected to have opposite signs [7]A χ2 t is performed in the plane ∆adir

CP vs aindCP For the BABAR result the dierence of

the quoted values for ACP(K+Kminus) and ACP(π+πminus) is calculated adding all uncertainties inquadrature This may overestimate the systematic uncertainty for the dierence as it neglectscorrelated errors however the result is conservative and the eect is small as all measurementsare statistically limited For all measurements statistical and systematic uncertainties areadded in quadrature when calculating the χ2 We use the current world average value yCP =(0866plusmn 0155) (see Sec ) and the measurements listed in Table 1

6

Table 1 Inputs to the t for direct and indirect CP violation The rst uncertainty listed isstatistical and the second is systematic

Year Experiment Results ∆〈t〉τ 〈t〉τ Reference2012 BABAR AΓ = (009plusmn 026plusmn 006) - - [9]2013 LHCb prompt AΓ(KK) = (minus0035plusmn 0062plusmn 0012) - - [10]

AΓ(ππ) = (0033plusmn 0106plusmn 0014) - -2014 CDF AΓ = (minus012plusmn 012) - - [11]2015 LHCb SL AΓ = (minus0125plusmn 0073) - - [12]2015 Belle AΓ = (minus003plusmn 020plusmn 007) - - [13]2008 BABAR ACP(KK) = (000plusmn 034plusmn 013)

ACP(ππ) = (minus024plusmn 052plusmn 022) 000 100 [14]2012 Belle prel ∆ACP = (minus087plusmn 041plusmn 006) 000 100 [15]2012 CDF ∆ACP = (minus062plusmn 021plusmn 010) 025 258 [16]2014 LHCb SL ∆ACP = (014plusmn 016plusmn 008) 001 107 [17]2016 LHCb prompt ∆ACP = (minus010plusmn 008plusmn 003) 012 210 [18]

In this t AΓ(KK) and AΓ(ππ) are assumed to be identical This assumption is sup-ported by all measurements to date A signicant relative shift due to nal-state dependentAΓ values between ∆ACP measurements with dierent mean decay times is excluded by thesemeasurements

The combination plot (see Fig 1) shows the measurements listed in Table 1 for ∆ACP andAΓ where the bands represent plusmn1σ intervals The point of no CP violation (00) is shownas a lled circle and two-dimensional 68 CL 95 CL and 997 CL regions are plotted asellipses The best t value is indicated by a cross showing the one-dimensional errors

From the t the change in χ2 from the minimum value for the no-CPV point (00) is55 which corresponds to a CL of 65 times 10minus2 for two degrees of freedom Thus the data areconsistent with the no-CP -violation hypothesis at 65 CL This p-value corresponds to 18σThe central values and plusmn1σ uncertainties for the individual parameters are

aindCP = (0056plusmn 0040)

∆adirCP = (minus0137plusmn 0070) (6)

Compared to the previous average the tension in the dierence between direct CP violationin the two nal states reduced while the common indirect CP violation moved away from theno CP violation point by about one standard deviation

7

0015 0010 0005 0000 0005 0010

aindCP

0015

0010

0005

0000

0005

0010

0015

∆adirCP

Contours contain 68 95 99 CL

CD

F

LHC

b S

L

LHC

b p

rom

pt

BaBarBelleCDF KK+ππLHCb SL KK+ππ

LHCb prompt KKLHCb prompt ππ

HFAG-charmWinter 16

no CPV

BaBar

Belle

CDF

LHCb

Figure 1 Plot of all data and the t result Individual measurements are plotted as bandsshowing their plusmn1σ range The no-CPV point (00) is shown as a lled circle and the best tvalue is indicated by a cross showing the one-dimensional uncertainties Two-dimensional 68CL 95 CL and 997 CL regions are plotted as ellipses

8

22 Semileptonic decays

221 Introduction

Semileptonic decays of D mesons involve the interaction of a leptonic current with a hadroniccurrent The latter is nonperturbative and cannot be calculated from rst principles thus it isusually parameterized in terms of form factors The transition matrix element is written

M = minusi GFradic2Vcq L

microHmicro (7)

where GF is the Fermi constant and Vcq is a CKM matrix element The leptonic current Lmicro isevaluated directly from the lepton spinors and has a simple structure this allows one to extractinformation about the form factors (in Hmicro) from data on semileptonic decays [19] Converselybecause there are no strong nal-state interactions between the leptonic and hadronic systemssemileptonic decays for which the form factors can be calculated allow one to determine Vcq [2]

222 DrarrP`ν` decays

When the nal state hadron is a pseudoscalar the hadronic current is given by

Hmicro = 〈P (p)|qγmicroc|D(pprime)〉 = f+(q2)

[(pprime + p)micro minus

m2D minusm2

P

q2qmicro

]+ f0(q2)

m2D minusm2

P

q2qmicro (8)

where mD and pprime are the mass and four momentum of the parent D meson mP and p are thoseof the daughter meson f+(q2) and f0(q2) are form factors and q = pprime minus p Kinematics requirethat f+(0) = f0(0) The contraction qmicroL

micro results in terms proportional to m` [20] and thus for` = e the terms proportionals to qmicro in Eq (8) are negligible For light leptons only the f+(q2)vector form factor is relevant and the dierential partial width is

dΓ(D rarr P`ν`)

dq2 d cos θ`=

G2F |Vcq|2

32π3plowast 3|f+(q2)|2 sin θ2

` (9)

where plowast is the magnitude of the momentum of the nal state hadron in the D rest frame andθ` is the angle of the lepton in the `ν rest frame with respect to the direction of the pseudoscalarmeson in the D rest frame

223 Form factor parameterizations

The form factor is traditionally parameterized with an explicit pole and a sum of eective poles

f+(q2) =f+(0)

(1minus α)

[(1

1minus q2m2pole

)+

Nsumk=1

ρk1minus q2(γkm2

pole)

] (10)

where ρk and γk are expansion parameters and α is a parameter that normalizes the formfactor at q2 = 0 f+(0) The parameter mpole is the mass of the lowest-lying cq resonance withthe vector quantum numbers this is expected to provide the largest contribution to the formfactor for the crarr q transition The sum over N gives the contribution of higher mass statesFor example for D rarr π transitions the dominant resonance is expected to be Dlowast(2010) andthus mpole = mDlowast(2010) For D rarr K transitions the dominant contribution is expected from

Dlowasts(2112) with mpole = mDlowasts (2112)

9

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Comparison between CLEO-c and BABAR results for the quantities q2H20 (q2) and

q2h0(q2)H0(q2)

Table 11 Results for rV and r2 from various experiments

Experiment Ref rV r2

D+ rarr Klowast0l+ν

E691 [54] 20plusmn 06plusmn 03 00plusmn 05plusmn 02E653 [55] 200plusmn 033plusmn 016 082plusmn 022plusmn 011E687 [56] 174plusmn 027plusmn 028 078plusmn 018plusmn 011

E791 (e) [57] 190plusmn 011plusmn 009 071plusmn 008plusmn 009E791 (micro) [58] 184plusmn011plusmn009 075plusmn008plusmn009Beatrice [59] 145plusmn 023plusmn 007 100plusmn 015plusmn 003FOCUS [60] 1504plusmn0057plusmn0039 0875plusmn0049plusmn0064

D0 rarr K0πminusmicro+ν

FOCUS [61] 1706plusmn0677plusmn0342 0912plusmn0370plusmn0104BABAR [62] 1493plusmn 0014plusmn 0021 0775plusmn 0011plusmn 0011

D+s rarr φ e+νBABAR [63] 1849plusmn0060plusmn0095 0763plusmn0071plusmn0065

D0 D+ rarr ρ eνCLEO [64] 140plusmn025plusmn003 057plusmn018plusmn006

23

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

HFLAV())+-amp

Figure 7 A comparison of r2 (lled inverted triangles) and rV (open triangles) values fromvarious experiments The rst seven measurements are for D+ rarr Kminusπ+l+νl decays Alsoshown as a line with 1-σ limits is the average of these The last two points are D+

s and D0

decays

24

23 Excited D(s) mesons

Excited charm meson states have received increased attention since the rst observation ofstates that could not be accommodated by QCD predictions [70 71 72 73] Tables 12 13and 14 summarize recent measurements of the masses and widths of excited D and Ds mesonsrespectively If a preferred assignment of spin and parity was measured it is listed in the columnJP where the label natural denotes JP = 0minus 1+ 2minus and unnatural JP = 0+ 1minus 2+ Ifpossible an average mass and width was calculated which is listed in the gray shaded rowThe calculation of the averages assumes no correlation between individual measurements Asummary of the averaged masses and widths is shown in Figure 8

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

0+ 1+ 2+ 1minus 1 3minus

unnatu

ral

Dlowast s0

(2317)plusmn

Ds1

(2460)plusmn

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn D

sJ(3

040)plusmn

HFAG-charmAugust 2016

(a)

Mas

s[M

eVc

2]

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

0+ 1+ 2+ 0minus 1minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ralDlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn

D(2

550)0

D(2

580)0

D(2

600)0

D(2

600)plusmn

Dlowast (

2640)plusmn

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(b)

Mas

s[M

eVc

2]

0

50

100

150

200

250

300

350

400

450

500

550

1+ 2+ 1minus 1 3minus

unnatu

ral

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn

DsJ

(3040)plusmn

HFAG-charmAugust 2016

(c)

Wid

th[M

eV]

50100150200250300350400450500550600650700

0+ 1+ 2+ 0minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ral

Dlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn D(2

550)0

D(2

580)0

D(2

600)0

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(d)

Wid

th[M

eV]

Figure 8 Averaged masses for Ds mesons are shown in subgure (a) and for D mesons insubgure (b) The average widths for Ds mesons are shown in subgure (c) and for D mesonsin subgure (d) The vertical shaded regions distinguish between dierent spin parity states

The masses and widths of narrow (Γ lt 50 MeV) orbitally excited D mesons (denotedDlowastlowast) both neutral and charged are well established Measurements of broad states (Γ sim200400 MeV) are less abundant as identifying the signal is more challenging There is aslight discrepancy between the Dlowast0(2400)0 masses measured by the Belle [74] and FOCUS [75]experiments No data exist yet for the D1(2430)plusmn state Dalitz plot analyses of B rarr D(lowast)ππ

25

decays strongly favor the assignments 0+ and 1+ for the spin-parity quantum numbers of theDlowast0(2400)0Dlowast0(2400)plusmn and D1(2430)0 states respectively The measured masses and widthsas well as the JP values are in agreement with theoretical predictions based on potentialmodels [76777879]

Tables 15 and 16 summarizes the branching fractions of B mesons decays to excited D andDs states respectively It can be noted that the branching fractions for B mesons decaying to anarrow Dlowastlowast state and a pion are similar for charged and neutral B initial states the branchingfractions to a broad Dlowastlowast state and π+ are much larger for B+ than for B0 This may be dueto the fact that color-suppressed amplitudes contribute only to the B+ decay and not to theB0 decay (for a theoretical discussion see Ref [8081]) Measurements of individual branchingfractions of D mesons are dicult due to the unknown fragmentation of cc rarr Dlowastlowast or due tothe unknown B rarr DlowastlowastX branching fractions

The discoveries of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn have triggered increased interest in prop-erties of and searches for excited Ds mesons (here generically denoted D

lowastlowasts ) While the masses

and widths of Ds1(2536)plusmn and Ds2(2573)plusmn states are in relatively good agreement with po-tential model predictions the masses of Dlowasts0(2317)plusmn and Ds1(2460)plusmn states are signicantlylower than expected (see Ref [82] for a discussion of cs models) Moreover the mass splittingbetween these two states greatly exceeds that between the Ds1(2536)plusmn and Ds2(2573)plusmn Theseunexpected properties have led to interpretations of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn as exoticfour-quark states [8384]

While there are few measurements of the JP values of Dlowasts0(2317)plusmn andDs1(2460)plusmn the avail-able data favor 0+ and 1+ respectively A molecule-like (DK) interpretation of the Dlowasts0(2317)plusmn

and Ds1(2460)plusmn [8384] that can account for their low masses and isospin-breaking decay modesis tested by searching for charged and neutral isospin partners of these states thus far suchsearches have yielded negative results Therefore the subset of models that predict equal pro-duction rates for dierent charged states is excluded The molecular picture can also be testedby measuring the rates for the radiative processes Dlowasts0(2317)plusmnDs1(2460)plusmn rarr D

(lowast)s γ and com-

paring to theoretical predictions The predicted rates however are below the sensitivity ofcurrent experiments

Another model successful in explaining the total widths and the Dlowasts0(2317)plusmn Ds1(2460)plusmn

mass splitting is based on the assumption that these states are chiral partners of the groundstates D+

s and Dlowasts [85] While some measured branching fraction ratios agree with predictedvalues further experimental tests with better sensitivity are needed to conrm or refute thisscenario A summary of the mass dierence measurements is given in Table 17

Measurements by BABAR [86] and LHCb [87] rst indicated the existence of a strange-charm DlowastsJ(2860)plusmn meson An LHCb study of B0

s rarr D0Kminusπ+ decays in which they searchedfor excited Ds mesons [88] showed with 10σ signicance that this state is comprised of twodierent particles one of spin 1 and one of spin 3 This represents the rst measurement of aheavy avored spin-3 particle and the rst observation B mesons decays to spin 3 particlesA subsequent study of DsJ mesons by the LHCb collaboration [89] supports the natural parityassignment for this state (JP = 3minus) This study also shows weak evidence for a further structureat a mass around 3040 MeVc2 with unnatural parity which was rst hinted at by a Babaranalysis [86]

Recent evidence shows that the 1D family of charm resonances can be explored in the Dalitzplot analyses of B-meson decays in the same way as seen for the charm-strange resonances TheLHCb collaboration performed an analysis of B0 rarr D0π+πminus decays in which they measured

26

the spin-parity assignment of the stateDlowast3(2760)plusmn which was observed previously by BABAR [29]and LHCb [30] to be JP = 3minus The measurement suggests a spectroscopic assignment of 3D3This is the second observation of a spin-3 charm meson

Other observed excited Ds states include Ds1(2700)plusmn and Ds2(2573)plusmn The properties ofboth (mass width JP ) have been measured and determined in several analyses A theoreticaldiscussion [90] investigates the possibility that theDs1(2700)plusmn could represent radial excitationsof the Dlowastplusmns Similarly the Ds1(2860)plusmn and DsJ(3040)plusmn could be excitations of Dlowasts0(2317)plusmn andDs1(2460)plusmn or Ds1(2536)plusmn respectively

Table 18 summarizes measurements of the polarization amplitude AD (sometimes also re-ferred as helicity parameter) which describes the initial polarization of the D meson In Dlowastlowast

meson decay the helicity distribution varies like 1 + AD cos2 θH where θH is the angle in theDlowast rest frame between the two pions emitted by decay Dlowastlowast rarr Dlowastπ and the Dlowast rarr Dπ Theparameter is sensitive to possible S-wave contributions in the decay In the case of an unpolar-ized D meson decay decaying purely via D-wave the polarization amplitude is predicted to giveAD = 3 Studies of the D1(2420)0 meson by the ZEUS and BABAR collaborations suggest thatthere is an S-wave admixture in the decay which is contrary to Heavy Quark Eective Theorycalculations [9192]

27

Table 12 Recent measurements of mass and width for dierent excited Ds mesons Thecolumn JP list the most signicant assignment of spin and parity If possible an average massor width is calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowasts0(2317)plusmn 0+

D+s π

0 23196plusmn 02plusmn 14 BABAR [93]D+s π

0 23173plusmn 04plusmn 08 BABAR [73]

23180plusmn 08 Our average

Ds1(2460)plusmn 1+

D+s π

0γD+s γD

+s π

+πminus 24601plusmn 02plusmn 08 BABAR [93]D+s π

0γ 2458plusmn 10plusmn 10 BABAR [73]

24596plusmn 07 Our average

Ds1(2536)plusmn 1+

Dlowast+K0S 25357plusmn 06plusmn 05 DOslash [94]

Dlowast+K0S D

lowast0K+ 253478plusmn 031plusmn 040 BABAR [95]D+s π

+πminus 25346plusmn 03plusmn 07 BABAR [93]Dlowast+K0

S Dlowast0K+ 25350plusmn 06plusmn 10 E687 [96]

Dlowast0K+ 25353plusmn 02plusmn 05 CLEO [97]Dlowast+K0

S 25348plusmn 06plusmn 06 CLEO [97]Dlowast0K+ 25352plusmn 05plusmn 15 ARGUS [98]Dlowast+K0

S 25356plusmn 07plusmn 04 CLEO [99]Dlowast+K0

S 25359plusmn 06plusmn 20 ARGUS [100]Dlowast+K0

S 092plusmn 003plusmn 004 BABAR [101]

253510plusmn 026 092plusmn 005 Our average

Dlowasts2(2573)plusmn 2+

D0K+ Dlowast+K0S 256839plusmn 029plusmn 026 169plusmn 05plusmn 06 LHCb [102]

D+K0S D

0K+ 25694plusmn 16plusmn 05 121plusmn 45plusmn 16 LHCb [103]D+K0

S D0K+ 25722plusmn 03plusmn 10 271plusmn 06plusmn 56 BABAR [104]

D0K+ 257425plusmn 33plusmn 16 104plusmn 83plusmn 30 ARGUS [105]D0K+ 25732+17

minus16 plusmn 09 16+5minus4 plusmn 3 CLEO [106]

256908plusmn 035 169plusmn 08 Our average

Dlowasts1(2700)plusmn 1minus

Dlowast+K0S D

lowast0K+ 27323plusmn 43plusmn 58 136plusmn 19plusmn 24 LHCb [89]D0K+ 2699+14

minus7 127+24minus19 BABAR [107]

Dlowast+K0S D

lowast0K+ 27092plusmn 19plusmn 45 1158plusmn 73plusmn 121 LHCb [87]DKDlowastK 2710plusmn 2+12

minus7 149plusmn 7+39minus52 BABAR [86]

D0K+ 2708plusmn 9+11minus10 108plusmn 2+36

minus31 Belle [108]

27120plusmn 15 1215plusmn 102 Our average

Dlowasts1(2860)plusmn 1 D0K+ 2859plusmn 12plusmn 24 159plusmn 23plusmn 77 LHCb [88]

Dlowasts3(2860)plusmn 3minusDlowast+K0

S Dlowast0K+ 28671plusmn 43plusmn 19 50plusmn 11plusmn 13 LHCb [89]

D0K+ 28605plusmn 26plusmn 65 53plusmn 7plusmn 7 LHCb [88]

28650plusmn 39 522plusmn 86 Our average

DsJ(3040)plusmn Unnatural DlowastK 3044plusmn 8+30minus5 239plusmn 35+46

minus42 BABAR (m amp Γ) + LHCb(JP ) [86]+ [89]

28

Table 13 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast0(2400)0 0+

D+πminus 2297plusmn 8plusmn 20 273plusmn 12plusmn 48 BABAR [109]D+πminus 2308plusmn 17plusmn 32 276plusmn 21plusmn 63 Belle [74]D+πminus 2407plusmn 21plusmn 35 240plusmn 55plusmn 59 Focus [75]

23182plusmn 169 2674plusmn 356 Our average

Dlowast0(2400)plusmn 0+

D0π+ 2349plusmn 6plusmn 1plusmn 4 217plusmn 13plusmn 5plusmn 12 LHCb [110]D0π+ 2360plusmn 15plusmn 12plusmn 28 255plusmn 26plusmn 20plusmn 47 LHCb [111]D0π+ 2403plusmn 14plusmn 35 283plusmn 24plusmn 34 Focus(m ampΓ) + Belle(JP ) [75] + [112]

23506plusmn 59 2337plusmn 155 Our average

D1(2420)0 1+

Dlowast+πminus 24196plusmn 01plusmn 07 352plusmn 04plusmn 09 LHCb [30]Dlowast+πminus 24231plusmn 15+04

minus10 388plusmn 5+19minus54 Zeus [113]

Dlowast+πminus 24201plusmn 01plusmn 08 314plusmn 05plusmn 13 BABAR [29]Dlowast+πminus 200plusmn 17plusmn 13 CDF [114]D0π+πminus 2426plusmn 3plusmn 1 24plusmn 7plusmn 8 Belle [115]Dlowast+πminus 24214plusmn 15plusmn 09 237plusmn 27plusmn 40 Belle [74]Dlowast+πminus 2421+1

minus2 plusmn 2 20+6minus5

+3minus3 CLEO [116]

Dlowast+πminus 2422plusmn 2plusmn 2 15plusmn 8plusmn 4 E687 [96]Dlowast+πminus 2428plusmn 3plusmn 2 23+8

minus6+10minus4 CLEO [99]

Dlowast+πminus 2414plusmn 2plusmn 5 13plusmn 6+10minus5 ARGUS [117]

Dlowast+πminus 2428plusmn 8plusmn 5 58plusmn 14plusmn 10 TPS [118]

24205plusmn 05 317plusmn 07 Our average

D1(2420)plusmn 1+

Dlowast0π+ 24219plusmn 47+34minus12 Zeus [113]

D+πminusπ+ 2421plusmn 2plusmn 1 21plusmn 5plusmn 8 Belle [115]Dlowast0π+ 2425plusmn 2plusmn 2 26+8

minus7 plusmn 4 CLEO [119]Dlowast0π+ 2443plusmn 7plusmn 5 41plusmn 19plusmn 8 TPS [118]

24232plusmn 16 252plusmn 60 Our average

D1(2430)0 1+ Dlowast+πminus 2427plusmn 26plusmn 25 384+107minus75 plusmn 74 Belle [74]

Dlowast2(2460)0 2+

Dlowast+πminus 24640plusmn 14plusmn 05plusmn 02 438plusmn 29plusmn 17plusmn 06 LHCb [120]Dlowast+πminus 24604plusmn 04plusmn 12 432plusmn 12plusmn 30 LHCb [30]D+πminus 24604plusmn 01plusmn 01 456plusmn 04plusmn 11 LHCb [30]

Dlowast+πminus D+πminus 24625plusmn 24+13minus11 466plusmn 81+59

minus38 Zeus [113]D+πminus 24622plusmn 01plusmn 08 505plusmn 06plusmn 07 BABAR [29]D+πminus 24604plusmn 12plusmn 22 418plusmn 25plusmn 29 BABAR [109]D+πminus 492plusmn 23plusmn 13 CDF [114]D+πminus 24616plusmn 21plusmn 33 456plusmn 44plusmn 67 Belle [74]D+πminus 24645plusmn 11plusmn 19 387plusmn 53plusmn 29 Focus [75]D+πminus 2465plusmn 3plusmn 3 28+8

minus7 plusmn 6 CLEO [116]D+πminus 2453plusmn 3plusmn 2 25plusmn 10plusmn 5 E687 [96]Dlowast+πminus 2461plusmn 3plusmn 1 20+9

minus12+9minus10 CLEO [99]

D+πminus 2455plusmn 3plusmn 5 15+13minus10

+5minus10 ARGUS [121]

D+πminus 2459plusmn 3plusmn 2 20plusmn 10plusmn 5 TPS [118]

246049plusmn 017 4752plusmn 065 Our average

29

Table 14 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast2(2460)plusmn 2+

D0π+ 24686plusmn 06plusmn 00plusmn 03 473plusmn 15plusmn 03plusmn 06 LHCb [110]D0π+ 24656plusmn 18plusmn 05plusmn 12 460plusmn 34plusmn 14plusmn 29 LHCb [111]D0π+ 24631plusmn 02plusmn 06 486plusmn 13plusmn 19 LHCb [30]

Dlowast0π+ D0π+ 24606plusmn 44+36minus08 Zeus [113]

D0π+ 24654plusmn 02plusmn 11 BABAR [29]D0π+ 24657plusmn 18+14

minus48 497plusmn 38plusmn 64 Belle [112]D0π+ 24676plusmn 15plusmn 08 341plusmn 65plusmn 42 Focus [75]D0π+ 2463plusmn 3plusmn 3 27+11

minus8 plusmn 5 CLEO [119]D0π+ 2453plusmn 3plusmn 2 23plusmn 9plusmn 5 E687 [96]D0π+ 2469plusmn 4plusmn 6 ARGUS [122]

246555plusmn 040 467plusmn 12 Our average

D(2550)0 0minus Dlowast+πminus 25394plusmn 45plusmn 68 130plusmn 12plusmn 13 BABAR [29]

D(2580)0 Unnatural Dlowast+πminus 25795plusmn 34plusmn 55 1175plusmn 178plusmn 460 LHCb [30]

D(2600)0 Natural D+πminus 26087plusmn 24plusmn 25 93plusmn 6plusmn 13 BABAR [29]

D(2600)plusmn Natural D0π+ 26213plusmn 37plusmn 42 BABAR [29]

Dlowast(2640)plusmn 1minus Dlowast+π+πminus 2637plusmn 2plusmn 6 Delphi [123]

Dlowast(2650)0 Natural Dlowast+πminus 26492plusmn 35plusmn 35 1402plusmn 171plusmn 186 LHCb [30]

D(2740)0 Unnatural Dlowast+πminus 27370plusmn 35plusmn 112 732plusmn 134plusmn 250 LHCb [30]

D(2750)0 Dlowast+πminus 27524plusmn 17plusmn 27 71plusmn 6plusmn 11 BABAR [29]

Dlowast1(2760)0 1+

D+πminus 2781plusmn 18plusmn 11plusmn 6 177plusmn 32plusmn 20plusmn 7 LHCb [120]Dlowast+πminus 27611plusmn 51plusmn 65 744plusmn 34plusmn 370 LHCb [30]D+πminus 27601plusmn 11plusmn 37 744plusmn 34plusmn 191 LHCb [30]D+πminus 27633plusmn 23plusmn 23 609plusmn 51plusmn 36 BABAR [29]

27621plusmn 24 651plusmn 58 Our average

Dlowast3(2760)plusmn 3minus

D0π+ 2798plusmn 7plusmn 1plusmn 7 105plusmn 18plusmn 6plusmn 23 LHCb [110]D0π+ 27717plusmn 17plusmn 38 667plusmn 66plusmn 105 LHCb [30]D0π+ 27697plusmn 38plusmn 15 BABAR [29]

27739plusmn 33 723plusmn 115 Our average

30

Table 15 Product of B meson branching fraction and (daughter) excited D meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowast0(2400)0

Bminus rarr Dlowast0(2400)0(rarr D+π+)πminus61plusmn 06plusmn 18 Belle [74]68plusmn 03plusmn 20 BABAR [109]

64plusmn 14 Our average

Bminus rarr Dlowast0(2400)0(rarr D+π+)Kminus 0061plusmn 0019plusmn 0005plusmn 0014plusmn 0004 LHCb [120]

Dlowast0(2400)plusmnB0 rarr Dlowast0(2400)+(rarr D0π+)πminus

077plusmn 005plusmn 003plusmn 003plusmn 004 LHCb [110]060plusmn 013plusmn 027 Belle [112]

076plusmn 007 Our average

B0 rarr Dlowast0(2400)+(rarr D0π+)Kminus 0177plusmn 0026plusmn 0019plusmn 0067plusmn 020 LHCb [111]

D1(2420)0

Bminus rarr D1(2420)0(rarr Dlowast+πminus)πminus 68plusmn 07plusmn 13 Belle [74]

Bminus rarr D1(2420)0(rarr D0π+πminus)πminus 185plusmn 029plusmn 027plusmn 041 Belle [115]

B0 rarr D1(2420)0(rarr Dlowast+πminus)ω 07plusmn 02+01minus00 plusmn 01 Belle [124]

D1(2420)plusmn B0 rarr D1(2420)+(rarr D+πminusπ+)πminus 089plusmn 015plusmn 022 Belle [115]

D1(2430)0Bminus rarr D1(2430)0(rarr Dlowast+πminus)πminus 50plusmn 04plusmn 108 Belle [74]

B0 rarr D1(2430)0(rarr Dlowast+πminus)ω 25plusmn 04+07minus02

+04minus01 Belle [124]

Dlowast2(2460)0

Bminus rarr Dlowast2(2460)0(rarr D+πminus)πminus34plusmn 03plusmn 07 Belle [74]35plusmn 02plusmn 05 BABAR [109]

34plusmn 03 Our average

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)πminus 18plusmn 03plusmn 04 Belle [74]

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)ω 04plusmn 01+00minus01 plusmn 01 Belle [124]

Bminus rarr Dlowast2(2460)0(rarr D+π+)Kminus 0232plusmn 0011plusmn 0006plusmn 0010plusmn 0016 LHCb [120]

Dlowast2(2460)plusmnB0 rarr Dlowast2(2460)+(rarr D0π+)πminus

244plusmn 007plusmn 010plusmn 004plusmn 012 LHCb [110]215plusmn 017plusmn 031 Belle [112]

238plusmn 016 Our average

B0 rarr Dlowast2(2460)+(rarr D0π+)Kminus 0212plusmn 0010plusmn 0011plusmn 0011plusmn 025 LHCb [111]

Dlowast1(2760)0 Bminus rarr Dlowast1(2760)0(rarr D+π+)Kminus 0036plusmn 0009plusmn 0003plusmn 0007plusmn 0002 LHCb [120]

Dlowast3(2760)plusmn B0 rarr Dlowast3(2760)0(rarr D0π+)πminus 0103plusmn 0016plusmn 0007plusmn 0008plusmn 0005 LHCb [110]

31

Table 16 Product of B meson branching fraction and (daughter) excited Ds meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowasts0(2317)plusmnB0 rarr Dlowasts0(2317)+(rarr D+

s π0)Dminus

86+33minus26 plusmn 26 Belle [125]

180plusmn 40+67minus50 BABAR [126]

101+13minus12 plusmn 10plusmn 04 Belle [127]

102plusmn 15 Our average

B+ rarr Dlowasts0(2317)+(rarr D+s π

0)D0 80+13minus12 plusmn 10plusmn 04 Belle [127]

B0 rarr Dlowasts0(2317)+(rarr D+s π

0)Kminus 053+015minus013 plusmn 016 Belle [128]

Ds1(2460)plusmn

B0 rarr Ds1(2460)+(rarr Dlowast+s π0)Dminus227+73

minus62 plusmn 68 Belle [125]280plusmn 80+112

minus78 BABAR [126]

247plusmn 76 Our average

B0 rarr Ds1(2460)+(rarr Dlowast+s γ)Dminus82+22minus19 plusmn 25 Belle [125]

80plusmn 20+32minus23 BABAR [126]

81plusmn 23 Our average

Ds1(2460)+ rarr Dlowast+s π0 (56plusmn 13plusmn 9) BABAR [129]

Ds1(2460)+ rarr Dlowast+s γ (16plusmn 4plusmn 3) BABAR [129]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dminus 171plusmn 048plusmn 032 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast+K0)Dminus 261plusmn 103plusmn 031 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dlowastminus 332plusmn 088plusmn 066 BABAR [95]

Ds1(2536)plusmnB0 rarr Ds1(2536)+(rarr Dlowast+K0)Dlowastminus 500plusmn 151plusmn 067 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)D0 216plusmn 052plusmn 045 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)D0 230plusmn 098plusmn 043 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)Dlowast0 546plusmn 117plusmn 104 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)Dlowast0 392plusmn 246plusmn 083 BABAR [95]

Ds2(2573)plusmnB0 rarr Ds2(2573)(rarr D0K+)Dminus 034plusmn 017plusmn 005 BABAR [107]

B+ rarr Ds2(2573)(rarr D0K+)D0 008plusmn 14plusmn 005 BABAR [107]

Ds1(2700)plusmn B+ rarr Ds1(2700)+(rarr D0K+)D0

113plusmn 22+14minus28 Belle [108]

502plusmn 071plusmn 093 BABAR [107]

583plusmn 109 Our average

B0 rarr Ds1(2700)+(rarr D0K+)Dminus 714plusmn 096plusmn 069 BABAR [107]

32

Table 17 Mass dierence measurements for excited D mesons

Resonance Relative to ∆m [MeVc2] Measured by Reference

Dlowast1(2420)0 Dlowast+4102plusmn 21plusmn 09 Zeus [130]4117plusmn 07plusmn 04 CDF [114]

4115plusmn 08 Our average

D1(2420)plusmn Dlowast1(2420)0 4+2minus3 plusmn 3 CLEO [119]

Dlowast2(2460)0 D+ 5939plusmn 06plusmn 05 CDF [114]

Dlowast+ 4588plusmn 37+12minus13 Zeus [130]

Dlowast2(2460)plusmn Dlowast2(2460)0

31plusmn 19plusmn 09 Focus [75]minus2plusmn 4plusmn 4 CLEO [119]14plusmn 5plusmn 8 ARGUS [122]

30plusmn 19 Our average

Dlowasts0(2317)plusmn Dplusmns

3487plusmn 05plusmn 07 Belle [72]3500plusmn 12plusmn 10 CLEO [71]3513plusmn 21plusmn 19 Belle [125]

3492plusmn 07 Our average

Ds1(2460)plusmn

Dlowastplusmns

3441plusmn 13plusmn 11 Belle [72]3512plusmn 17plusmn 10 CLEO [71]3468plusmn 16plusmn 19 Belle [125]

3471plusmn 11 Our average

Dplusmns

4910plusmn 13plusmn 19 Belle [72]4914plusmn 09plusmn 15 Belle [72]

4913plusmn 14 Our average

Ds1(2536)plusmnDlowast(2010)plusmn

52483plusmn 001plusmn 004 BABAR [101]52530+044

minus041 plusmn 010 Zeus [130]5253plusmn 06plusmn 01 ALEPH [131]

52484plusmn 004 Our average

Dlowast(2007)0 5287plusmn 19plusmn 05 ALEPH [131]

Dlowasts2(2573)plusmn D0 704plusmn 3plusmn 1 ALEPH [131]

33

Table 18 Measurements of polarization amplitudes for excited D mesons

Resonance AD Measured by Reference

D1(2420)0

78+67minus27

+46minus18 ZEUS [113]

572plusmn 025 BABAR [29]59+30minus17

+24minus10 ZEUS [130]

38plusmn 06plusmn 08 BABAR [132]

561plusmn 024 Our average

D1(2420)plusmn 38plusmn 06plusmn 08 BABAR [132]

Dlowast2(2460)0 minus116plusmn 035 ZEUS [113]

D(2750)0 minus033plusmn 028 BABAR [29]

34

24 Rare and forbidden decays

This section provides a summary of rare and forbidden charm decays in tabular form The decaymodes can be categorized as avor-changing neutral currents lepton-avor-violating lepton-number-violating and both baryon- and lepton-number-violating decays Figures 9-11 plot theupper limits for D0 D+ D+

s and Λ+c decays Tables 19-22 give the corresponding numerical

results Some theoretical predictions are given in Refs [133134135136137138139140]In several cases the rare-decay nal states have been observed with the di-lepton pair being

the decay product of a hadronic resonance For these measurements the quoted limits are thoseexpected for the non-resonant di-lepton spectrum For the extrapolation to the full spectruma phase-space distribution of the non-resonant component has been assumed This applies tothe CLEO measurement of the decays D+

(s) rarr (K+π+)e+eminus [141] to the D0 measurements

of the decays D+(s) rarr π+micro+microminus [142] and to the BABAR measurements of the decays D+

(s) rarr(K+π+)e+eminus and D+

(s) rarr (K+π+)micro+microminus where the contribution from φ rarr l+lminus (l = e micro) has

been excluded In the case of the LHCb measurements of the decays D0 rarr π+πminusmicro+microminus [143]as well as the decays D+

(s) rarr π+micro+microminus [144] the contributions from φ rarr l+lminus as well as from

ρ ω rarr l+lminus (l = e micro) have been excluded

Table 19 Upper limits at 90 CL for D0 decays

Decay Limit times106 Experiment Referenceγγ 260 CLEO II [145]

38 BESIII [146]22 BaBar [147]085 Belle [148]

e+eminus 2200 CLEO [149]1700 Argus [150]1300 Mark3 [151]130 CLEO II [152]819 E789 [153]62 E791 [154]12 BaBar [155]0079 Belle [156]

micro+microminus 700 Argus [150]440 E653 [157]340 CLEO II [152]156 E789 [153]52 E791 [154]20 HERAb [158]13 BaBar [155]021 CDF [159]014 Belle [156]00062 LHCb [160]

π0e+eminus 450 CLEO II [152]π0micro+microminus 5400 CLEO II [152]

1800 E653 [157]

35

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceη e+eminus 1100 CLEO II [152]η micro+microminus 5300 CLEO II [152]π+πminuse+eminus 3700 E791 [161]ρ0e+eminus 4500 CLEO [149]

1240 E791 [161]1000 CLEO II [152]

π+πminusmicro+microminus 300 E791 [161]055 LHCb [143]

ρ0micro+microminus 8100 CLEO [149]4900 CLEO II [152]2300 E653 [157]220 E791 [161]

ω e+eminus 1800 CLEO II [152]ω micro+microminus 8300 CLEO II [152]K+Kminuse+eminus 3150 E791 [161]φ e+eminus 590 E791 [161]

520 CLEO II [152]K+Kminusmicro+microminus 330 E791 [161]φmicro+microminus 4100 CLEO II [152]

310 E791 [161]

K0e+eminus 17000 Mark3 [162]

1100 CLEO II [152]

K0micro+microminus 6700 CLEO II [152]

2600 E653 [157]Kminusπ+e+eminus 3850 E791 [161]

Klowast0

(892)e+eminus 1400 CLEO II [152]470 E791 [161]

Kminusπ+micro+microminus 3600 E791 [161]

Klowast0

(892)micro+microminus 11800 CLEO II [152]240 E791 [161]

π+πminusπ0micro+microminus 8100 E653 [157]microplusmne∓ 2700 CLEO [149]

1200 Mark3 [163]1000 Argus [150]190 CLEO II [152]172 E789 [153]81 E791 [154]081 BaBar [155]026 Belle [156]0016 LHCb [164]

π0eplusmnmicro∓ 860 CLEO II [152]η eplusmnmicro∓ 1000 CLEO II [152]

36

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceπ+πminuseplusmnmicro∓ 150 E791 [161]ρ0eplusmnmicro∓ 660 E791 [161]

490 CLEO II [152]ω eplusmnmicro∓ 1200 CLEO II [152]K+Kminuseplusmnmicro∓ 1800 E791 [161]φ eplusmnmicro∓ 470 E791 [161]

340 CLEO II [152]

K0eplusmnmicro∓ 1000 CLEO II [152]

Kminusπ+eplusmnmicro∓ 5500 E791 [161]Klowast0(892)eplusmnmicro∓ 1000 CLEO II [152]

830 E791 [161]π∓π∓eplusmneplusmn 1120 E791 [161]π∓π∓microplusmnmicroplusmn 290 E791 [161]K∓π∓eplusmneplusmn 2060 E791 [161]K∓π∓microplusmnmicroplusmn 3900 E791 [161]K∓K∓eplusmneplusmn 1520 E791 [161]K∓K∓microplusmnmicroplusmn 940 E791 [161]π∓π∓eplusmnmicroplusmn 790 E791 [161]K∓π∓eplusmnmicroplusmn 2180 E791 [161]K∓K∓eplusmnmicroplusmn 570 E791 [161]p eminus 100 CLEO [165]p e+ 110 CLEO [165]

37

γγ

ρ0micro

+microminus

π+πminusπ

0micro

+microminus

K+K

minuse

+eminus

ηe

+eminus

φmicro

+microminus

π0e

+eminus

φe

+eminus

ωmicro

+microminus

Kminusπ

+micro

+microminus

ρ0e

+eminus

K0micro

+microminus

Klowast0

(892

)e+eminus

π+πminusmicro

+microminus

micro+microminus

π+πminuse

+eminus

e+eminus

Klowast0

(892

)micro+microminus

K+K

minusmicro

+microminus

Kminusπ

+e

+eminus

π0micro

+microminus

K0e

+eminus

ωe

+eminus

ηmicro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

HFAG-charm

Belle

BESIII

CLEO II

BaBar

E791

CLEO

E653

LHCb

E789

HERAB

CDF

Argus

Mark3

June 16

K∓π∓microplusmnmicroplusmn

ωeplusmnmicro∓

Kminusπ

+eplusmnmicro∓

K∓K∓eplusmnmicroplusmn

π∓π∓eplusmnmicroplusmn

peminus

K∓π∓eplusmnmicroplusmn

π∓π∓eplusmneplusmn

ηeplusmnmicro∓

π∓π∓microplusmnmicroplusmn

K∓K∓eplusmneplusmn

K0eplusmnmicro∓

π+πminuseplusmnmicro∓

K∓K∓microplusmnmicroplusmn

ρ0eplusmnmicro∓

pe

+

φeplusmnmicro∓

microplusmne∓

K+K

minuseplusmnmicro∓

Klowast0

(892

)eplusmnmicro∓

π0eplusmnmicro∓

K∓π∓eplusmneplusmn

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

L BLHFAG-charm

E791

CLEO II

CLEO

Belle

E789

Mark3

Argus

LHCb

BaBar

June 16

Figure 9 Upper limits at 90 CL for D0 decays The top plot shows avor-changing neu-tral current decays and the bottom plot shows lepton-avor-changing (LF) lepton-number-changing (L) and both baryon- and lepton-number-changing (BL) decays38

Kminuse

+micro

+

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminusmicro

+micro

+

K+e

+eminus

π+e

+eminus

πminuse

+micro

+

Kminuse

+e

+

K+micro

+eminus

ρminusmicro

+micro

+

K+e

+microminus

K+eplusmnmicro∓

π+micro

+eminus

π+e

+microminus

πminusmicro

+micro

+

πminuse

+e

+

π+micro

+microminus

ρ+micro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E687

E653

E791

BaBar

Focus

CLEO

BESIII

LHCb

D0

June 16

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminuse

+micro

+

K+e

+eminus

π+e

+eminus

K+eplusmnmicro∓

Kminuse

+e

+

K+micro

+eminus

K+e

+microminus

Klowast+

(892

)micro+microminus

π+micro

+eminus

Kminusmicro

+micro

+

πminusmicro

+micro

+

πminuse

+e

+

πminuse

+micro

+

π+micro

+microminus

K+micro

+microminus

π+e

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E653

E791

CLEO

BaBar

Focus

LHCb

June 16

Figure 10 Upper limits at 90 CL for D+ (top) and D+s (bottom) decays Each plot shows

avor-changing neutral current decays lepton-avor-changing decays (LF) and lepton-number-changing (L) decays 39

pmicro

+microminus

pe

+microminus

σ+micro

+microminus

pe

+e

+

pe

+eminus

pe

+micro

+

pmicro

+micro

+

pmicro

+eminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

LHFAG-charm

BaBar E653

June 16

Figure 11 Upper limits at 90 CL for Λ+c decays Shown are avor-changing neutral current

decays lepton-avor-changing (LF) decays and lepton-number-changing (L) decays

40

Table 20 Upper limits at 90 CL for D+ decays

Decay Limit times106 Experiment Referenceπ+e+eminus 1100 E687 [166]

520 E791 [154]59 CLEO [141]11 BaBar [167]03 BESIII [168]

π+micro+microminus 2200 E653 [157]890 E687 [166]150 E791 [154]88 Focus [169]65 BaBar [167]39 D0 [142]0073 LHCb [144]

ρ+micro+microminus 5600 E653 [157]K+e+eminus 2000 E687 [166]

30 CLEO [141]12 BESIII [168]10 BaBar [167]

π+eplusmnmicro∓ 340 E791 [154]π+e+microminus 1100 E687 [166]

29 BaBar [167]π+micro+eminus 1300 E687 [166]

36 BaBar [167]K+eplusmnmicro∓ 680 E791 [154]K+e+microminus 1300 E687 [166]

12 BaBar [167]K+micro+eminus 1200 E687 [166]

28 BaBar [167]πminuse+e+ 1100 E687 [166]

960 E791 [154]19 BaBar [167]12 BESIII [168]11 CLEO [141]

πminusmicro+micro+ 870 E687 [166]170 E791 [154]48 Focus [169]20 BaBar [167]0022 LHCb [144]

πminuse+micro+ 1100 E687 [166]500 E791 [154]

ρminusmicro+micro+ 5600 E653 [157]Kminuse+e+ 1200 E687 [166]

35 CLEO [141]09 BaBar [167]

41

Table 20 continued from previous pageDecay Limit times106 Experiment Reference

06 BESIII [168]Kminusmicro+micro+ 3200 E653 [157]

1200 E687 [166]130 Focus [169]100 BaBar [167]

Kminuse+micro+ 1300 E687 [166]Klowastminus(892)micro+micro+ 8500 E653 [157]

Table 21 Upper limits at 90 CL for D+s decays

Decay Limit times106 Experiment Referenceπ+e+eminus 2700 E791 [154]

220 CLEO [141]130 BaBar [167]

π+micro+microminus 4300 E653 [157]1400 E791 [154]430 BaBar [167]260 Focus [169]041 LHCb [144]

K+e+eminus 16000 E791 [154]520 CLEO [141]37 BaBar [167]

K+micro+microminus 1400 E791 [154]360 Focus [169]210 BaBar [167]

Klowast+(892)micro+microminus 14000 E653 [157]π+eplusmnmicro∓ 6100 E791 [154]π+e+microminus 120 BaBar [167]π+micro+eminus 200 BaBar [167]K+eplusmnmicro∓ 6300 E791 [154]K+e+microminus 140 BaBar [167]K+micro+eminus 97 BaBar [167]πminuse+e+ 6900 E791 [154]

180 CLEO [141]41 BaBar [167]

πminusmicro+micro+ 4300 E653 [157]820 E791 [154]290 Focus [169]140 BaBar [167]012 LHCb [144]

πminuse+micro+ 7300 E791 [154]Kminuse+e+ 6300 E791 [154]

170 CLEO [141]

42

Table 21 continued from previous pageDecay Limit times106 Experiment Reference

52 BaBar [167]Kminusmicro+micro+ 5900 E653 [157]

1800 E791 [154]130 BaBar [167]

Kminuse+micro+ 6800 E791 [154]Klowastminus(892)micro+micro+ 14000 E653 [157]

Table 22 Upper limits at 90 CL for Λ+c decays

Decay Limit times106 Experiment Referencepe+eminus 55 BaBar [167]pmicro+microminus 3400 E653 [157]

440 BaBar [167]σ+micro+microminus 7000 E653 [157]pe+microminus 99 BaBar [167]pmicro+eminus 190 BaBar [167]p e+e+ 27 BaBar [167]p micro+micro+ 94 BaBar [167]

43

References

[1] N Cabibbo Phys Rev Lett 10 531533 (1963)

[2] M Kobayashi and T Maskawa Prog Theor Phys 49 652657 (1973)

[3] D Abbaneo et al (ALEPH CDF DELPHI L3 OPAL and SLD collaborations)arXivhep-ex0009052 (2000) CERN-EP-2000-096 arXivhep-ex0112028 (2001)CERN-EP-2001-050

[4] Y Amhis et al (Heavy Flavor Averaging Group) (2012) arXiv12071158 [hep-ex]

[5] K Olive et al (Particle Data Group) Chin Phys C38 090001 (2014)

[6] A L Kagan and M D Sokolo Phys Rev D80 076008 (2009) arXiv09073917 [hep-ph]

[7] Y Grossman A L Kagan and Y Nir Phys Rev D75 036008 (2007)arXivhep-ph0609178 [hep-ph]

[8] M Gersabeck M Alexander S Borghi V Gligorov and C Parkes J Phys G39 045005(2012) arXiv11116515 [hep-ex]

[9] J P Lees et al (BABAR collaboration) Phys Rev D87 012004 (2013) arXiv12093896[hep-ex]

[10] R Aaij et al (LHCb collaboration) Phys Rev Lett 112 041801 (2014) arXiv13107201[hep-ex]

[11] T A Aaltonen et al (CDF collaboration) Phys Rev D90 no 11 111103 (2014)arXiv14105435 [hep-ex]

[12] R Aaij et al (LHCb collaboration) JHEP 04 043 (2015) arXiv150106777 [hep-ex]

[13] M Staripound et al (Belle collaboration) Phys Lett B753 412418 (2016) arXiv150908266[hep-ex]

[14] B Aubert et al (BABAR collaboration) Phys Rev Lett 100 061803 (2008)arXiv07092715 [hep-ex]

[15] B Ko (Belle collaboration) PoS ICHEP2012 353 (2013) arXiv12121975

[16] T Aaltonen et al (CDF collaboration) Phys Rev Lett 109 111801 (2012)arXiv12072158 [hep-ex]

[17] R Aaij et al (LHCb collaboration) JHEP 07 041 (2014) arXiv14052797 [hep-ex]

[18] R Aaij et al (LHCb collaboration) Phys Rev Lett 116 no 19 191601 (2016)arXiv160203160 [hep-ex]

[19] T Becher and R J Hill Phys Lett B633 6169 (2006) arXivhep-ph0509090 [hep-ph]

[20] F J Gilman and R L Singleton Phys Rev D41 142 (1990)

[21] R J Hill eConf C060409 027 (2006) arXivhep-ph0606023 [hep-ph]

[22] D Becirevic and A B Kaidalov Phys Lett B478 417423 (2000) arXivhep-ph9904490[hep-ph]

44

[23] C G Boyd B Grinstein and R F Lebed Phys Rev Lett 74 46034606 (1995)arXivhep-ph9412324 [hep-ph]

[24] C G Boyd and M J Savage Phys Rev D56 303311 (1997) arXivhep-ph9702300[hep-ph]

[25] M C Arnesen B Grinstein I Z Rothstein and I W Stewart Phys Rev Lett 95 071802(2005)

[26] C Bourrely B Machet and E de Rafael Nucl Phys B189 157 (1981)

[27] D Becirevic A L Yaouanc A Oyanguren P Roudeau and F Sanlippo (2014)arXiv14071019 [hep-ph]

[28] J P Lees et al (BABAR collaboration) Phys Rev D88 052003 (2013) arXiv13045009[hep-ex]

[29] P del Amo Sanchez et al (BaBar Collaboration collaboration) PhysRev D82 111101(2010) arXiv10092076 [hep-ex]

[30] R Aaij et al (LHCb collaboration) JHEP 1309 145 (2013) arXiv13074556

[31] G Burdman and J Kambor Phys Rev D55 28172826 (1997) arXivhep-ph9602353[hep-ph]

[32] D Becirevic A Le Yaouanc L Oliver J-C Raynal P Roudeau and J Serrano Phys RevD87 no 5 054007 (2013) arXiv12065869 [hep-ph]

[33] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052022 (2015)arXiv14125502 [hep-ex]

[34] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 7 072012 (2015)arXiv150807560 [hep-ex]

[35] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 11 112008 (2015)arXiv151000308 [hep-ex]

[36] L Widhalm et al (Belle collaboration) Phys Rev Lett 97 061804 (2006)arXivhep-ex0604049 [hep-ex]

[37] B Aubert et al (BABAR collaboration) Phys Rev D76 052005 (2007) arXiv07040020[hep-ex]

[38] D Besson et al (CLEO collaboration) Phys Rev D80 032005 (2009) arXiv09062983[hep-ex]

[39] S Dobbs et al (CLEO collaboration) Phys Rev D77 112005 (2008) arXiv07121020[hep-ex]

[40] G Huang et al (CLEO collaboration) Phys Rev Lett 94 011802 (2005)arXivhep-ex0407035 [hep-ex]

[41] J Link et al (FOCUS collaboration) Phys Lett B607 233242 (2005)arXivhep-ex0410037 [hep-ex]

[42] J Adler et al (MARK-III collaboration) Phys Rev Lett 62 1821 (1989)

45

[43] K Kodama et al (Fermilab E653 collaboration) Phys Rev Lett 66 18191822 (1991)

[44] K Kodama et al (E653 collaboration) Phys Lett B336 605613 (1994)

[45] P L Frabetti et al (E687 collaboration) Phys Lett B364 127136 (1995)

[46] P L Frabetti et al (E687 collaboration) Phys Lett B315 203208 (1993)

[47] J C Anjos et al (Tagged Photon Spectrometer collaboration) Phys Rev Lett 6215871590 (1989)

[48] M Ablikim et al (BES collaboration) Phys Lett B597 3946 (2004)arXivhep-ex0406028 [hep-ex]

[49] M Ablikim et al (BES collaboration) (2006) arXivhep-ex0610019 [hep-ex]

[50] A Bean et al (CLEO collaboration) Phys Lett B317 647654 (1993)

[51] BESIII collaboration presented at ICHEP 2014 conference 2014httpindicoificuvesindicogetFilepyaccesscontribId=69ampsessionId=25ampresId=

0ampmaterialId=slidesampconfId=2025

[52] J G Korner and G A Schuler Z Phys C46 93 (1990)

[53] FLAG collaboration httpitpwikiunibechagimages44bFLAGpdf 2014httpitpwikiunibechflagimages44bFLAGpdf

[54] J Anjos et al (Fermilab E691 collaboration) Phys Rev Lett 65 26302633 (1990)

[55] K Kodama et al (Fermilab E653 collaboration) Phys Lett B274 246252 (1992)

[56] P Frabetti et al (Fermilab E687 collaboration) Phys Lett B307 262268 (1993)

[57] E Aitala et al (E791 collaboration) Phys Rev Lett 80 13931397 (1998)arXivhep-ph9710216 [hep-ph]

[58] E Aitala et al (E791 collaboration) Phys Lett B440 435441 (1998)arXivhep-ex9809026 [hep-ex]

[59] M Adamovich et al (BEATRICE collaboration) Eur Phys J C6 3541 (1999)

[60] J Link et al (FOCUS collaboration) Phys Lett B544 8996 (2002)arXivhep-ex0207049 [hep-ex]

[61] J Link et al (FOCUS collaboration) Phys Lett B607 6777 (2005)arXivhep-ex0410067 [hep-ex]

[62] P del Amo Sanchez et al (BABAR collaboration) Phys Rev D83 072001 (2011)arXiv10121810 [hep-ex]

[63] B Aubert et al (BABAR collaboration) Phys Rev D78 051101 (2008) arXiv08071599[hep-ex]

[64] H Mahlke eConf C0610161 014 (2006) arXivhep-ex0702014 [hep-ex]

[65] J Link et al (FOCUS collaboration) Phys Lett B535 4351 (2002)arXivhep-ex0203031 [hep-ex]

46

[66] K M Ecklund et al (CLEO collaboration) Phys Rev D80 052009 (2009)arXiv09073201 [hep-ex]

[67] R A Briere et al (CLEO collaboration) Phys Rev D81 112001 (2010) arXiv10041954[hep-ex]

[68] P Estabrooks R Carnegie A D Martin W Dunwoodie T Lasinski et al Nucl PhysB133 490 (1978)

[69] D Aston et al Nucl Phys B296 493 (1988)

[70] B Aubert et al (BABAR collaboration) Phys Rev Lett 90 242001 (2003)arXivhep-ex0304021 [hep-ex]

[71] D Besson et al (CLEO Collaboration collaboration) PhysRev D68 032002 (2003)arXivhep-ex0305100 [hep-ex]

[72] K Abe et al (Belle Collaboration collaboration) PhysRevLett 92 012002 (2004)arXivhep-ex0307052 [hep-ex]

[73] B Aubert et al (BaBar Collaboration collaboration) PhysRev D69 031101 (2004)arXivhep-ex0310050 [hep-ex]

[74] K Abe et al (Belle collaboration) Phys Rev D69 112002 (2004) arXivhep-ex0307021[hep-ex]

[75] J M Link et al (FOCUS Collaboration collaboration) PhysLett B586 1120 (2004)arXivhep-ex0312060 [hep-ex]

[76] S Godfrey and N Isgur Phys Rev D32 189231 (1985)

[77] S Godfrey and R Kokoski Phys Rev D43 16791687 (1991)

[78] N Isgur and M B Wise Phys Rev Lett 66 11301133 (1991)

[79] P Schweitzer S Bo and M Radici Phys Rev D66 114004 (2002)arXivhep-ph0207230 [hep-ph]

[80] F Jugeau A Le Yaouanc L Oliver and J-C Raynal Phys Rev D72 094010 (2005)arXivhep-ph0504206 [hep-ph]

[81] P Colangelo F De Fazio and R Ferrandes ModPhysLett A19 20832102 (2004)arXivhep-ph0407137 [hep-ph]

[82] R N Cahn and J D Jackson Phys Rev D68 037502 (2003) arXivhep-ph0305012[hep-ph]

[83] T Barnes F E Close and H J Lipkin PhysRev D68 054006 (2003)arXivhep-ph0305025 [hep-ph]

[84] H Lipkin PhysLett B580 5053 (2004) arXivhep-ph0306204 [hep-ph]

[85] W A Bardeen E J Eichten and C T Hill Phys Rev D68 054024 (2003)arXivhep-ph0305049 [hep-ph]

[86] B Aubert et al (BaBar Collaboration collaboration) PhysRev D80 092003 (2009)arXiv09080806 [hep-ex]

47

[87] R Aaij et al (LHCb Collaboration collaboration) JHEP 1210 151 (2012) arXiv12076016[hep-ex]

[88] R Aaij et al (LHCb collaboration) Phys Rev Lett 113 162001 (2014) arXiv14077574[hep-ex]

[89] R Aaij et al (LHCb collaboration) JHEP 02 133 (2016) arXiv160101495 [hep-ex]

[90] T Matsuki T Morii and K Sudoh EurPhysJ A31 701704 (2007)arXivhep-ph0610186 [hep-ph]

[91] N Isgur and M B Wise PhysLett B232 113117 (1989)

[92] M Neubert PhysRept 245 259396 (1994) arXivhep-ph9306320 [hep-ph]

[93] B Aubert et al (BaBar Collaboration collaboration) PhysRev D74 032007 (2006)arXivhep-ex0604030 [hep-ex]

[94] V M Abazov et al (D0 Collaboration collaboration) PhysRevLett 102 051801 (2009)arXiv07123789 [hep-ex]

[95] B Aubert et al (BABAR collaboration) Phys Rev D77 011102 (2008) arXiv07081565[hep-ex]

[96] P L Frabetti et al (E687 Collaboration collaboration) PhysRevLett 72 324327 (1994)

[97] J P Alexander et al (CLEO Collaboration collaboration) PhysLett B303 377384 (1993)

[98] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B297 425431 (1992)

[99] P Avery et al (CLEO Collaboration collaboration) PhysRev D41 774 (1990)

[100] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B230 162 (1989)

[101] J P Lees et al (BaBar Collaboration collaboration) PhysRev D83 072003 (2011)arXiv11032675 [hep-ex]

[102] R Aaij et al (LHCb collaboration) Phys Rev D90 no 7 072003 (2014) arXiv14077712[hep-ex]

[103] R Aaij et al (LHCb collaboration) PhysLett B698 1420 (2011) arXiv11020348[hep-ex]

[104] B Aubert et al (BaBar Collaboration collaboration) PhysRevLett 97 222001 (2006)arXivhep-ex0607082 [hep-ex]

[105] H Albrecht et al (ARGUS Collaboration collaboration) ZPhys C69 405408 (1996)

[106] Y Kubota et al (CLEO Collaboration collaboration) PhysRevLett 72 19721976 (1994)arXivhep-ph9403325 [hep-ph]

[107] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052002 (2015)arXiv14126751 [hep-ex]

[108] J Brodzicka et al (Belle collaboration) Phys Rev Lett 100 092001 (2008)arXiv07073491 [hep-ex]

48

[109] B Aubert et al (BABAR collaboration) Phys Rev D79 112004 (2009) arXiv09011291[hep-ex]

[110] R Aaij et al (LHCb collaboration) Phys Rev D92 no 3 032002 (2015)arXiv150501710 [hep-ex]

[111] R Aaij et al (LHCb collaboration) Phys Rev D92 no 1 012012 (2015)arXiv150501505 [hep-ex]

[112] A Kuzmin et al (Belle Collaboration collaboration) PhysRev D76 012006 (2007)arXivhep-ex0611054 [hep-ex]

[113] H Abramowicz et al (ZEUS Collaboration collaboration) NuclPhys B866 229254 (2013)arXiv12084468 [hep-ex]

[114] A Abulencia et al (CDF Collaboration collaboration) PhysRev D73 051104 (2006)arXivhep-ex0512069 [hep-ex]

[115] K Abe et al (Belle collaboration) Phys Rev Lett 94 221805 (2005)arXivhep-ex0410091 [hep-ex]

[116] P Avery et al (CLEO Collaboration collaboration) PhysLett B331 236244 (1994)arXivhep-ph9403359 [hep-ph]

[117] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B232 398 (1989)

[118] J C Anjos et al (Tagged Photon Spectrometer Collaboration collaboration) PhysRevLett62 1717 (1989)

[119] T Bergfeld et al (CLEO Collaboration collaboration) PhysLett B340 194204 (1994)

[120] R Aaij et al (LHCb collaboration) Phys Rev D91 no 9 092002 (2015)arXiv150302995 [hep-ex] [Erratum Phys RevD93no11119901(2016)]

[121] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B221 422 (1989)

[122] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B231 208 (1989)

[123] P Abreu et al (DELPHI Collaboration collaboration) PhysLett B426 231242 (1998)

[124] D Matvienko et al (Belle collaboration) Phys Rev D92 no 1 012013 (2015)arXiv150503362 [hep-ex]

[125] P Krokovny et al (Belle collaboration) Phys Rev Lett 91 262002 (2003)arXivhep-ex0308019 [hep-ex]

[126] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 181801 (2004)arXivhep-ex0408041 [hep-ex]

[127] S K Choi et al (Belle collaboration) Phys Rev D91 no 9 092011 (2015)arXiv150402637 [hep-ex] [Addendum Phys RevD92no3039905(2015)]

[128] A Drutskoy et al (Belle collaboration) Phys Rev Lett 94 061802 (2005)arXivhep-ex0409026 [hep-ex]

[129] B Aubert et al (BABAR collaboration) Phys Rev D74 031103 (2006)arXivhep-ex0605036 [hep-ex]

49

[130] S Chekanov et al (ZEUS Collaboration collaboration) EurPhysJ C60 2545 (2009)arXiv08071290 [hep-ex]

[131] A Heister et al (ALEPH Collaboration collaboration) PhysLett B526 3449 (2002)arXivhep-ex0112010 [hep-ex]

[132] B Aubert et al (BABAR collaboration) Phys Rev Lett 103 051803 (2009)arXiv08080333 [hep-ex]

[133] G Burdman E Golowich J L Hewett and S Pakvasa Phys Rev D66 014009 (2002)arXivhep-ph0112235 [hep-ph]

[134] S Fajfer A Prapotnik S Prelovsek P Singer and J Zupan Nucl Phys Proc Suppl 1159397 (2003) arXivhep-ph0208201 [hep-ph]

[135] S Fajfer N Kosnik and S Prelovsek Phys Rev D76 074010 (2007) arXiv07061133[hep-ph]

[136] E Golowich J Hewett S Pakvasa and A A Petrov Phys Rev D79 114030 (2009)arXiv09032830 [hep-ph]

[137] A Paul I I Bigi and S Recksiegel Phys Rev D82 094006 (2010) arXiv10083141[hep-ph]

[138] A Borisov (2011) arXiv11123269 [hep-ph]

[139] R-M Wang J-H Sheng J Zhu Y-Y Fan and Y Gao Int J Mod Phys A29 no 291450169 (2014)

[140] S de Boer and G Hiller Phys Rev D93 no 7 074001 (2016) arXiv151000311 [hep-ph]

[141] P Rubin et al (CLEO collaboration) Phys Rev D82 092007 (2010) arXiv10091606[hep-ex]

[142] V Abazov et al (D0 collaboration) Phys Rev Lett 100 101801 (2008) arXiv07082094[hep-ex]

[143] R Aaij et al (LHCb collaboration) Phys Lett B728 234243 (2014) arXiv13102535[hep-ex]

[144] R Aaij et al (LHCb collaboration) Phys Lett B724 203212 (2013) arXiv13046365[hep-ex]

[145] T Coan et al (CLEO collaboration) Phys Rev Lett 90 101801 (2003)arXivhep-ex0212045 [hep-ex]

[146] M Ablikim et al (BESIII collaboration) Phys Rev D91 no 11 112015 (2015)arXiv150503087 [hep-ex]

[147] J P Lees et al (BABAR collaboration) Phys Rev D85 091107 (2012) arXiv11106480[hep-ex]

[148] N K Nisar et al (Belle collaboration) Phys Rev D93 no 5 051102 (2016)arXiv151202992 [hep-ex]

[149] P Haas et al (CLEO collaboration) Phys Rev Lett 60 1614 (1988)

50

[150] H Albrecht et al (ARGUS collaboration) Phys Lett B209 380 (1988)

[151] J Adler et al (MARK-III collaboration) Phys Rev D37 2023 (1988) Erratum ibid D40(1989) 3788

[152] A Freyberger et al (CLEO collaboration) Phys Rev Lett 76 30653069 (1996)

[153] D Pripstein et al (E789 collaboration) Phys Rev D61 032005 (2000)arXivhep-ex9906022 [hep-ex]

[154] E Aitala et al (E791 collaboration) Phys Lett B462 401409 (1999)arXivhep-ex9906045 [hep-ex]

[155] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 191801 (2004)arXivhep-ex0408023 [hep-ex]

[156] M Petric et al (Belle collaboration) Phys Rev D81 091102 (2010) arXiv10032345[hep-ex]

[157] K Kodama et al (E653 collaboration) Phys Lett B345 8592 (1995)

[158] I Abt et al (HERA-B collaboration) Phys Lett B596 173183 (2004)arXivhep-ex0405059 [hep-ex]

[159] T Aaltonen et al (CDF collaboration) Phys Rev D82 091105 (2010) arXiv10085077[hep-ex]

[160] R Aaij et al (LHCb collaboration) Phys Lett B725 1524 (2013) arXiv13055059[hep-ex]

[161] E Aitala et al (E791 collaboration) Phys Rev Lett 86 39693972 (2001)arXivhep-ex0011077 [hep-ex]

[162] J Adler et al (MARK-III collaboration) Phys Rev D40 906 (1989)

[163] J Becker et al (MARK-III collaboration) Phys Lett B193 147 (1987)

[164] R Aaij et al (LHCb collaboration) Phys Lett B754 167175 (2016) arXiv151200322[hep-ex]

[165] P Rubin et al (CLEO collaboration) Phys Rev D79 097101 (2009) arXiv09041619[hep-ex]

[166] P Frabetti et al (E687 collaboration) Phys Lett B398 239244 (1997)

[167] J P Lees et al (BABAR collaboration) Phys Rev D84 072006 (2011) arXiv11074465[hep-ex]

[168] (BESIII collaboration) M-G Zhao D rareforbidden decays at BESIII in 7th International

Workshop on Charm Physics (Charm 2015) Detroit MI USA May 18-22 2015 2016arXiv160508952 [hep-ex]httpinspirehepnetrecord1466292filesarXiv160508952pdf

[169] J Link et al (FOCUS collaboration) Phys Lett B572 2131 (2003)arXivhep-ex0306049 [hep-ex]

51

  • Introduction
  • D decays
    • Interplay of direct and indirect CP violation
    • Semileptonic decays
      • Introduction
      • DP decays
      • Form factor parameterizations
      • Simple pole
      • z expansion
      • Three-pole formalism
      • Experimental techniques and results
      • Combined results for the DK channel
      • Combined results for the D channel
      • Vcs and Vcd determination
      • DV decays
      • Form factor measurements
        • Excited D(s) mesons
        • Rare and forbidden decays
          • References
Page 7: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

Table 1 Inputs to the t for direct and indirect CP violation The rst uncertainty listed isstatistical and the second is systematic

Year Experiment Results ∆〈t〉τ 〈t〉τ Reference2012 BABAR AΓ = (009plusmn 026plusmn 006) - - [9]2013 LHCb prompt AΓ(KK) = (minus0035plusmn 0062plusmn 0012) - - [10]

AΓ(ππ) = (0033plusmn 0106plusmn 0014) - -2014 CDF AΓ = (minus012plusmn 012) - - [11]2015 LHCb SL AΓ = (minus0125plusmn 0073) - - [12]2015 Belle AΓ = (minus003plusmn 020plusmn 007) - - [13]2008 BABAR ACP(KK) = (000plusmn 034plusmn 013)

ACP(ππ) = (minus024plusmn 052plusmn 022) 000 100 [14]2012 Belle prel ∆ACP = (minus087plusmn 041plusmn 006) 000 100 [15]2012 CDF ∆ACP = (minus062plusmn 021plusmn 010) 025 258 [16]2014 LHCb SL ∆ACP = (014plusmn 016plusmn 008) 001 107 [17]2016 LHCb prompt ∆ACP = (minus010plusmn 008plusmn 003) 012 210 [18]

In this t AΓ(KK) and AΓ(ππ) are assumed to be identical This assumption is sup-ported by all measurements to date A signicant relative shift due to nal-state dependentAΓ values between ∆ACP measurements with dierent mean decay times is excluded by thesemeasurements

The combination plot (see Fig 1) shows the measurements listed in Table 1 for ∆ACP andAΓ where the bands represent plusmn1σ intervals The point of no CP violation (00) is shownas a lled circle and two-dimensional 68 CL 95 CL and 997 CL regions are plotted asellipses The best t value is indicated by a cross showing the one-dimensional errors

From the t the change in χ2 from the minimum value for the no-CPV point (00) is55 which corresponds to a CL of 65 times 10minus2 for two degrees of freedom Thus the data areconsistent with the no-CP -violation hypothesis at 65 CL This p-value corresponds to 18σThe central values and plusmn1σ uncertainties for the individual parameters are

aindCP = (0056plusmn 0040)

∆adirCP = (minus0137plusmn 0070) (6)

Compared to the previous average the tension in the dierence between direct CP violationin the two nal states reduced while the common indirect CP violation moved away from theno CP violation point by about one standard deviation

7

0015 0010 0005 0000 0005 0010

aindCP

0015

0010

0005

0000

0005

0010

0015

∆adirCP

Contours contain 68 95 99 CL

CD

F

LHC

b S

L

LHC

b p

rom

pt

BaBarBelleCDF KK+ππLHCb SL KK+ππ

LHCb prompt KKLHCb prompt ππ

HFAG-charmWinter 16

no CPV

BaBar

Belle

CDF

LHCb

Figure 1 Plot of all data and the t result Individual measurements are plotted as bandsshowing their plusmn1σ range The no-CPV point (00) is shown as a lled circle and the best tvalue is indicated by a cross showing the one-dimensional uncertainties Two-dimensional 68CL 95 CL and 997 CL regions are plotted as ellipses

8

22 Semileptonic decays

221 Introduction

Semileptonic decays of D mesons involve the interaction of a leptonic current with a hadroniccurrent The latter is nonperturbative and cannot be calculated from rst principles thus it isusually parameterized in terms of form factors The transition matrix element is written

M = minusi GFradic2Vcq L

microHmicro (7)

where GF is the Fermi constant and Vcq is a CKM matrix element The leptonic current Lmicro isevaluated directly from the lepton spinors and has a simple structure this allows one to extractinformation about the form factors (in Hmicro) from data on semileptonic decays [19] Converselybecause there are no strong nal-state interactions between the leptonic and hadronic systemssemileptonic decays for which the form factors can be calculated allow one to determine Vcq [2]

222 DrarrP`ν` decays

When the nal state hadron is a pseudoscalar the hadronic current is given by

Hmicro = 〈P (p)|qγmicroc|D(pprime)〉 = f+(q2)

[(pprime + p)micro minus

m2D minusm2

P

q2qmicro

]+ f0(q2)

m2D minusm2

P

q2qmicro (8)

where mD and pprime are the mass and four momentum of the parent D meson mP and p are thoseof the daughter meson f+(q2) and f0(q2) are form factors and q = pprime minus p Kinematics requirethat f+(0) = f0(0) The contraction qmicroL

micro results in terms proportional to m` [20] and thus for` = e the terms proportionals to qmicro in Eq (8) are negligible For light leptons only the f+(q2)vector form factor is relevant and the dierential partial width is

dΓ(D rarr P`ν`)

dq2 d cos θ`=

G2F |Vcq|2

32π3plowast 3|f+(q2)|2 sin θ2

` (9)

where plowast is the magnitude of the momentum of the nal state hadron in the D rest frame andθ` is the angle of the lepton in the `ν rest frame with respect to the direction of the pseudoscalarmeson in the D rest frame

223 Form factor parameterizations

The form factor is traditionally parameterized with an explicit pole and a sum of eective poles

f+(q2) =f+(0)

(1minus α)

[(1

1minus q2m2pole

)+

Nsumk=1

ρk1minus q2(γkm2

pole)

] (10)

where ρk and γk are expansion parameters and α is a parameter that normalizes the formfactor at q2 = 0 f+(0) The parameter mpole is the mass of the lowest-lying cq resonance withthe vector quantum numbers this is expected to provide the largest contribution to the formfactor for the crarr q transition The sum over N gives the contribution of higher mass statesFor example for D rarr π transitions the dominant resonance is expected to be Dlowast(2010) andthus mpole = mDlowast(2010) For D rarr K transitions the dominant contribution is expected from

Dlowasts(2112) with mpole = mDlowasts (2112)

9

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Comparison between CLEO-c and BABAR results for the quantities q2H20 (q2) and

q2h0(q2)H0(q2)

Table 11 Results for rV and r2 from various experiments

Experiment Ref rV r2

D+ rarr Klowast0l+ν

E691 [54] 20plusmn 06plusmn 03 00plusmn 05plusmn 02E653 [55] 200plusmn 033plusmn 016 082plusmn 022plusmn 011E687 [56] 174plusmn 027plusmn 028 078plusmn 018plusmn 011

E791 (e) [57] 190plusmn 011plusmn 009 071plusmn 008plusmn 009E791 (micro) [58] 184plusmn011plusmn009 075plusmn008plusmn009Beatrice [59] 145plusmn 023plusmn 007 100plusmn 015plusmn 003FOCUS [60] 1504plusmn0057plusmn0039 0875plusmn0049plusmn0064

D0 rarr K0πminusmicro+ν

FOCUS [61] 1706plusmn0677plusmn0342 0912plusmn0370plusmn0104BABAR [62] 1493plusmn 0014plusmn 0021 0775plusmn 0011plusmn 0011

D+s rarr φ e+νBABAR [63] 1849plusmn0060plusmn0095 0763plusmn0071plusmn0065

D0 D+ rarr ρ eνCLEO [64] 140plusmn025plusmn003 057plusmn018plusmn006

23

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

HFLAV())+-amp

Figure 7 A comparison of r2 (lled inverted triangles) and rV (open triangles) values fromvarious experiments The rst seven measurements are for D+ rarr Kminusπ+l+νl decays Alsoshown as a line with 1-σ limits is the average of these The last two points are D+

s and D0

decays

24

23 Excited D(s) mesons

Excited charm meson states have received increased attention since the rst observation ofstates that could not be accommodated by QCD predictions [70 71 72 73] Tables 12 13and 14 summarize recent measurements of the masses and widths of excited D and Ds mesonsrespectively If a preferred assignment of spin and parity was measured it is listed in the columnJP where the label natural denotes JP = 0minus 1+ 2minus and unnatural JP = 0+ 1minus 2+ Ifpossible an average mass and width was calculated which is listed in the gray shaded rowThe calculation of the averages assumes no correlation between individual measurements Asummary of the averaged masses and widths is shown in Figure 8

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

0+ 1+ 2+ 1minus 1 3minus

unnatu

ral

Dlowast s0

(2317)plusmn

Ds1

(2460)plusmn

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn D

sJ(3

040)plusmn

HFAG-charmAugust 2016

(a)

Mas

s[M

eVc

2]

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

0+ 1+ 2+ 0minus 1minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ralDlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn

D(2

550)0

D(2

580)0

D(2

600)0

D(2

600)plusmn

Dlowast (

2640)plusmn

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(b)

Mas

s[M

eVc

2]

0

50

100

150

200

250

300

350

400

450

500

550

1+ 2+ 1minus 1 3minus

unnatu

ral

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn

DsJ

(3040)plusmn

HFAG-charmAugust 2016

(c)

Wid

th[M

eV]

50100150200250300350400450500550600650700

0+ 1+ 2+ 0minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ral

Dlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn D(2

550)0

D(2

580)0

D(2

600)0

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(d)

Wid

th[M

eV]

Figure 8 Averaged masses for Ds mesons are shown in subgure (a) and for D mesons insubgure (b) The average widths for Ds mesons are shown in subgure (c) and for D mesonsin subgure (d) The vertical shaded regions distinguish between dierent spin parity states

The masses and widths of narrow (Γ lt 50 MeV) orbitally excited D mesons (denotedDlowastlowast) both neutral and charged are well established Measurements of broad states (Γ sim200400 MeV) are less abundant as identifying the signal is more challenging There is aslight discrepancy between the Dlowast0(2400)0 masses measured by the Belle [74] and FOCUS [75]experiments No data exist yet for the D1(2430)plusmn state Dalitz plot analyses of B rarr D(lowast)ππ

25

decays strongly favor the assignments 0+ and 1+ for the spin-parity quantum numbers of theDlowast0(2400)0Dlowast0(2400)plusmn and D1(2430)0 states respectively The measured masses and widthsas well as the JP values are in agreement with theoretical predictions based on potentialmodels [76777879]

Tables 15 and 16 summarizes the branching fractions of B mesons decays to excited D andDs states respectively It can be noted that the branching fractions for B mesons decaying to anarrow Dlowastlowast state and a pion are similar for charged and neutral B initial states the branchingfractions to a broad Dlowastlowast state and π+ are much larger for B+ than for B0 This may be dueto the fact that color-suppressed amplitudes contribute only to the B+ decay and not to theB0 decay (for a theoretical discussion see Ref [8081]) Measurements of individual branchingfractions of D mesons are dicult due to the unknown fragmentation of cc rarr Dlowastlowast or due tothe unknown B rarr DlowastlowastX branching fractions

The discoveries of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn have triggered increased interest in prop-erties of and searches for excited Ds mesons (here generically denoted D

lowastlowasts ) While the masses

and widths of Ds1(2536)plusmn and Ds2(2573)plusmn states are in relatively good agreement with po-tential model predictions the masses of Dlowasts0(2317)plusmn and Ds1(2460)plusmn states are signicantlylower than expected (see Ref [82] for a discussion of cs models) Moreover the mass splittingbetween these two states greatly exceeds that between the Ds1(2536)plusmn and Ds2(2573)plusmn Theseunexpected properties have led to interpretations of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn as exoticfour-quark states [8384]

While there are few measurements of the JP values of Dlowasts0(2317)plusmn andDs1(2460)plusmn the avail-able data favor 0+ and 1+ respectively A molecule-like (DK) interpretation of the Dlowasts0(2317)plusmn

and Ds1(2460)plusmn [8384] that can account for their low masses and isospin-breaking decay modesis tested by searching for charged and neutral isospin partners of these states thus far suchsearches have yielded negative results Therefore the subset of models that predict equal pro-duction rates for dierent charged states is excluded The molecular picture can also be testedby measuring the rates for the radiative processes Dlowasts0(2317)plusmnDs1(2460)plusmn rarr D

(lowast)s γ and com-

paring to theoretical predictions The predicted rates however are below the sensitivity ofcurrent experiments

Another model successful in explaining the total widths and the Dlowasts0(2317)plusmn Ds1(2460)plusmn

mass splitting is based on the assumption that these states are chiral partners of the groundstates D+

s and Dlowasts [85] While some measured branching fraction ratios agree with predictedvalues further experimental tests with better sensitivity are needed to conrm or refute thisscenario A summary of the mass dierence measurements is given in Table 17

Measurements by BABAR [86] and LHCb [87] rst indicated the existence of a strange-charm DlowastsJ(2860)plusmn meson An LHCb study of B0

s rarr D0Kminusπ+ decays in which they searchedfor excited Ds mesons [88] showed with 10σ signicance that this state is comprised of twodierent particles one of spin 1 and one of spin 3 This represents the rst measurement of aheavy avored spin-3 particle and the rst observation B mesons decays to spin 3 particlesA subsequent study of DsJ mesons by the LHCb collaboration [89] supports the natural parityassignment for this state (JP = 3minus) This study also shows weak evidence for a further structureat a mass around 3040 MeVc2 with unnatural parity which was rst hinted at by a Babaranalysis [86]

Recent evidence shows that the 1D family of charm resonances can be explored in the Dalitzplot analyses of B-meson decays in the same way as seen for the charm-strange resonances TheLHCb collaboration performed an analysis of B0 rarr D0π+πminus decays in which they measured

26

the spin-parity assignment of the stateDlowast3(2760)plusmn which was observed previously by BABAR [29]and LHCb [30] to be JP = 3minus The measurement suggests a spectroscopic assignment of 3D3This is the second observation of a spin-3 charm meson

Other observed excited Ds states include Ds1(2700)plusmn and Ds2(2573)plusmn The properties ofboth (mass width JP ) have been measured and determined in several analyses A theoreticaldiscussion [90] investigates the possibility that theDs1(2700)plusmn could represent radial excitationsof the Dlowastplusmns Similarly the Ds1(2860)plusmn and DsJ(3040)plusmn could be excitations of Dlowasts0(2317)plusmn andDs1(2460)plusmn or Ds1(2536)plusmn respectively

Table 18 summarizes measurements of the polarization amplitude AD (sometimes also re-ferred as helicity parameter) which describes the initial polarization of the D meson In Dlowastlowast

meson decay the helicity distribution varies like 1 + AD cos2 θH where θH is the angle in theDlowast rest frame between the two pions emitted by decay Dlowastlowast rarr Dlowastπ and the Dlowast rarr Dπ Theparameter is sensitive to possible S-wave contributions in the decay In the case of an unpolar-ized D meson decay decaying purely via D-wave the polarization amplitude is predicted to giveAD = 3 Studies of the D1(2420)0 meson by the ZEUS and BABAR collaborations suggest thatthere is an S-wave admixture in the decay which is contrary to Heavy Quark Eective Theorycalculations [9192]

27

Table 12 Recent measurements of mass and width for dierent excited Ds mesons Thecolumn JP list the most signicant assignment of spin and parity If possible an average massor width is calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowasts0(2317)plusmn 0+

D+s π

0 23196plusmn 02plusmn 14 BABAR [93]D+s π

0 23173plusmn 04plusmn 08 BABAR [73]

23180plusmn 08 Our average

Ds1(2460)plusmn 1+

D+s π

0γD+s γD

+s π

+πminus 24601plusmn 02plusmn 08 BABAR [93]D+s π

0γ 2458plusmn 10plusmn 10 BABAR [73]

24596plusmn 07 Our average

Ds1(2536)plusmn 1+

Dlowast+K0S 25357plusmn 06plusmn 05 DOslash [94]

Dlowast+K0S D

lowast0K+ 253478plusmn 031plusmn 040 BABAR [95]D+s π

+πminus 25346plusmn 03plusmn 07 BABAR [93]Dlowast+K0

S Dlowast0K+ 25350plusmn 06plusmn 10 E687 [96]

Dlowast0K+ 25353plusmn 02plusmn 05 CLEO [97]Dlowast+K0

S 25348plusmn 06plusmn 06 CLEO [97]Dlowast0K+ 25352plusmn 05plusmn 15 ARGUS [98]Dlowast+K0

S 25356plusmn 07plusmn 04 CLEO [99]Dlowast+K0

S 25359plusmn 06plusmn 20 ARGUS [100]Dlowast+K0

S 092plusmn 003plusmn 004 BABAR [101]

253510plusmn 026 092plusmn 005 Our average

Dlowasts2(2573)plusmn 2+

D0K+ Dlowast+K0S 256839plusmn 029plusmn 026 169plusmn 05plusmn 06 LHCb [102]

D+K0S D

0K+ 25694plusmn 16plusmn 05 121plusmn 45plusmn 16 LHCb [103]D+K0

S D0K+ 25722plusmn 03plusmn 10 271plusmn 06plusmn 56 BABAR [104]

D0K+ 257425plusmn 33plusmn 16 104plusmn 83plusmn 30 ARGUS [105]D0K+ 25732+17

minus16 plusmn 09 16+5minus4 plusmn 3 CLEO [106]

256908plusmn 035 169plusmn 08 Our average

Dlowasts1(2700)plusmn 1minus

Dlowast+K0S D

lowast0K+ 27323plusmn 43plusmn 58 136plusmn 19plusmn 24 LHCb [89]D0K+ 2699+14

minus7 127+24minus19 BABAR [107]

Dlowast+K0S D

lowast0K+ 27092plusmn 19plusmn 45 1158plusmn 73plusmn 121 LHCb [87]DKDlowastK 2710plusmn 2+12

minus7 149plusmn 7+39minus52 BABAR [86]

D0K+ 2708plusmn 9+11minus10 108plusmn 2+36

minus31 Belle [108]

27120plusmn 15 1215plusmn 102 Our average

Dlowasts1(2860)plusmn 1 D0K+ 2859plusmn 12plusmn 24 159plusmn 23plusmn 77 LHCb [88]

Dlowasts3(2860)plusmn 3minusDlowast+K0

S Dlowast0K+ 28671plusmn 43plusmn 19 50plusmn 11plusmn 13 LHCb [89]

D0K+ 28605plusmn 26plusmn 65 53plusmn 7plusmn 7 LHCb [88]

28650plusmn 39 522plusmn 86 Our average

DsJ(3040)plusmn Unnatural DlowastK 3044plusmn 8+30minus5 239plusmn 35+46

minus42 BABAR (m amp Γ) + LHCb(JP ) [86]+ [89]

28

Table 13 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast0(2400)0 0+

D+πminus 2297plusmn 8plusmn 20 273plusmn 12plusmn 48 BABAR [109]D+πminus 2308plusmn 17plusmn 32 276plusmn 21plusmn 63 Belle [74]D+πminus 2407plusmn 21plusmn 35 240plusmn 55plusmn 59 Focus [75]

23182plusmn 169 2674plusmn 356 Our average

Dlowast0(2400)plusmn 0+

D0π+ 2349plusmn 6plusmn 1plusmn 4 217plusmn 13plusmn 5plusmn 12 LHCb [110]D0π+ 2360plusmn 15plusmn 12plusmn 28 255plusmn 26plusmn 20plusmn 47 LHCb [111]D0π+ 2403plusmn 14plusmn 35 283plusmn 24plusmn 34 Focus(m ampΓ) + Belle(JP ) [75] + [112]

23506plusmn 59 2337plusmn 155 Our average

D1(2420)0 1+

Dlowast+πminus 24196plusmn 01plusmn 07 352plusmn 04plusmn 09 LHCb [30]Dlowast+πminus 24231plusmn 15+04

minus10 388plusmn 5+19minus54 Zeus [113]

Dlowast+πminus 24201plusmn 01plusmn 08 314plusmn 05plusmn 13 BABAR [29]Dlowast+πminus 200plusmn 17plusmn 13 CDF [114]D0π+πminus 2426plusmn 3plusmn 1 24plusmn 7plusmn 8 Belle [115]Dlowast+πminus 24214plusmn 15plusmn 09 237plusmn 27plusmn 40 Belle [74]Dlowast+πminus 2421+1

minus2 plusmn 2 20+6minus5

+3minus3 CLEO [116]

Dlowast+πminus 2422plusmn 2plusmn 2 15plusmn 8plusmn 4 E687 [96]Dlowast+πminus 2428plusmn 3plusmn 2 23+8

minus6+10minus4 CLEO [99]

Dlowast+πminus 2414plusmn 2plusmn 5 13plusmn 6+10minus5 ARGUS [117]

Dlowast+πminus 2428plusmn 8plusmn 5 58plusmn 14plusmn 10 TPS [118]

24205plusmn 05 317plusmn 07 Our average

D1(2420)plusmn 1+

Dlowast0π+ 24219plusmn 47+34minus12 Zeus [113]

D+πminusπ+ 2421plusmn 2plusmn 1 21plusmn 5plusmn 8 Belle [115]Dlowast0π+ 2425plusmn 2plusmn 2 26+8

minus7 plusmn 4 CLEO [119]Dlowast0π+ 2443plusmn 7plusmn 5 41plusmn 19plusmn 8 TPS [118]

24232plusmn 16 252plusmn 60 Our average

D1(2430)0 1+ Dlowast+πminus 2427plusmn 26plusmn 25 384+107minus75 plusmn 74 Belle [74]

Dlowast2(2460)0 2+

Dlowast+πminus 24640plusmn 14plusmn 05plusmn 02 438plusmn 29plusmn 17plusmn 06 LHCb [120]Dlowast+πminus 24604plusmn 04plusmn 12 432plusmn 12plusmn 30 LHCb [30]D+πminus 24604plusmn 01plusmn 01 456plusmn 04plusmn 11 LHCb [30]

Dlowast+πminus D+πminus 24625plusmn 24+13minus11 466plusmn 81+59

minus38 Zeus [113]D+πminus 24622plusmn 01plusmn 08 505plusmn 06plusmn 07 BABAR [29]D+πminus 24604plusmn 12plusmn 22 418plusmn 25plusmn 29 BABAR [109]D+πminus 492plusmn 23plusmn 13 CDF [114]D+πminus 24616plusmn 21plusmn 33 456plusmn 44plusmn 67 Belle [74]D+πminus 24645plusmn 11plusmn 19 387plusmn 53plusmn 29 Focus [75]D+πminus 2465plusmn 3plusmn 3 28+8

minus7 plusmn 6 CLEO [116]D+πminus 2453plusmn 3plusmn 2 25plusmn 10plusmn 5 E687 [96]Dlowast+πminus 2461plusmn 3plusmn 1 20+9

minus12+9minus10 CLEO [99]

D+πminus 2455plusmn 3plusmn 5 15+13minus10

+5minus10 ARGUS [121]

D+πminus 2459plusmn 3plusmn 2 20plusmn 10plusmn 5 TPS [118]

246049plusmn 017 4752plusmn 065 Our average

29

Table 14 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast2(2460)plusmn 2+

D0π+ 24686plusmn 06plusmn 00plusmn 03 473plusmn 15plusmn 03plusmn 06 LHCb [110]D0π+ 24656plusmn 18plusmn 05plusmn 12 460plusmn 34plusmn 14plusmn 29 LHCb [111]D0π+ 24631plusmn 02plusmn 06 486plusmn 13plusmn 19 LHCb [30]

Dlowast0π+ D0π+ 24606plusmn 44+36minus08 Zeus [113]

D0π+ 24654plusmn 02plusmn 11 BABAR [29]D0π+ 24657plusmn 18+14

minus48 497plusmn 38plusmn 64 Belle [112]D0π+ 24676plusmn 15plusmn 08 341plusmn 65plusmn 42 Focus [75]D0π+ 2463plusmn 3plusmn 3 27+11

minus8 plusmn 5 CLEO [119]D0π+ 2453plusmn 3plusmn 2 23plusmn 9plusmn 5 E687 [96]D0π+ 2469plusmn 4plusmn 6 ARGUS [122]

246555plusmn 040 467plusmn 12 Our average

D(2550)0 0minus Dlowast+πminus 25394plusmn 45plusmn 68 130plusmn 12plusmn 13 BABAR [29]

D(2580)0 Unnatural Dlowast+πminus 25795plusmn 34plusmn 55 1175plusmn 178plusmn 460 LHCb [30]

D(2600)0 Natural D+πminus 26087plusmn 24plusmn 25 93plusmn 6plusmn 13 BABAR [29]

D(2600)plusmn Natural D0π+ 26213plusmn 37plusmn 42 BABAR [29]

Dlowast(2640)plusmn 1minus Dlowast+π+πminus 2637plusmn 2plusmn 6 Delphi [123]

Dlowast(2650)0 Natural Dlowast+πminus 26492plusmn 35plusmn 35 1402plusmn 171plusmn 186 LHCb [30]

D(2740)0 Unnatural Dlowast+πminus 27370plusmn 35plusmn 112 732plusmn 134plusmn 250 LHCb [30]

D(2750)0 Dlowast+πminus 27524plusmn 17plusmn 27 71plusmn 6plusmn 11 BABAR [29]

Dlowast1(2760)0 1+

D+πminus 2781plusmn 18plusmn 11plusmn 6 177plusmn 32plusmn 20plusmn 7 LHCb [120]Dlowast+πminus 27611plusmn 51plusmn 65 744plusmn 34plusmn 370 LHCb [30]D+πminus 27601plusmn 11plusmn 37 744plusmn 34plusmn 191 LHCb [30]D+πminus 27633plusmn 23plusmn 23 609plusmn 51plusmn 36 BABAR [29]

27621plusmn 24 651plusmn 58 Our average

Dlowast3(2760)plusmn 3minus

D0π+ 2798plusmn 7plusmn 1plusmn 7 105plusmn 18plusmn 6plusmn 23 LHCb [110]D0π+ 27717plusmn 17plusmn 38 667plusmn 66plusmn 105 LHCb [30]D0π+ 27697plusmn 38plusmn 15 BABAR [29]

27739plusmn 33 723plusmn 115 Our average

30

Table 15 Product of B meson branching fraction and (daughter) excited D meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowast0(2400)0

Bminus rarr Dlowast0(2400)0(rarr D+π+)πminus61plusmn 06plusmn 18 Belle [74]68plusmn 03plusmn 20 BABAR [109]

64plusmn 14 Our average

Bminus rarr Dlowast0(2400)0(rarr D+π+)Kminus 0061plusmn 0019plusmn 0005plusmn 0014plusmn 0004 LHCb [120]

Dlowast0(2400)plusmnB0 rarr Dlowast0(2400)+(rarr D0π+)πminus

077plusmn 005plusmn 003plusmn 003plusmn 004 LHCb [110]060plusmn 013plusmn 027 Belle [112]

076plusmn 007 Our average

B0 rarr Dlowast0(2400)+(rarr D0π+)Kminus 0177plusmn 0026plusmn 0019plusmn 0067plusmn 020 LHCb [111]

D1(2420)0

Bminus rarr D1(2420)0(rarr Dlowast+πminus)πminus 68plusmn 07plusmn 13 Belle [74]

Bminus rarr D1(2420)0(rarr D0π+πminus)πminus 185plusmn 029plusmn 027plusmn 041 Belle [115]

B0 rarr D1(2420)0(rarr Dlowast+πminus)ω 07plusmn 02+01minus00 plusmn 01 Belle [124]

D1(2420)plusmn B0 rarr D1(2420)+(rarr D+πminusπ+)πminus 089plusmn 015plusmn 022 Belle [115]

D1(2430)0Bminus rarr D1(2430)0(rarr Dlowast+πminus)πminus 50plusmn 04plusmn 108 Belle [74]

B0 rarr D1(2430)0(rarr Dlowast+πminus)ω 25plusmn 04+07minus02

+04minus01 Belle [124]

Dlowast2(2460)0

Bminus rarr Dlowast2(2460)0(rarr D+πminus)πminus34plusmn 03plusmn 07 Belle [74]35plusmn 02plusmn 05 BABAR [109]

34plusmn 03 Our average

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)πminus 18plusmn 03plusmn 04 Belle [74]

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)ω 04plusmn 01+00minus01 plusmn 01 Belle [124]

Bminus rarr Dlowast2(2460)0(rarr D+π+)Kminus 0232plusmn 0011plusmn 0006plusmn 0010plusmn 0016 LHCb [120]

Dlowast2(2460)plusmnB0 rarr Dlowast2(2460)+(rarr D0π+)πminus

244plusmn 007plusmn 010plusmn 004plusmn 012 LHCb [110]215plusmn 017plusmn 031 Belle [112]

238plusmn 016 Our average

B0 rarr Dlowast2(2460)+(rarr D0π+)Kminus 0212plusmn 0010plusmn 0011plusmn 0011plusmn 025 LHCb [111]

Dlowast1(2760)0 Bminus rarr Dlowast1(2760)0(rarr D+π+)Kminus 0036plusmn 0009plusmn 0003plusmn 0007plusmn 0002 LHCb [120]

Dlowast3(2760)plusmn B0 rarr Dlowast3(2760)0(rarr D0π+)πminus 0103plusmn 0016plusmn 0007plusmn 0008plusmn 0005 LHCb [110]

31

Table 16 Product of B meson branching fraction and (daughter) excited Ds meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowasts0(2317)plusmnB0 rarr Dlowasts0(2317)+(rarr D+

s π0)Dminus

86+33minus26 plusmn 26 Belle [125]

180plusmn 40+67minus50 BABAR [126]

101+13minus12 plusmn 10plusmn 04 Belle [127]

102plusmn 15 Our average

B+ rarr Dlowasts0(2317)+(rarr D+s π

0)D0 80+13minus12 plusmn 10plusmn 04 Belle [127]

B0 rarr Dlowasts0(2317)+(rarr D+s π

0)Kminus 053+015minus013 plusmn 016 Belle [128]

Ds1(2460)plusmn

B0 rarr Ds1(2460)+(rarr Dlowast+s π0)Dminus227+73

minus62 plusmn 68 Belle [125]280plusmn 80+112

minus78 BABAR [126]

247plusmn 76 Our average

B0 rarr Ds1(2460)+(rarr Dlowast+s γ)Dminus82+22minus19 plusmn 25 Belle [125]

80plusmn 20+32minus23 BABAR [126]

81plusmn 23 Our average

Ds1(2460)+ rarr Dlowast+s π0 (56plusmn 13plusmn 9) BABAR [129]

Ds1(2460)+ rarr Dlowast+s γ (16plusmn 4plusmn 3) BABAR [129]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dminus 171plusmn 048plusmn 032 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast+K0)Dminus 261plusmn 103plusmn 031 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dlowastminus 332plusmn 088plusmn 066 BABAR [95]

Ds1(2536)plusmnB0 rarr Ds1(2536)+(rarr Dlowast+K0)Dlowastminus 500plusmn 151plusmn 067 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)D0 216plusmn 052plusmn 045 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)D0 230plusmn 098plusmn 043 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)Dlowast0 546plusmn 117plusmn 104 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)Dlowast0 392plusmn 246plusmn 083 BABAR [95]

Ds2(2573)plusmnB0 rarr Ds2(2573)(rarr D0K+)Dminus 034plusmn 017plusmn 005 BABAR [107]

B+ rarr Ds2(2573)(rarr D0K+)D0 008plusmn 14plusmn 005 BABAR [107]

Ds1(2700)plusmn B+ rarr Ds1(2700)+(rarr D0K+)D0

113plusmn 22+14minus28 Belle [108]

502plusmn 071plusmn 093 BABAR [107]

583plusmn 109 Our average

B0 rarr Ds1(2700)+(rarr D0K+)Dminus 714plusmn 096plusmn 069 BABAR [107]

32

Table 17 Mass dierence measurements for excited D mesons

Resonance Relative to ∆m [MeVc2] Measured by Reference

Dlowast1(2420)0 Dlowast+4102plusmn 21plusmn 09 Zeus [130]4117plusmn 07plusmn 04 CDF [114]

4115plusmn 08 Our average

D1(2420)plusmn Dlowast1(2420)0 4+2minus3 plusmn 3 CLEO [119]

Dlowast2(2460)0 D+ 5939plusmn 06plusmn 05 CDF [114]

Dlowast+ 4588plusmn 37+12minus13 Zeus [130]

Dlowast2(2460)plusmn Dlowast2(2460)0

31plusmn 19plusmn 09 Focus [75]minus2plusmn 4plusmn 4 CLEO [119]14plusmn 5plusmn 8 ARGUS [122]

30plusmn 19 Our average

Dlowasts0(2317)plusmn Dplusmns

3487plusmn 05plusmn 07 Belle [72]3500plusmn 12plusmn 10 CLEO [71]3513plusmn 21plusmn 19 Belle [125]

3492plusmn 07 Our average

Ds1(2460)plusmn

Dlowastplusmns

3441plusmn 13plusmn 11 Belle [72]3512plusmn 17plusmn 10 CLEO [71]3468plusmn 16plusmn 19 Belle [125]

3471plusmn 11 Our average

Dplusmns

4910plusmn 13plusmn 19 Belle [72]4914plusmn 09plusmn 15 Belle [72]

4913plusmn 14 Our average

Ds1(2536)plusmnDlowast(2010)plusmn

52483plusmn 001plusmn 004 BABAR [101]52530+044

minus041 plusmn 010 Zeus [130]5253plusmn 06plusmn 01 ALEPH [131]

52484plusmn 004 Our average

Dlowast(2007)0 5287plusmn 19plusmn 05 ALEPH [131]

Dlowasts2(2573)plusmn D0 704plusmn 3plusmn 1 ALEPH [131]

33

Table 18 Measurements of polarization amplitudes for excited D mesons

Resonance AD Measured by Reference

D1(2420)0

78+67minus27

+46minus18 ZEUS [113]

572plusmn 025 BABAR [29]59+30minus17

+24minus10 ZEUS [130]

38plusmn 06plusmn 08 BABAR [132]

561plusmn 024 Our average

D1(2420)plusmn 38plusmn 06plusmn 08 BABAR [132]

Dlowast2(2460)0 minus116plusmn 035 ZEUS [113]

D(2750)0 minus033plusmn 028 BABAR [29]

34

24 Rare and forbidden decays

This section provides a summary of rare and forbidden charm decays in tabular form The decaymodes can be categorized as avor-changing neutral currents lepton-avor-violating lepton-number-violating and both baryon- and lepton-number-violating decays Figures 9-11 plot theupper limits for D0 D+ D+

s and Λ+c decays Tables 19-22 give the corresponding numerical

results Some theoretical predictions are given in Refs [133134135136137138139140]In several cases the rare-decay nal states have been observed with the di-lepton pair being

the decay product of a hadronic resonance For these measurements the quoted limits are thoseexpected for the non-resonant di-lepton spectrum For the extrapolation to the full spectruma phase-space distribution of the non-resonant component has been assumed This applies tothe CLEO measurement of the decays D+

(s) rarr (K+π+)e+eminus [141] to the D0 measurements

of the decays D+(s) rarr π+micro+microminus [142] and to the BABAR measurements of the decays D+

(s) rarr(K+π+)e+eminus and D+

(s) rarr (K+π+)micro+microminus where the contribution from φ rarr l+lminus (l = e micro) has

been excluded In the case of the LHCb measurements of the decays D0 rarr π+πminusmicro+microminus [143]as well as the decays D+

(s) rarr π+micro+microminus [144] the contributions from φ rarr l+lminus as well as from

ρ ω rarr l+lminus (l = e micro) have been excluded

Table 19 Upper limits at 90 CL for D0 decays

Decay Limit times106 Experiment Referenceγγ 260 CLEO II [145]

38 BESIII [146]22 BaBar [147]085 Belle [148]

e+eminus 2200 CLEO [149]1700 Argus [150]1300 Mark3 [151]130 CLEO II [152]819 E789 [153]62 E791 [154]12 BaBar [155]0079 Belle [156]

micro+microminus 700 Argus [150]440 E653 [157]340 CLEO II [152]156 E789 [153]52 E791 [154]20 HERAb [158]13 BaBar [155]021 CDF [159]014 Belle [156]00062 LHCb [160]

π0e+eminus 450 CLEO II [152]π0micro+microminus 5400 CLEO II [152]

1800 E653 [157]

35

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceη e+eminus 1100 CLEO II [152]η micro+microminus 5300 CLEO II [152]π+πminuse+eminus 3700 E791 [161]ρ0e+eminus 4500 CLEO [149]

1240 E791 [161]1000 CLEO II [152]

π+πminusmicro+microminus 300 E791 [161]055 LHCb [143]

ρ0micro+microminus 8100 CLEO [149]4900 CLEO II [152]2300 E653 [157]220 E791 [161]

ω e+eminus 1800 CLEO II [152]ω micro+microminus 8300 CLEO II [152]K+Kminuse+eminus 3150 E791 [161]φ e+eminus 590 E791 [161]

520 CLEO II [152]K+Kminusmicro+microminus 330 E791 [161]φmicro+microminus 4100 CLEO II [152]

310 E791 [161]

K0e+eminus 17000 Mark3 [162]

1100 CLEO II [152]

K0micro+microminus 6700 CLEO II [152]

2600 E653 [157]Kminusπ+e+eminus 3850 E791 [161]

Klowast0

(892)e+eminus 1400 CLEO II [152]470 E791 [161]

Kminusπ+micro+microminus 3600 E791 [161]

Klowast0

(892)micro+microminus 11800 CLEO II [152]240 E791 [161]

π+πminusπ0micro+microminus 8100 E653 [157]microplusmne∓ 2700 CLEO [149]

1200 Mark3 [163]1000 Argus [150]190 CLEO II [152]172 E789 [153]81 E791 [154]081 BaBar [155]026 Belle [156]0016 LHCb [164]

π0eplusmnmicro∓ 860 CLEO II [152]η eplusmnmicro∓ 1000 CLEO II [152]

36

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceπ+πminuseplusmnmicro∓ 150 E791 [161]ρ0eplusmnmicro∓ 660 E791 [161]

490 CLEO II [152]ω eplusmnmicro∓ 1200 CLEO II [152]K+Kminuseplusmnmicro∓ 1800 E791 [161]φ eplusmnmicro∓ 470 E791 [161]

340 CLEO II [152]

K0eplusmnmicro∓ 1000 CLEO II [152]

Kminusπ+eplusmnmicro∓ 5500 E791 [161]Klowast0(892)eplusmnmicro∓ 1000 CLEO II [152]

830 E791 [161]π∓π∓eplusmneplusmn 1120 E791 [161]π∓π∓microplusmnmicroplusmn 290 E791 [161]K∓π∓eplusmneplusmn 2060 E791 [161]K∓π∓microplusmnmicroplusmn 3900 E791 [161]K∓K∓eplusmneplusmn 1520 E791 [161]K∓K∓microplusmnmicroplusmn 940 E791 [161]π∓π∓eplusmnmicroplusmn 790 E791 [161]K∓π∓eplusmnmicroplusmn 2180 E791 [161]K∓K∓eplusmnmicroplusmn 570 E791 [161]p eminus 100 CLEO [165]p e+ 110 CLEO [165]

37

γγ

ρ0micro

+microminus

π+πminusπ

0micro

+microminus

K+K

minuse

+eminus

ηe

+eminus

φmicro

+microminus

π0e

+eminus

φe

+eminus

ωmicro

+microminus

Kminusπ

+micro

+microminus

ρ0e

+eminus

K0micro

+microminus

Klowast0

(892

)e+eminus

π+πminusmicro

+microminus

micro+microminus

π+πminuse

+eminus

e+eminus

Klowast0

(892

)micro+microminus

K+K

minusmicro

+microminus

Kminusπ

+e

+eminus

π0micro

+microminus

K0e

+eminus

ωe

+eminus

ηmicro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

HFAG-charm

Belle

BESIII

CLEO II

BaBar

E791

CLEO

E653

LHCb

E789

HERAB

CDF

Argus

Mark3

June 16

K∓π∓microplusmnmicroplusmn

ωeplusmnmicro∓

Kminusπ

+eplusmnmicro∓

K∓K∓eplusmnmicroplusmn

π∓π∓eplusmnmicroplusmn

peminus

K∓π∓eplusmnmicroplusmn

π∓π∓eplusmneplusmn

ηeplusmnmicro∓

π∓π∓microplusmnmicroplusmn

K∓K∓eplusmneplusmn

K0eplusmnmicro∓

π+πminuseplusmnmicro∓

K∓K∓microplusmnmicroplusmn

ρ0eplusmnmicro∓

pe

+

φeplusmnmicro∓

microplusmne∓

K+K

minuseplusmnmicro∓

Klowast0

(892

)eplusmnmicro∓

π0eplusmnmicro∓

K∓π∓eplusmneplusmn

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

L BLHFAG-charm

E791

CLEO II

CLEO

Belle

E789

Mark3

Argus

LHCb

BaBar

June 16

Figure 9 Upper limits at 90 CL for D0 decays The top plot shows avor-changing neu-tral current decays and the bottom plot shows lepton-avor-changing (LF) lepton-number-changing (L) and both baryon- and lepton-number-changing (BL) decays38

Kminuse

+micro

+

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminusmicro

+micro

+

K+e

+eminus

π+e

+eminus

πminuse

+micro

+

Kminuse

+e

+

K+micro

+eminus

ρminusmicro

+micro

+

K+e

+microminus

K+eplusmnmicro∓

π+micro

+eminus

π+e

+microminus

πminusmicro

+micro

+

πminuse

+e

+

π+micro

+microminus

ρ+micro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E687

E653

E791

BaBar

Focus

CLEO

BESIII

LHCb

D0

June 16

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminuse

+micro

+

K+e

+eminus

π+e

+eminus

K+eplusmnmicro∓

Kminuse

+e

+

K+micro

+eminus

K+e

+microminus

Klowast+

(892

)micro+microminus

π+micro

+eminus

Kminusmicro

+micro

+

πminusmicro

+micro

+

πminuse

+e

+

πminuse

+micro

+

π+micro

+microminus

K+micro

+microminus

π+e

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E653

E791

CLEO

BaBar

Focus

LHCb

June 16

Figure 10 Upper limits at 90 CL for D+ (top) and D+s (bottom) decays Each plot shows

avor-changing neutral current decays lepton-avor-changing decays (LF) and lepton-number-changing (L) decays 39

pmicro

+microminus

pe

+microminus

σ+micro

+microminus

pe

+e

+

pe

+eminus

pe

+micro

+

pmicro

+micro

+

pmicro

+eminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

LHFAG-charm

BaBar E653

June 16

Figure 11 Upper limits at 90 CL for Λ+c decays Shown are avor-changing neutral current

decays lepton-avor-changing (LF) decays and lepton-number-changing (L) decays

40

Table 20 Upper limits at 90 CL for D+ decays

Decay Limit times106 Experiment Referenceπ+e+eminus 1100 E687 [166]

520 E791 [154]59 CLEO [141]11 BaBar [167]03 BESIII [168]

π+micro+microminus 2200 E653 [157]890 E687 [166]150 E791 [154]88 Focus [169]65 BaBar [167]39 D0 [142]0073 LHCb [144]

ρ+micro+microminus 5600 E653 [157]K+e+eminus 2000 E687 [166]

30 CLEO [141]12 BESIII [168]10 BaBar [167]

π+eplusmnmicro∓ 340 E791 [154]π+e+microminus 1100 E687 [166]

29 BaBar [167]π+micro+eminus 1300 E687 [166]

36 BaBar [167]K+eplusmnmicro∓ 680 E791 [154]K+e+microminus 1300 E687 [166]

12 BaBar [167]K+micro+eminus 1200 E687 [166]

28 BaBar [167]πminuse+e+ 1100 E687 [166]

960 E791 [154]19 BaBar [167]12 BESIII [168]11 CLEO [141]

πminusmicro+micro+ 870 E687 [166]170 E791 [154]48 Focus [169]20 BaBar [167]0022 LHCb [144]

πminuse+micro+ 1100 E687 [166]500 E791 [154]

ρminusmicro+micro+ 5600 E653 [157]Kminuse+e+ 1200 E687 [166]

35 CLEO [141]09 BaBar [167]

41

Table 20 continued from previous pageDecay Limit times106 Experiment Reference

06 BESIII [168]Kminusmicro+micro+ 3200 E653 [157]

1200 E687 [166]130 Focus [169]100 BaBar [167]

Kminuse+micro+ 1300 E687 [166]Klowastminus(892)micro+micro+ 8500 E653 [157]

Table 21 Upper limits at 90 CL for D+s decays

Decay Limit times106 Experiment Referenceπ+e+eminus 2700 E791 [154]

220 CLEO [141]130 BaBar [167]

π+micro+microminus 4300 E653 [157]1400 E791 [154]430 BaBar [167]260 Focus [169]041 LHCb [144]

K+e+eminus 16000 E791 [154]520 CLEO [141]37 BaBar [167]

K+micro+microminus 1400 E791 [154]360 Focus [169]210 BaBar [167]

Klowast+(892)micro+microminus 14000 E653 [157]π+eplusmnmicro∓ 6100 E791 [154]π+e+microminus 120 BaBar [167]π+micro+eminus 200 BaBar [167]K+eplusmnmicro∓ 6300 E791 [154]K+e+microminus 140 BaBar [167]K+micro+eminus 97 BaBar [167]πminuse+e+ 6900 E791 [154]

180 CLEO [141]41 BaBar [167]

πminusmicro+micro+ 4300 E653 [157]820 E791 [154]290 Focus [169]140 BaBar [167]012 LHCb [144]

πminuse+micro+ 7300 E791 [154]Kminuse+e+ 6300 E791 [154]

170 CLEO [141]

42

Table 21 continued from previous pageDecay Limit times106 Experiment Reference

52 BaBar [167]Kminusmicro+micro+ 5900 E653 [157]

1800 E791 [154]130 BaBar [167]

Kminuse+micro+ 6800 E791 [154]Klowastminus(892)micro+micro+ 14000 E653 [157]

Table 22 Upper limits at 90 CL for Λ+c decays

Decay Limit times106 Experiment Referencepe+eminus 55 BaBar [167]pmicro+microminus 3400 E653 [157]

440 BaBar [167]σ+micro+microminus 7000 E653 [157]pe+microminus 99 BaBar [167]pmicro+eminus 190 BaBar [167]p e+e+ 27 BaBar [167]p micro+micro+ 94 BaBar [167]

43

References

[1] N Cabibbo Phys Rev Lett 10 531533 (1963)

[2] M Kobayashi and T Maskawa Prog Theor Phys 49 652657 (1973)

[3] D Abbaneo et al (ALEPH CDF DELPHI L3 OPAL and SLD collaborations)arXivhep-ex0009052 (2000) CERN-EP-2000-096 arXivhep-ex0112028 (2001)CERN-EP-2001-050

[4] Y Amhis et al (Heavy Flavor Averaging Group) (2012) arXiv12071158 [hep-ex]

[5] K Olive et al (Particle Data Group) Chin Phys C38 090001 (2014)

[6] A L Kagan and M D Sokolo Phys Rev D80 076008 (2009) arXiv09073917 [hep-ph]

[7] Y Grossman A L Kagan and Y Nir Phys Rev D75 036008 (2007)arXivhep-ph0609178 [hep-ph]

[8] M Gersabeck M Alexander S Borghi V Gligorov and C Parkes J Phys G39 045005(2012) arXiv11116515 [hep-ex]

[9] J P Lees et al (BABAR collaboration) Phys Rev D87 012004 (2013) arXiv12093896[hep-ex]

[10] R Aaij et al (LHCb collaboration) Phys Rev Lett 112 041801 (2014) arXiv13107201[hep-ex]

[11] T A Aaltonen et al (CDF collaboration) Phys Rev D90 no 11 111103 (2014)arXiv14105435 [hep-ex]

[12] R Aaij et al (LHCb collaboration) JHEP 04 043 (2015) arXiv150106777 [hep-ex]

[13] M Staripound et al (Belle collaboration) Phys Lett B753 412418 (2016) arXiv150908266[hep-ex]

[14] B Aubert et al (BABAR collaboration) Phys Rev Lett 100 061803 (2008)arXiv07092715 [hep-ex]

[15] B Ko (Belle collaboration) PoS ICHEP2012 353 (2013) arXiv12121975

[16] T Aaltonen et al (CDF collaboration) Phys Rev Lett 109 111801 (2012)arXiv12072158 [hep-ex]

[17] R Aaij et al (LHCb collaboration) JHEP 07 041 (2014) arXiv14052797 [hep-ex]

[18] R Aaij et al (LHCb collaboration) Phys Rev Lett 116 no 19 191601 (2016)arXiv160203160 [hep-ex]

[19] T Becher and R J Hill Phys Lett B633 6169 (2006) arXivhep-ph0509090 [hep-ph]

[20] F J Gilman and R L Singleton Phys Rev D41 142 (1990)

[21] R J Hill eConf C060409 027 (2006) arXivhep-ph0606023 [hep-ph]

[22] D Becirevic and A B Kaidalov Phys Lett B478 417423 (2000) arXivhep-ph9904490[hep-ph]

44

[23] C G Boyd B Grinstein and R F Lebed Phys Rev Lett 74 46034606 (1995)arXivhep-ph9412324 [hep-ph]

[24] C G Boyd and M J Savage Phys Rev D56 303311 (1997) arXivhep-ph9702300[hep-ph]

[25] M C Arnesen B Grinstein I Z Rothstein and I W Stewart Phys Rev Lett 95 071802(2005)

[26] C Bourrely B Machet and E de Rafael Nucl Phys B189 157 (1981)

[27] D Becirevic A L Yaouanc A Oyanguren P Roudeau and F Sanlippo (2014)arXiv14071019 [hep-ph]

[28] J P Lees et al (BABAR collaboration) Phys Rev D88 052003 (2013) arXiv13045009[hep-ex]

[29] P del Amo Sanchez et al (BaBar Collaboration collaboration) PhysRev D82 111101(2010) arXiv10092076 [hep-ex]

[30] R Aaij et al (LHCb collaboration) JHEP 1309 145 (2013) arXiv13074556

[31] G Burdman and J Kambor Phys Rev D55 28172826 (1997) arXivhep-ph9602353[hep-ph]

[32] D Becirevic A Le Yaouanc L Oliver J-C Raynal P Roudeau and J Serrano Phys RevD87 no 5 054007 (2013) arXiv12065869 [hep-ph]

[33] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052022 (2015)arXiv14125502 [hep-ex]

[34] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 7 072012 (2015)arXiv150807560 [hep-ex]

[35] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 11 112008 (2015)arXiv151000308 [hep-ex]

[36] L Widhalm et al (Belle collaboration) Phys Rev Lett 97 061804 (2006)arXivhep-ex0604049 [hep-ex]

[37] B Aubert et al (BABAR collaboration) Phys Rev D76 052005 (2007) arXiv07040020[hep-ex]

[38] D Besson et al (CLEO collaboration) Phys Rev D80 032005 (2009) arXiv09062983[hep-ex]

[39] S Dobbs et al (CLEO collaboration) Phys Rev D77 112005 (2008) arXiv07121020[hep-ex]

[40] G Huang et al (CLEO collaboration) Phys Rev Lett 94 011802 (2005)arXivhep-ex0407035 [hep-ex]

[41] J Link et al (FOCUS collaboration) Phys Lett B607 233242 (2005)arXivhep-ex0410037 [hep-ex]

[42] J Adler et al (MARK-III collaboration) Phys Rev Lett 62 1821 (1989)

45

[43] K Kodama et al (Fermilab E653 collaboration) Phys Rev Lett 66 18191822 (1991)

[44] K Kodama et al (E653 collaboration) Phys Lett B336 605613 (1994)

[45] P L Frabetti et al (E687 collaboration) Phys Lett B364 127136 (1995)

[46] P L Frabetti et al (E687 collaboration) Phys Lett B315 203208 (1993)

[47] J C Anjos et al (Tagged Photon Spectrometer collaboration) Phys Rev Lett 6215871590 (1989)

[48] M Ablikim et al (BES collaboration) Phys Lett B597 3946 (2004)arXivhep-ex0406028 [hep-ex]

[49] M Ablikim et al (BES collaboration) (2006) arXivhep-ex0610019 [hep-ex]

[50] A Bean et al (CLEO collaboration) Phys Lett B317 647654 (1993)

[51] BESIII collaboration presented at ICHEP 2014 conference 2014httpindicoificuvesindicogetFilepyaccesscontribId=69ampsessionId=25ampresId=

0ampmaterialId=slidesampconfId=2025

[52] J G Korner and G A Schuler Z Phys C46 93 (1990)

[53] FLAG collaboration httpitpwikiunibechagimages44bFLAGpdf 2014httpitpwikiunibechflagimages44bFLAGpdf

[54] J Anjos et al (Fermilab E691 collaboration) Phys Rev Lett 65 26302633 (1990)

[55] K Kodama et al (Fermilab E653 collaboration) Phys Lett B274 246252 (1992)

[56] P Frabetti et al (Fermilab E687 collaboration) Phys Lett B307 262268 (1993)

[57] E Aitala et al (E791 collaboration) Phys Rev Lett 80 13931397 (1998)arXivhep-ph9710216 [hep-ph]

[58] E Aitala et al (E791 collaboration) Phys Lett B440 435441 (1998)arXivhep-ex9809026 [hep-ex]

[59] M Adamovich et al (BEATRICE collaboration) Eur Phys J C6 3541 (1999)

[60] J Link et al (FOCUS collaboration) Phys Lett B544 8996 (2002)arXivhep-ex0207049 [hep-ex]

[61] J Link et al (FOCUS collaboration) Phys Lett B607 6777 (2005)arXivhep-ex0410067 [hep-ex]

[62] P del Amo Sanchez et al (BABAR collaboration) Phys Rev D83 072001 (2011)arXiv10121810 [hep-ex]

[63] B Aubert et al (BABAR collaboration) Phys Rev D78 051101 (2008) arXiv08071599[hep-ex]

[64] H Mahlke eConf C0610161 014 (2006) arXivhep-ex0702014 [hep-ex]

[65] J Link et al (FOCUS collaboration) Phys Lett B535 4351 (2002)arXivhep-ex0203031 [hep-ex]

46

[66] K M Ecklund et al (CLEO collaboration) Phys Rev D80 052009 (2009)arXiv09073201 [hep-ex]

[67] R A Briere et al (CLEO collaboration) Phys Rev D81 112001 (2010) arXiv10041954[hep-ex]

[68] P Estabrooks R Carnegie A D Martin W Dunwoodie T Lasinski et al Nucl PhysB133 490 (1978)

[69] D Aston et al Nucl Phys B296 493 (1988)

[70] B Aubert et al (BABAR collaboration) Phys Rev Lett 90 242001 (2003)arXivhep-ex0304021 [hep-ex]

[71] D Besson et al (CLEO Collaboration collaboration) PhysRev D68 032002 (2003)arXivhep-ex0305100 [hep-ex]

[72] K Abe et al (Belle Collaboration collaboration) PhysRevLett 92 012002 (2004)arXivhep-ex0307052 [hep-ex]

[73] B Aubert et al (BaBar Collaboration collaboration) PhysRev D69 031101 (2004)arXivhep-ex0310050 [hep-ex]

[74] K Abe et al (Belle collaboration) Phys Rev D69 112002 (2004) arXivhep-ex0307021[hep-ex]

[75] J M Link et al (FOCUS Collaboration collaboration) PhysLett B586 1120 (2004)arXivhep-ex0312060 [hep-ex]

[76] S Godfrey and N Isgur Phys Rev D32 189231 (1985)

[77] S Godfrey and R Kokoski Phys Rev D43 16791687 (1991)

[78] N Isgur and M B Wise Phys Rev Lett 66 11301133 (1991)

[79] P Schweitzer S Bo and M Radici Phys Rev D66 114004 (2002)arXivhep-ph0207230 [hep-ph]

[80] F Jugeau A Le Yaouanc L Oliver and J-C Raynal Phys Rev D72 094010 (2005)arXivhep-ph0504206 [hep-ph]

[81] P Colangelo F De Fazio and R Ferrandes ModPhysLett A19 20832102 (2004)arXivhep-ph0407137 [hep-ph]

[82] R N Cahn and J D Jackson Phys Rev D68 037502 (2003) arXivhep-ph0305012[hep-ph]

[83] T Barnes F E Close and H J Lipkin PhysRev D68 054006 (2003)arXivhep-ph0305025 [hep-ph]

[84] H Lipkin PhysLett B580 5053 (2004) arXivhep-ph0306204 [hep-ph]

[85] W A Bardeen E J Eichten and C T Hill Phys Rev D68 054024 (2003)arXivhep-ph0305049 [hep-ph]

[86] B Aubert et al (BaBar Collaboration collaboration) PhysRev D80 092003 (2009)arXiv09080806 [hep-ex]

47

[87] R Aaij et al (LHCb Collaboration collaboration) JHEP 1210 151 (2012) arXiv12076016[hep-ex]

[88] R Aaij et al (LHCb collaboration) Phys Rev Lett 113 162001 (2014) arXiv14077574[hep-ex]

[89] R Aaij et al (LHCb collaboration) JHEP 02 133 (2016) arXiv160101495 [hep-ex]

[90] T Matsuki T Morii and K Sudoh EurPhysJ A31 701704 (2007)arXivhep-ph0610186 [hep-ph]

[91] N Isgur and M B Wise PhysLett B232 113117 (1989)

[92] M Neubert PhysRept 245 259396 (1994) arXivhep-ph9306320 [hep-ph]

[93] B Aubert et al (BaBar Collaboration collaboration) PhysRev D74 032007 (2006)arXivhep-ex0604030 [hep-ex]

[94] V M Abazov et al (D0 Collaboration collaboration) PhysRevLett 102 051801 (2009)arXiv07123789 [hep-ex]

[95] B Aubert et al (BABAR collaboration) Phys Rev D77 011102 (2008) arXiv07081565[hep-ex]

[96] P L Frabetti et al (E687 Collaboration collaboration) PhysRevLett 72 324327 (1994)

[97] J P Alexander et al (CLEO Collaboration collaboration) PhysLett B303 377384 (1993)

[98] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B297 425431 (1992)

[99] P Avery et al (CLEO Collaboration collaboration) PhysRev D41 774 (1990)

[100] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B230 162 (1989)

[101] J P Lees et al (BaBar Collaboration collaboration) PhysRev D83 072003 (2011)arXiv11032675 [hep-ex]

[102] R Aaij et al (LHCb collaboration) Phys Rev D90 no 7 072003 (2014) arXiv14077712[hep-ex]

[103] R Aaij et al (LHCb collaboration) PhysLett B698 1420 (2011) arXiv11020348[hep-ex]

[104] B Aubert et al (BaBar Collaboration collaboration) PhysRevLett 97 222001 (2006)arXivhep-ex0607082 [hep-ex]

[105] H Albrecht et al (ARGUS Collaboration collaboration) ZPhys C69 405408 (1996)

[106] Y Kubota et al (CLEO Collaboration collaboration) PhysRevLett 72 19721976 (1994)arXivhep-ph9403325 [hep-ph]

[107] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052002 (2015)arXiv14126751 [hep-ex]

[108] J Brodzicka et al (Belle collaboration) Phys Rev Lett 100 092001 (2008)arXiv07073491 [hep-ex]

48

[109] B Aubert et al (BABAR collaboration) Phys Rev D79 112004 (2009) arXiv09011291[hep-ex]

[110] R Aaij et al (LHCb collaboration) Phys Rev D92 no 3 032002 (2015)arXiv150501710 [hep-ex]

[111] R Aaij et al (LHCb collaboration) Phys Rev D92 no 1 012012 (2015)arXiv150501505 [hep-ex]

[112] A Kuzmin et al (Belle Collaboration collaboration) PhysRev D76 012006 (2007)arXivhep-ex0611054 [hep-ex]

[113] H Abramowicz et al (ZEUS Collaboration collaboration) NuclPhys B866 229254 (2013)arXiv12084468 [hep-ex]

[114] A Abulencia et al (CDF Collaboration collaboration) PhysRev D73 051104 (2006)arXivhep-ex0512069 [hep-ex]

[115] K Abe et al (Belle collaboration) Phys Rev Lett 94 221805 (2005)arXivhep-ex0410091 [hep-ex]

[116] P Avery et al (CLEO Collaboration collaboration) PhysLett B331 236244 (1994)arXivhep-ph9403359 [hep-ph]

[117] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B232 398 (1989)

[118] J C Anjos et al (Tagged Photon Spectrometer Collaboration collaboration) PhysRevLett62 1717 (1989)

[119] T Bergfeld et al (CLEO Collaboration collaboration) PhysLett B340 194204 (1994)

[120] R Aaij et al (LHCb collaboration) Phys Rev D91 no 9 092002 (2015)arXiv150302995 [hep-ex] [Erratum Phys RevD93no11119901(2016)]

[121] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B221 422 (1989)

[122] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B231 208 (1989)

[123] P Abreu et al (DELPHI Collaboration collaboration) PhysLett B426 231242 (1998)

[124] D Matvienko et al (Belle collaboration) Phys Rev D92 no 1 012013 (2015)arXiv150503362 [hep-ex]

[125] P Krokovny et al (Belle collaboration) Phys Rev Lett 91 262002 (2003)arXivhep-ex0308019 [hep-ex]

[126] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 181801 (2004)arXivhep-ex0408041 [hep-ex]

[127] S K Choi et al (Belle collaboration) Phys Rev D91 no 9 092011 (2015)arXiv150402637 [hep-ex] [Addendum Phys RevD92no3039905(2015)]

[128] A Drutskoy et al (Belle collaboration) Phys Rev Lett 94 061802 (2005)arXivhep-ex0409026 [hep-ex]

[129] B Aubert et al (BABAR collaboration) Phys Rev D74 031103 (2006)arXivhep-ex0605036 [hep-ex]

49

[130] S Chekanov et al (ZEUS Collaboration collaboration) EurPhysJ C60 2545 (2009)arXiv08071290 [hep-ex]

[131] A Heister et al (ALEPH Collaboration collaboration) PhysLett B526 3449 (2002)arXivhep-ex0112010 [hep-ex]

[132] B Aubert et al (BABAR collaboration) Phys Rev Lett 103 051803 (2009)arXiv08080333 [hep-ex]

[133] G Burdman E Golowich J L Hewett and S Pakvasa Phys Rev D66 014009 (2002)arXivhep-ph0112235 [hep-ph]

[134] S Fajfer A Prapotnik S Prelovsek P Singer and J Zupan Nucl Phys Proc Suppl 1159397 (2003) arXivhep-ph0208201 [hep-ph]

[135] S Fajfer N Kosnik and S Prelovsek Phys Rev D76 074010 (2007) arXiv07061133[hep-ph]

[136] E Golowich J Hewett S Pakvasa and A A Petrov Phys Rev D79 114030 (2009)arXiv09032830 [hep-ph]

[137] A Paul I I Bigi and S Recksiegel Phys Rev D82 094006 (2010) arXiv10083141[hep-ph]

[138] A Borisov (2011) arXiv11123269 [hep-ph]

[139] R-M Wang J-H Sheng J Zhu Y-Y Fan and Y Gao Int J Mod Phys A29 no 291450169 (2014)

[140] S de Boer and G Hiller Phys Rev D93 no 7 074001 (2016) arXiv151000311 [hep-ph]

[141] P Rubin et al (CLEO collaboration) Phys Rev D82 092007 (2010) arXiv10091606[hep-ex]

[142] V Abazov et al (D0 collaboration) Phys Rev Lett 100 101801 (2008) arXiv07082094[hep-ex]

[143] R Aaij et al (LHCb collaboration) Phys Lett B728 234243 (2014) arXiv13102535[hep-ex]

[144] R Aaij et al (LHCb collaboration) Phys Lett B724 203212 (2013) arXiv13046365[hep-ex]

[145] T Coan et al (CLEO collaboration) Phys Rev Lett 90 101801 (2003)arXivhep-ex0212045 [hep-ex]

[146] M Ablikim et al (BESIII collaboration) Phys Rev D91 no 11 112015 (2015)arXiv150503087 [hep-ex]

[147] J P Lees et al (BABAR collaboration) Phys Rev D85 091107 (2012) arXiv11106480[hep-ex]

[148] N K Nisar et al (Belle collaboration) Phys Rev D93 no 5 051102 (2016)arXiv151202992 [hep-ex]

[149] P Haas et al (CLEO collaboration) Phys Rev Lett 60 1614 (1988)

50

[150] H Albrecht et al (ARGUS collaboration) Phys Lett B209 380 (1988)

[151] J Adler et al (MARK-III collaboration) Phys Rev D37 2023 (1988) Erratum ibid D40(1989) 3788

[152] A Freyberger et al (CLEO collaboration) Phys Rev Lett 76 30653069 (1996)

[153] D Pripstein et al (E789 collaboration) Phys Rev D61 032005 (2000)arXivhep-ex9906022 [hep-ex]

[154] E Aitala et al (E791 collaboration) Phys Lett B462 401409 (1999)arXivhep-ex9906045 [hep-ex]

[155] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 191801 (2004)arXivhep-ex0408023 [hep-ex]

[156] M Petric et al (Belle collaboration) Phys Rev D81 091102 (2010) arXiv10032345[hep-ex]

[157] K Kodama et al (E653 collaboration) Phys Lett B345 8592 (1995)

[158] I Abt et al (HERA-B collaboration) Phys Lett B596 173183 (2004)arXivhep-ex0405059 [hep-ex]

[159] T Aaltonen et al (CDF collaboration) Phys Rev D82 091105 (2010) arXiv10085077[hep-ex]

[160] R Aaij et al (LHCb collaboration) Phys Lett B725 1524 (2013) arXiv13055059[hep-ex]

[161] E Aitala et al (E791 collaboration) Phys Rev Lett 86 39693972 (2001)arXivhep-ex0011077 [hep-ex]

[162] J Adler et al (MARK-III collaboration) Phys Rev D40 906 (1989)

[163] J Becker et al (MARK-III collaboration) Phys Lett B193 147 (1987)

[164] R Aaij et al (LHCb collaboration) Phys Lett B754 167175 (2016) arXiv151200322[hep-ex]

[165] P Rubin et al (CLEO collaboration) Phys Rev D79 097101 (2009) arXiv09041619[hep-ex]

[166] P Frabetti et al (E687 collaboration) Phys Lett B398 239244 (1997)

[167] J P Lees et al (BABAR collaboration) Phys Rev D84 072006 (2011) arXiv11074465[hep-ex]

[168] (BESIII collaboration) M-G Zhao D rareforbidden decays at BESIII in 7th International

Workshop on Charm Physics (Charm 2015) Detroit MI USA May 18-22 2015 2016arXiv160508952 [hep-ex]httpinspirehepnetrecord1466292filesarXiv160508952pdf

[169] J Link et al (FOCUS collaboration) Phys Lett B572 2131 (2003)arXivhep-ex0306049 [hep-ex]

51

  • Introduction
  • D decays
    • Interplay of direct and indirect CP violation
    • Semileptonic decays
      • Introduction
      • DP decays
      • Form factor parameterizations
      • Simple pole
      • z expansion
      • Three-pole formalism
      • Experimental techniques and results
      • Combined results for the DK channel
      • Combined results for the D channel
      • Vcs and Vcd determination
      • DV decays
      • Form factor measurements
        • Excited D(s) mesons
        • Rare and forbidden decays
          • References
Page 8: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

0015 0010 0005 0000 0005 0010

aindCP

0015

0010

0005

0000

0005

0010

0015

∆adirCP

Contours contain 68 95 99 CL

CD

F

LHC

b S

L

LHC

b p

rom

pt

BaBarBelleCDF KK+ππLHCb SL KK+ππ

LHCb prompt KKLHCb prompt ππ

HFAG-charmWinter 16

no CPV

BaBar

Belle

CDF

LHCb

Figure 1 Plot of all data and the t result Individual measurements are plotted as bandsshowing their plusmn1σ range The no-CPV point (00) is shown as a lled circle and the best tvalue is indicated by a cross showing the one-dimensional uncertainties Two-dimensional 68CL 95 CL and 997 CL regions are plotted as ellipses

8

22 Semileptonic decays

221 Introduction

Semileptonic decays of D mesons involve the interaction of a leptonic current with a hadroniccurrent The latter is nonperturbative and cannot be calculated from rst principles thus it isusually parameterized in terms of form factors The transition matrix element is written

M = minusi GFradic2Vcq L

microHmicro (7)

where GF is the Fermi constant and Vcq is a CKM matrix element The leptonic current Lmicro isevaluated directly from the lepton spinors and has a simple structure this allows one to extractinformation about the form factors (in Hmicro) from data on semileptonic decays [19] Converselybecause there are no strong nal-state interactions between the leptonic and hadronic systemssemileptonic decays for which the form factors can be calculated allow one to determine Vcq [2]

222 DrarrP`ν` decays

When the nal state hadron is a pseudoscalar the hadronic current is given by

Hmicro = 〈P (p)|qγmicroc|D(pprime)〉 = f+(q2)

[(pprime + p)micro minus

m2D minusm2

P

q2qmicro

]+ f0(q2)

m2D minusm2

P

q2qmicro (8)

where mD and pprime are the mass and four momentum of the parent D meson mP and p are thoseof the daughter meson f+(q2) and f0(q2) are form factors and q = pprime minus p Kinematics requirethat f+(0) = f0(0) The contraction qmicroL

micro results in terms proportional to m` [20] and thus for` = e the terms proportionals to qmicro in Eq (8) are negligible For light leptons only the f+(q2)vector form factor is relevant and the dierential partial width is

dΓ(D rarr P`ν`)

dq2 d cos θ`=

G2F |Vcq|2

32π3plowast 3|f+(q2)|2 sin θ2

` (9)

where plowast is the magnitude of the momentum of the nal state hadron in the D rest frame andθ` is the angle of the lepton in the `ν rest frame with respect to the direction of the pseudoscalarmeson in the D rest frame

223 Form factor parameterizations

The form factor is traditionally parameterized with an explicit pole and a sum of eective poles

f+(q2) =f+(0)

(1minus α)

[(1

1minus q2m2pole

)+

Nsumk=1

ρk1minus q2(γkm2

pole)

] (10)

where ρk and γk are expansion parameters and α is a parameter that normalizes the formfactor at q2 = 0 f+(0) The parameter mpole is the mass of the lowest-lying cq resonance withthe vector quantum numbers this is expected to provide the largest contribution to the formfactor for the crarr q transition The sum over N gives the contribution of higher mass statesFor example for D rarr π transitions the dominant resonance is expected to be Dlowast(2010) andthus mpole = mDlowast(2010) For D rarr K transitions the dominant contribution is expected from

Dlowasts(2112) with mpole = mDlowasts (2112)

9

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Comparison between CLEO-c and BABAR results for the quantities q2H20 (q2) and

q2h0(q2)H0(q2)

Table 11 Results for rV and r2 from various experiments

Experiment Ref rV r2

D+ rarr Klowast0l+ν

E691 [54] 20plusmn 06plusmn 03 00plusmn 05plusmn 02E653 [55] 200plusmn 033plusmn 016 082plusmn 022plusmn 011E687 [56] 174plusmn 027plusmn 028 078plusmn 018plusmn 011

E791 (e) [57] 190plusmn 011plusmn 009 071plusmn 008plusmn 009E791 (micro) [58] 184plusmn011plusmn009 075plusmn008plusmn009Beatrice [59] 145plusmn 023plusmn 007 100plusmn 015plusmn 003FOCUS [60] 1504plusmn0057plusmn0039 0875plusmn0049plusmn0064

D0 rarr K0πminusmicro+ν

FOCUS [61] 1706plusmn0677plusmn0342 0912plusmn0370plusmn0104BABAR [62] 1493plusmn 0014plusmn 0021 0775plusmn 0011plusmn 0011

D+s rarr φ e+νBABAR [63] 1849plusmn0060plusmn0095 0763plusmn0071plusmn0065

D0 D+ rarr ρ eνCLEO [64] 140plusmn025plusmn003 057plusmn018plusmn006

23

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

HFLAV())+-amp

Figure 7 A comparison of r2 (lled inverted triangles) and rV (open triangles) values fromvarious experiments The rst seven measurements are for D+ rarr Kminusπ+l+νl decays Alsoshown as a line with 1-σ limits is the average of these The last two points are D+

s and D0

decays

24

23 Excited D(s) mesons

Excited charm meson states have received increased attention since the rst observation ofstates that could not be accommodated by QCD predictions [70 71 72 73] Tables 12 13and 14 summarize recent measurements of the masses and widths of excited D and Ds mesonsrespectively If a preferred assignment of spin and parity was measured it is listed in the columnJP where the label natural denotes JP = 0minus 1+ 2minus and unnatural JP = 0+ 1minus 2+ Ifpossible an average mass and width was calculated which is listed in the gray shaded rowThe calculation of the averages assumes no correlation between individual measurements Asummary of the averaged masses and widths is shown in Figure 8

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

0+ 1+ 2+ 1minus 1 3minus

unnatu

ral

Dlowast s0

(2317)plusmn

Ds1

(2460)plusmn

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn D

sJ(3

040)plusmn

HFAG-charmAugust 2016

(a)

Mas

s[M

eVc

2]

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

0+ 1+ 2+ 0minus 1minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ralDlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn

D(2

550)0

D(2

580)0

D(2

600)0

D(2

600)plusmn

Dlowast (

2640)plusmn

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(b)

Mas

s[M

eVc

2]

0

50

100

150

200

250

300

350

400

450

500

550

1+ 2+ 1minus 1 3minus

unnatu

ral

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn

DsJ

(3040)plusmn

HFAG-charmAugust 2016

(c)

Wid

th[M

eV]

50100150200250300350400450500550600650700

0+ 1+ 2+ 0minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ral

Dlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn D(2

550)0

D(2

580)0

D(2

600)0

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(d)

Wid

th[M

eV]

Figure 8 Averaged masses for Ds mesons are shown in subgure (a) and for D mesons insubgure (b) The average widths for Ds mesons are shown in subgure (c) and for D mesonsin subgure (d) The vertical shaded regions distinguish between dierent spin parity states

The masses and widths of narrow (Γ lt 50 MeV) orbitally excited D mesons (denotedDlowastlowast) both neutral and charged are well established Measurements of broad states (Γ sim200400 MeV) are less abundant as identifying the signal is more challenging There is aslight discrepancy between the Dlowast0(2400)0 masses measured by the Belle [74] and FOCUS [75]experiments No data exist yet for the D1(2430)plusmn state Dalitz plot analyses of B rarr D(lowast)ππ

25

decays strongly favor the assignments 0+ and 1+ for the spin-parity quantum numbers of theDlowast0(2400)0Dlowast0(2400)plusmn and D1(2430)0 states respectively The measured masses and widthsas well as the JP values are in agreement with theoretical predictions based on potentialmodels [76777879]

Tables 15 and 16 summarizes the branching fractions of B mesons decays to excited D andDs states respectively It can be noted that the branching fractions for B mesons decaying to anarrow Dlowastlowast state and a pion are similar for charged and neutral B initial states the branchingfractions to a broad Dlowastlowast state and π+ are much larger for B+ than for B0 This may be dueto the fact that color-suppressed amplitudes contribute only to the B+ decay and not to theB0 decay (for a theoretical discussion see Ref [8081]) Measurements of individual branchingfractions of D mesons are dicult due to the unknown fragmentation of cc rarr Dlowastlowast or due tothe unknown B rarr DlowastlowastX branching fractions

The discoveries of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn have triggered increased interest in prop-erties of and searches for excited Ds mesons (here generically denoted D

lowastlowasts ) While the masses

and widths of Ds1(2536)plusmn and Ds2(2573)plusmn states are in relatively good agreement with po-tential model predictions the masses of Dlowasts0(2317)plusmn and Ds1(2460)plusmn states are signicantlylower than expected (see Ref [82] for a discussion of cs models) Moreover the mass splittingbetween these two states greatly exceeds that between the Ds1(2536)plusmn and Ds2(2573)plusmn Theseunexpected properties have led to interpretations of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn as exoticfour-quark states [8384]

While there are few measurements of the JP values of Dlowasts0(2317)plusmn andDs1(2460)plusmn the avail-able data favor 0+ and 1+ respectively A molecule-like (DK) interpretation of the Dlowasts0(2317)plusmn

and Ds1(2460)plusmn [8384] that can account for their low masses and isospin-breaking decay modesis tested by searching for charged and neutral isospin partners of these states thus far suchsearches have yielded negative results Therefore the subset of models that predict equal pro-duction rates for dierent charged states is excluded The molecular picture can also be testedby measuring the rates for the radiative processes Dlowasts0(2317)plusmnDs1(2460)plusmn rarr D

(lowast)s γ and com-

paring to theoretical predictions The predicted rates however are below the sensitivity ofcurrent experiments

Another model successful in explaining the total widths and the Dlowasts0(2317)plusmn Ds1(2460)plusmn

mass splitting is based on the assumption that these states are chiral partners of the groundstates D+

s and Dlowasts [85] While some measured branching fraction ratios agree with predictedvalues further experimental tests with better sensitivity are needed to conrm or refute thisscenario A summary of the mass dierence measurements is given in Table 17

Measurements by BABAR [86] and LHCb [87] rst indicated the existence of a strange-charm DlowastsJ(2860)plusmn meson An LHCb study of B0

s rarr D0Kminusπ+ decays in which they searchedfor excited Ds mesons [88] showed with 10σ signicance that this state is comprised of twodierent particles one of spin 1 and one of spin 3 This represents the rst measurement of aheavy avored spin-3 particle and the rst observation B mesons decays to spin 3 particlesA subsequent study of DsJ mesons by the LHCb collaboration [89] supports the natural parityassignment for this state (JP = 3minus) This study also shows weak evidence for a further structureat a mass around 3040 MeVc2 with unnatural parity which was rst hinted at by a Babaranalysis [86]

Recent evidence shows that the 1D family of charm resonances can be explored in the Dalitzplot analyses of B-meson decays in the same way as seen for the charm-strange resonances TheLHCb collaboration performed an analysis of B0 rarr D0π+πminus decays in which they measured

26

the spin-parity assignment of the stateDlowast3(2760)plusmn which was observed previously by BABAR [29]and LHCb [30] to be JP = 3minus The measurement suggests a spectroscopic assignment of 3D3This is the second observation of a spin-3 charm meson

Other observed excited Ds states include Ds1(2700)plusmn and Ds2(2573)plusmn The properties ofboth (mass width JP ) have been measured and determined in several analyses A theoreticaldiscussion [90] investigates the possibility that theDs1(2700)plusmn could represent radial excitationsof the Dlowastplusmns Similarly the Ds1(2860)plusmn and DsJ(3040)plusmn could be excitations of Dlowasts0(2317)plusmn andDs1(2460)plusmn or Ds1(2536)plusmn respectively

Table 18 summarizes measurements of the polarization amplitude AD (sometimes also re-ferred as helicity parameter) which describes the initial polarization of the D meson In Dlowastlowast

meson decay the helicity distribution varies like 1 + AD cos2 θH where θH is the angle in theDlowast rest frame between the two pions emitted by decay Dlowastlowast rarr Dlowastπ and the Dlowast rarr Dπ Theparameter is sensitive to possible S-wave contributions in the decay In the case of an unpolar-ized D meson decay decaying purely via D-wave the polarization amplitude is predicted to giveAD = 3 Studies of the D1(2420)0 meson by the ZEUS and BABAR collaborations suggest thatthere is an S-wave admixture in the decay which is contrary to Heavy Quark Eective Theorycalculations [9192]

27

Table 12 Recent measurements of mass and width for dierent excited Ds mesons Thecolumn JP list the most signicant assignment of spin and parity If possible an average massor width is calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowasts0(2317)plusmn 0+

D+s π

0 23196plusmn 02plusmn 14 BABAR [93]D+s π

0 23173plusmn 04plusmn 08 BABAR [73]

23180plusmn 08 Our average

Ds1(2460)plusmn 1+

D+s π

0γD+s γD

+s π

+πminus 24601plusmn 02plusmn 08 BABAR [93]D+s π

0γ 2458plusmn 10plusmn 10 BABAR [73]

24596plusmn 07 Our average

Ds1(2536)plusmn 1+

Dlowast+K0S 25357plusmn 06plusmn 05 DOslash [94]

Dlowast+K0S D

lowast0K+ 253478plusmn 031plusmn 040 BABAR [95]D+s π

+πminus 25346plusmn 03plusmn 07 BABAR [93]Dlowast+K0

S Dlowast0K+ 25350plusmn 06plusmn 10 E687 [96]

Dlowast0K+ 25353plusmn 02plusmn 05 CLEO [97]Dlowast+K0

S 25348plusmn 06plusmn 06 CLEO [97]Dlowast0K+ 25352plusmn 05plusmn 15 ARGUS [98]Dlowast+K0

S 25356plusmn 07plusmn 04 CLEO [99]Dlowast+K0

S 25359plusmn 06plusmn 20 ARGUS [100]Dlowast+K0

S 092plusmn 003plusmn 004 BABAR [101]

253510plusmn 026 092plusmn 005 Our average

Dlowasts2(2573)plusmn 2+

D0K+ Dlowast+K0S 256839plusmn 029plusmn 026 169plusmn 05plusmn 06 LHCb [102]

D+K0S D

0K+ 25694plusmn 16plusmn 05 121plusmn 45plusmn 16 LHCb [103]D+K0

S D0K+ 25722plusmn 03plusmn 10 271plusmn 06plusmn 56 BABAR [104]

D0K+ 257425plusmn 33plusmn 16 104plusmn 83plusmn 30 ARGUS [105]D0K+ 25732+17

minus16 plusmn 09 16+5minus4 plusmn 3 CLEO [106]

256908plusmn 035 169plusmn 08 Our average

Dlowasts1(2700)plusmn 1minus

Dlowast+K0S D

lowast0K+ 27323plusmn 43plusmn 58 136plusmn 19plusmn 24 LHCb [89]D0K+ 2699+14

minus7 127+24minus19 BABAR [107]

Dlowast+K0S D

lowast0K+ 27092plusmn 19plusmn 45 1158plusmn 73plusmn 121 LHCb [87]DKDlowastK 2710plusmn 2+12

minus7 149plusmn 7+39minus52 BABAR [86]

D0K+ 2708plusmn 9+11minus10 108plusmn 2+36

minus31 Belle [108]

27120plusmn 15 1215plusmn 102 Our average

Dlowasts1(2860)plusmn 1 D0K+ 2859plusmn 12plusmn 24 159plusmn 23plusmn 77 LHCb [88]

Dlowasts3(2860)plusmn 3minusDlowast+K0

S Dlowast0K+ 28671plusmn 43plusmn 19 50plusmn 11plusmn 13 LHCb [89]

D0K+ 28605plusmn 26plusmn 65 53plusmn 7plusmn 7 LHCb [88]

28650plusmn 39 522plusmn 86 Our average

DsJ(3040)plusmn Unnatural DlowastK 3044plusmn 8+30minus5 239plusmn 35+46

minus42 BABAR (m amp Γ) + LHCb(JP ) [86]+ [89]

28

Table 13 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast0(2400)0 0+

D+πminus 2297plusmn 8plusmn 20 273plusmn 12plusmn 48 BABAR [109]D+πminus 2308plusmn 17plusmn 32 276plusmn 21plusmn 63 Belle [74]D+πminus 2407plusmn 21plusmn 35 240plusmn 55plusmn 59 Focus [75]

23182plusmn 169 2674plusmn 356 Our average

Dlowast0(2400)plusmn 0+

D0π+ 2349plusmn 6plusmn 1plusmn 4 217plusmn 13plusmn 5plusmn 12 LHCb [110]D0π+ 2360plusmn 15plusmn 12plusmn 28 255plusmn 26plusmn 20plusmn 47 LHCb [111]D0π+ 2403plusmn 14plusmn 35 283plusmn 24plusmn 34 Focus(m ampΓ) + Belle(JP ) [75] + [112]

23506plusmn 59 2337plusmn 155 Our average

D1(2420)0 1+

Dlowast+πminus 24196plusmn 01plusmn 07 352plusmn 04plusmn 09 LHCb [30]Dlowast+πminus 24231plusmn 15+04

minus10 388plusmn 5+19minus54 Zeus [113]

Dlowast+πminus 24201plusmn 01plusmn 08 314plusmn 05plusmn 13 BABAR [29]Dlowast+πminus 200plusmn 17plusmn 13 CDF [114]D0π+πminus 2426plusmn 3plusmn 1 24plusmn 7plusmn 8 Belle [115]Dlowast+πminus 24214plusmn 15plusmn 09 237plusmn 27plusmn 40 Belle [74]Dlowast+πminus 2421+1

minus2 plusmn 2 20+6minus5

+3minus3 CLEO [116]

Dlowast+πminus 2422plusmn 2plusmn 2 15plusmn 8plusmn 4 E687 [96]Dlowast+πminus 2428plusmn 3plusmn 2 23+8

minus6+10minus4 CLEO [99]

Dlowast+πminus 2414plusmn 2plusmn 5 13plusmn 6+10minus5 ARGUS [117]

Dlowast+πminus 2428plusmn 8plusmn 5 58plusmn 14plusmn 10 TPS [118]

24205plusmn 05 317plusmn 07 Our average

D1(2420)plusmn 1+

Dlowast0π+ 24219plusmn 47+34minus12 Zeus [113]

D+πminusπ+ 2421plusmn 2plusmn 1 21plusmn 5plusmn 8 Belle [115]Dlowast0π+ 2425plusmn 2plusmn 2 26+8

minus7 plusmn 4 CLEO [119]Dlowast0π+ 2443plusmn 7plusmn 5 41plusmn 19plusmn 8 TPS [118]

24232plusmn 16 252plusmn 60 Our average

D1(2430)0 1+ Dlowast+πminus 2427plusmn 26plusmn 25 384+107minus75 plusmn 74 Belle [74]

Dlowast2(2460)0 2+

Dlowast+πminus 24640plusmn 14plusmn 05plusmn 02 438plusmn 29plusmn 17plusmn 06 LHCb [120]Dlowast+πminus 24604plusmn 04plusmn 12 432plusmn 12plusmn 30 LHCb [30]D+πminus 24604plusmn 01plusmn 01 456plusmn 04plusmn 11 LHCb [30]

Dlowast+πminus D+πminus 24625plusmn 24+13minus11 466plusmn 81+59

minus38 Zeus [113]D+πminus 24622plusmn 01plusmn 08 505plusmn 06plusmn 07 BABAR [29]D+πminus 24604plusmn 12plusmn 22 418plusmn 25plusmn 29 BABAR [109]D+πminus 492plusmn 23plusmn 13 CDF [114]D+πminus 24616plusmn 21plusmn 33 456plusmn 44plusmn 67 Belle [74]D+πminus 24645plusmn 11plusmn 19 387plusmn 53plusmn 29 Focus [75]D+πminus 2465plusmn 3plusmn 3 28+8

minus7 plusmn 6 CLEO [116]D+πminus 2453plusmn 3plusmn 2 25plusmn 10plusmn 5 E687 [96]Dlowast+πminus 2461plusmn 3plusmn 1 20+9

minus12+9minus10 CLEO [99]

D+πminus 2455plusmn 3plusmn 5 15+13minus10

+5minus10 ARGUS [121]

D+πminus 2459plusmn 3plusmn 2 20plusmn 10plusmn 5 TPS [118]

246049plusmn 017 4752plusmn 065 Our average

29

Table 14 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast2(2460)plusmn 2+

D0π+ 24686plusmn 06plusmn 00plusmn 03 473plusmn 15plusmn 03plusmn 06 LHCb [110]D0π+ 24656plusmn 18plusmn 05plusmn 12 460plusmn 34plusmn 14plusmn 29 LHCb [111]D0π+ 24631plusmn 02plusmn 06 486plusmn 13plusmn 19 LHCb [30]

Dlowast0π+ D0π+ 24606plusmn 44+36minus08 Zeus [113]

D0π+ 24654plusmn 02plusmn 11 BABAR [29]D0π+ 24657plusmn 18+14

minus48 497plusmn 38plusmn 64 Belle [112]D0π+ 24676plusmn 15plusmn 08 341plusmn 65plusmn 42 Focus [75]D0π+ 2463plusmn 3plusmn 3 27+11

minus8 plusmn 5 CLEO [119]D0π+ 2453plusmn 3plusmn 2 23plusmn 9plusmn 5 E687 [96]D0π+ 2469plusmn 4plusmn 6 ARGUS [122]

246555plusmn 040 467plusmn 12 Our average

D(2550)0 0minus Dlowast+πminus 25394plusmn 45plusmn 68 130plusmn 12plusmn 13 BABAR [29]

D(2580)0 Unnatural Dlowast+πminus 25795plusmn 34plusmn 55 1175plusmn 178plusmn 460 LHCb [30]

D(2600)0 Natural D+πminus 26087plusmn 24plusmn 25 93plusmn 6plusmn 13 BABAR [29]

D(2600)plusmn Natural D0π+ 26213plusmn 37plusmn 42 BABAR [29]

Dlowast(2640)plusmn 1minus Dlowast+π+πminus 2637plusmn 2plusmn 6 Delphi [123]

Dlowast(2650)0 Natural Dlowast+πminus 26492plusmn 35plusmn 35 1402plusmn 171plusmn 186 LHCb [30]

D(2740)0 Unnatural Dlowast+πminus 27370plusmn 35plusmn 112 732plusmn 134plusmn 250 LHCb [30]

D(2750)0 Dlowast+πminus 27524plusmn 17plusmn 27 71plusmn 6plusmn 11 BABAR [29]

Dlowast1(2760)0 1+

D+πminus 2781plusmn 18plusmn 11plusmn 6 177plusmn 32plusmn 20plusmn 7 LHCb [120]Dlowast+πminus 27611plusmn 51plusmn 65 744plusmn 34plusmn 370 LHCb [30]D+πminus 27601plusmn 11plusmn 37 744plusmn 34plusmn 191 LHCb [30]D+πminus 27633plusmn 23plusmn 23 609plusmn 51plusmn 36 BABAR [29]

27621plusmn 24 651plusmn 58 Our average

Dlowast3(2760)plusmn 3minus

D0π+ 2798plusmn 7plusmn 1plusmn 7 105plusmn 18plusmn 6plusmn 23 LHCb [110]D0π+ 27717plusmn 17plusmn 38 667plusmn 66plusmn 105 LHCb [30]D0π+ 27697plusmn 38plusmn 15 BABAR [29]

27739plusmn 33 723plusmn 115 Our average

30

Table 15 Product of B meson branching fraction and (daughter) excited D meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowast0(2400)0

Bminus rarr Dlowast0(2400)0(rarr D+π+)πminus61plusmn 06plusmn 18 Belle [74]68plusmn 03plusmn 20 BABAR [109]

64plusmn 14 Our average

Bminus rarr Dlowast0(2400)0(rarr D+π+)Kminus 0061plusmn 0019plusmn 0005plusmn 0014plusmn 0004 LHCb [120]

Dlowast0(2400)plusmnB0 rarr Dlowast0(2400)+(rarr D0π+)πminus

077plusmn 005plusmn 003plusmn 003plusmn 004 LHCb [110]060plusmn 013plusmn 027 Belle [112]

076plusmn 007 Our average

B0 rarr Dlowast0(2400)+(rarr D0π+)Kminus 0177plusmn 0026plusmn 0019plusmn 0067plusmn 020 LHCb [111]

D1(2420)0

Bminus rarr D1(2420)0(rarr Dlowast+πminus)πminus 68plusmn 07plusmn 13 Belle [74]

Bminus rarr D1(2420)0(rarr D0π+πminus)πminus 185plusmn 029plusmn 027plusmn 041 Belle [115]

B0 rarr D1(2420)0(rarr Dlowast+πminus)ω 07plusmn 02+01minus00 plusmn 01 Belle [124]

D1(2420)plusmn B0 rarr D1(2420)+(rarr D+πminusπ+)πminus 089plusmn 015plusmn 022 Belle [115]

D1(2430)0Bminus rarr D1(2430)0(rarr Dlowast+πminus)πminus 50plusmn 04plusmn 108 Belle [74]

B0 rarr D1(2430)0(rarr Dlowast+πminus)ω 25plusmn 04+07minus02

+04minus01 Belle [124]

Dlowast2(2460)0

Bminus rarr Dlowast2(2460)0(rarr D+πminus)πminus34plusmn 03plusmn 07 Belle [74]35plusmn 02plusmn 05 BABAR [109]

34plusmn 03 Our average

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)πminus 18plusmn 03plusmn 04 Belle [74]

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)ω 04plusmn 01+00minus01 plusmn 01 Belle [124]

Bminus rarr Dlowast2(2460)0(rarr D+π+)Kminus 0232plusmn 0011plusmn 0006plusmn 0010plusmn 0016 LHCb [120]

Dlowast2(2460)plusmnB0 rarr Dlowast2(2460)+(rarr D0π+)πminus

244plusmn 007plusmn 010plusmn 004plusmn 012 LHCb [110]215plusmn 017plusmn 031 Belle [112]

238plusmn 016 Our average

B0 rarr Dlowast2(2460)+(rarr D0π+)Kminus 0212plusmn 0010plusmn 0011plusmn 0011plusmn 025 LHCb [111]

Dlowast1(2760)0 Bminus rarr Dlowast1(2760)0(rarr D+π+)Kminus 0036plusmn 0009plusmn 0003plusmn 0007plusmn 0002 LHCb [120]

Dlowast3(2760)plusmn B0 rarr Dlowast3(2760)0(rarr D0π+)πminus 0103plusmn 0016plusmn 0007plusmn 0008plusmn 0005 LHCb [110]

31

Table 16 Product of B meson branching fraction and (daughter) excited Ds meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowasts0(2317)plusmnB0 rarr Dlowasts0(2317)+(rarr D+

s π0)Dminus

86+33minus26 plusmn 26 Belle [125]

180plusmn 40+67minus50 BABAR [126]

101+13minus12 plusmn 10plusmn 04 Belle [127]

102plusmn 15 Our average

B+ rarr Dlowasts0(2317)+(rarr D+s π

0)D0 80+13minus12 plusmn 10plusmn 04 Belle [127]

B0 rarr Dlowasts0(2317)+(rarr D+s π

0)Kminus 053+015minus013 plusmn 016 Belle [128]

Ds1(2460)plusmn

B0 rarr Ds1(2460)+(rarr Dlowast+s π0)Dminus227+73

minus62 plusmn 68 Belle [125]280plusmn 80+112

minus78 BABAR [126]

247plusmn 76 Our average

B0 rarr Ds1(2460)+(rarr Dlowast+s γ)Dminus82+22minus19 plusmn 25 Belle [125]

80plusmn 20+32minus23 BABAR [126]

81plusmn 23 Our average

Ds1(2460)+ rarr Dlowast+s π0 (56plusmn 13plusmn 9) BABAR [129]

Ds1(2460)+ rarr Dlowast+s γ (16plusmn 4plusmn 3) BABAR [129]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dminus 171plusmn 048plusmn 032 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast+K0)Dminus 261plusmn 103plusmn 031 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dlowastminus 332plusmn 088plusmn 066 BABAR [95]

Ds1(2536)plusmnB0 rarr Ds1(2536)+(rarr Dlowast+K0)Dlowastminus 500plusmn 151plusmn 067 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)D0 216plusmn 052plusmn 045 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)D0 230plusmn 098plusmn 043 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)Dlowast0 546plusmn 117plusmn 104 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)Dlowast0 392plusmn 246plusmn 083 BABAR [95]

Ds2(2573)plusmnB0 rarr Ds2(2573)(rarr D0K+)Dminus 034plusmn 017plusmn 005 BABAR [107]

B+ rarr Ds2(2573)(rarr D0K+)D0 008plusmn 14plusmn 005 BABAR [107]

Ds1(2700)plusmn B+ rarr Ds1(2700)+(rarr D0K+)D0

113plusmn 22+14minus28 Belle [108]

502plusmn 071plusmn 093 BABAR [107]

583plusmn 109 Our average

B0 rarr Ds1(2700)+(rarr D0K+)Dminus 714plusmn 096plusmn 069 BABAR [107]

32

Table 17 Mass dierence measurements for excited D mesons

Resonance Relative to ∆m [MeVc2] Measured by Reference

Dlowast1(2420)0 Dlowast+4102plusmn 21plusmn 09 Zeus [130]4117plusmn 07plusmn 04 CDF [114]

4115plusmn 08 Our average

D1(2420)plusmn Dlowast1(2420)0 4+2minus3 plusmn 3 CLEO [119]

Dlowast2(2460)0 D+ 5939plusmn 06plusmn 05 CDF [114]

Dlowast+ 4588plusmn 37+12minus13 Zeus [130]

Dlowast2(2460)plusmn Dlowast2(2460)0

31plusmn 19plusmn 09 Focus [75]minus2plusmn 4plusmn 4 CLEO [119]14plusmn 5plusmn 8 ARGUS [122]

30plusmn 19 Our average

Dlowasts0(2317)plusmn Dplusmns

3487plusmn 05plusmn 07 Belle [72]3500plusmn 12plusmn 10 CLEO [71]3513plusmn 21plusmn 19 Belle [125]

3492plusmn 07 Our average

Ds1(2460)plusmn

Dlowastplusmns

3441plusmn 13plusmn 11 Belle [72]3512plusmn 17plusmn 10 CLEO [71]3468plusmn 16plusmn 19 Belle [125]

3471plusmn 11 Our average

Dplusmns

4910plusmn 13plusmn 19 Belle [72]4914plusmn 09plusmn 15 Belle [72]

4913plusmn 14 Our average

Ds1(2536)plusmnDlowast(2010)plusmn

52483plusmn 001plusmn 004 BABAR [101]52530+044

minus041 plusmn 010 Zeus [130]5253plusmn 06plusmn 01 ALEPH [131]

52484plusmn 004 Our average

Dlowast(2007)0 5287plusmn 19plusmn 05 ALEPH [131]

Dlowasts2(2573)plusmn D0 704plusmn 3plusmn 1 ALEPH [131]

33

Table 18 Measurements of polarization amplitudes for excited D mesons

Resonance AD Measured by Reference

D1(2420)0

78+67minus27

+46minus18 ZEUS [113]

572plusmn 025 BABAR [29]59+30minus17

+24minus10 ZEUS [130]

38plusmn 06plusmn 08 BABAR [132]

561plusmn 024 Our average

D1(2420)plusmn 38plusmn 06plusmn 08 BABAR [132]

Dlowast2(2460)0 minus116plusmn 035 ZEUS [113]

D(2750)0 minus033plusmn 028 BABAR [29]

34

24 Rare and forbidden decays

This section provides a summary of rare and forbidden charm decays in tabular form The decaymodes can be categorized as avor-changing neutral currents lepton-avor-violating lepton-number-violating and both baryon- and lepton-number-violating decays Figures 9-11 plot theupper limits for D0 D+ D+

s and Λ+c decays Tables 19-22 give the corresponding numerical

results Some theoretical predictions are given in Refs [133134135136137138139140]In several cases the rare-decay nal states have been observed with the di-lepton pair being

the decay product of a hadronic resonance For these measurements the quoted limits are thoseexpected for the non-resonant di-lepton spectrum For the extrapolation to the full spectruma phase-space distribution of the non-resonant component has been assumed This applies tothe CLEO measurement of the decays D+

(s) rarr (K+π+)e+eminus [141] to the D0 measurements

of the decays D+(s) rarr π+micro+microminus [142] and to the BABAR measurements of the decays D+

(s) rarr(K+π+)e+eminus and D+

(s) rarr (K+π+)micro+microminus where the contribution from φ rarr l+lminus (l = e micro) has

been excluded In the case of the LHCb measurements of the decays D0 rarr π+πminusmicro+microminus [143]as well as the decays D+

(s) rarr π+micro+microminus [144] the contributions from φ rarr l+lminus as well as from

ρ ω rarr l+lminus (l = e micro) have been excluded

Table 19 Upper limits at 90 CL for D0 decays

Decay Limit times106 Experiment Referenceγγ 260 CLEO II [145]

38 BESIII [146]22 BaBar [147]085 Belle [148]

e+eminus 2200 CLEO [149]1700 Argus [150]1300 Mark3 [151]130 CLEO II [152]819 E789 [153]62 E791 [154]12 BaBar [155]0079 Belle [156]

micro+microminus 700 Argus [150]440 E653 [157]340 CLEO II [152]156 E789 [153]52 E791 [154]20 HERAb [158]13 BaBar [155]021 CDF [159]014 Belle [156]00062 LHCb [160]

π0e+eminus 450 CLEO II [152]π0micro+microminus 5400 CLEO II [152]

1800 E653 [157]

35

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceη e+eminus 1100 CLEO II [152]η micro+microminus 5300 CLEO II [152]π+πminuse+eminus 3700 E791 [161]ρ0e+eminus 4500 CLEO [149]

1240 E791 [161]1000 CLEO II [152]

π+πminusmicro+microminus 300 E791 [161]055 LHCb [143]

ρ0micro+microminus 8100 CLEO [149]4900 CLEO II [152]2300 E653 [157]220 E791 [161]

ω e+eminus 1800 CLEO II [152]ω micro+microminus 8300 CLEO II [152]K+Kminuse+eminus 3150 E791 [161]φ e+eminus 590 E791 [161]

520 CLEO II [152]K+Kminusmicro+microminus 330 E791 [161]φmicro+microminus 4100 CLEO II [152]

310 E791 [161]

K0e+eminus 17000 Mark3 [162]

1100 CLEO II [152]

K0micro+microminus 6700 CLEO II [152]

2600 E653 [157]Kminusπ+e+eminus 3850 E791 [161]

Klowast0

(892)e+eminus 1400 CLEO II [152]470 E791 [161]

Kminusπ+micro+microminus 3600 E791 [161]

Klowast0

(892)micro+microminus 11800 CLEO II [152]240 E791 [161]

π+πminusπ0micro+microminus 8100 E653 [157]microplusmne∓ 2700 CLEO [149]

1200 Mark3 [163]1000 Argus [150]190 CLEO II [152]172 E789 [153]81 E791 [154]081 BaBar [155]026 Belle [156]0016 LHCb [164]

π0eplusmnmicro∓ 860 CLEO II [152]η eplusmnmicro∓ 1000 CLEO II [152]

36

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceπ+πminuseplusmnmicro∓ 150 E791 [161]ρ0eplusmnmicro∓ 660 E791 [161]

490 CLEO II [152]ω eplusmnmicro∓ 1200 CLEO II [152]K+Kminuseplusmnmicro∓ 1800 E791 [161]φ eplusmnmicro∓ 470 E791 [161]

340 CLEO II [152]

K0eplusmnmicro∓ 1000 CLEO II [152]

Kminusπ+eplusmnmicro∓ 5500 E791 [161]Klowast0(892)eplusmnmicro∓ 1000 CLEO II [152]

830 E791 [161]π∓π∓eplusmneplusmn 1120 E791 [161]π∓π∓microplusmnmicroplusmn 290 E791 [161]K∓π∓eplusmneplusmn 2060 E791 [161]K∓π∓microplusmnmicroplusmn 3900 E791 [161]K∓K∓eplusmneplusmn 1520 E791 [161]K∓K∓microplusmnmicroplusmn 940 E791 [161]π∓π∓eplusmnmicroplusmn 790 E791 [161]K∓π∓eplusmnmicroplusmn 2180 E791 [161]K∓K∓eplusmnmicroplusmn 570 E791 [161]p eminus 100 CLEO [165]p e+ 110 CLEO [165]

37

γγ

ρ0micro

+microminus

π+πminusπ

0micro

+microminus

K+K

minuse

+eminus

ηe

+eminus

φmicro

+microminus

π0e

+eminus

φe

+eminus

ωmicro

+microminus

Kminusπ

+micro

+microminus

ρ0e

+eminus

K0micro

+microminus

Klowast0

(892

)e+eminus

π+πminusmicro

+microminus

micro+microminus

π+πminuse

+eminus

e+eminus

Klowast0

(892

)micro+microminus

K+K

minusmicro

+microminus

Kminusπ

+e

+eminus

π0micro

+microminus

K0e

+eminus

ωe

+eminus

ηmicro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

HFAG-charm

Belle

BESIII

CLEO II

BaBar

E791

CLEO

E653

LHCb

E789

HERAB

CDF

Argus

Mark3

June 16

K∓π∓microplusmnmicroplusmn

ωeplusmnmicro∓

Kminusπ

+eplusmnmicro∓

K∓K∓eplusmnmicroplusmn

π∓π∓eplusmnmicroplusmn

peminus

K∓π∓eplusmnmicroplusmn

π∓π∓eplusmneplusmn

ηeplusmnmicro∓

π∓π∓microplusmnmicroplusmn

K∓K∓eplusmneplusmn

K0eplusmnmicro∓

π+πminuseplusmnmicro∓

K∓K∓microplusmnmicroplusmn

ρ0eplusmnmicro∓

pe

+

φeplusmnmicro∓

microplusmne∓

K+K

minuseplusmnmicro∓

Klowast0

(892

)eplusmnmicro∓

π0eplusmnmicro∓

K∓π∓eplusmneplusmn

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

L BLHFAG-charm

E791

CLEO II

CLEO

Belle

E789

Mark3

Argus

LHCb

BaBar

June 16

Figure 9 Upper limits at 90 CL for D0 decays The top plot shows avor-changing neu-tral current decays and the bottom plot shows lepton-avor-changing (LF) lepton-number-changing (L) and both baryon- and lepton-number-changing (BL) decays38

Kminuse

+micro

+

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminusmicro

+micro

+

K+e

+eminus

π+e

+eminus

πminuse

+micro

+

Kminuse

+e

+

K+micro

+eminus

ρminusmicro

+micro

+

K+e

+microminus

K+eplusmnmicro∓

π+micro

+eminus

π+e

+microminus

πminusmicro

+micro

+

πminuse

+e

+

π+micro

+microminus

ρ+micro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E687

E653

E791

BaBar

Focus

CLEO

BESIII

LHCb

D0

June 16

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminuse

+micro

+

K+e

+eminus

π+e

+eminus

K+eplusmnmicro∓

Kminuse

+e

+

K+micro

+eminus

K+e

+microminus

Klowast+

(892

)micro+microminus

π+micro

+eminus

Kminusmicro

+micro

+

πminusmicro

+micro

+

πminuse

+e

+

πminuse

+micro

+

π+micro

+microminus

K+micro

+microminus

π+e

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E653

E791

CLEO

BaBar

Focus

LHCb

June 16

Figure 10 Upper limits at 90 CL for D+ (top) and D+s (bottom) decays Each plot shows

avor-changing neutral current decays lepton-avor-changing decays (LF) and lepton-number-changing (L) decays 39

pmicro

+microminus

pe

+microminus

σ+micro

+microminus

pe

+e

+

pe

+eminus

pe

+micro

+

pmicro

+micro

+

pmicro

+eminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

LHFAG-charm

BaBar E653

June 16

Figure 11 Upper limits at 90 CL for Λ+c decays Shown are avor-changing neutral current

decays lepton-avor-changing (LF) decays and lepton-number-changing (L) decays

40

Table 20 Upper limits at 90 CL for D+ decays

Decay Limit times106 Experiment Referenceπ+e+eminus 1100 E687 [166]

520 E791 [154]59 CLEO [141]11 BaBar [167]03 BESIII [168]

π+micro+microminus 2200 E653 [157]890 E687 [166]150 E791 [154]88 Focus [169]65 BaBar [167]39 D0 [142]0073 LHCb [144]

ρ+micro+microminus 5600 E653 [157]K+e+eminus 2000 E687 [166]

30 CLEO [141]12 BESIII [168]10 BaBar [167]

π+eplusmnmicro∓ 340 E791 [154]π+e+microminus 1100 E687 [166]

29 BaBar [167]π+micro+eminus 1300 E687 [166]

36 BaBar [167]K+eplusmnmicro∓ 680 E791 [154]K+e+microminus 1300 E687 [166]

12 BaBar [167]K+micro+eminus 1200 E687 [166]

28 BaBar [167]πminuse+e+ 1100 E687 [166]

960 E791 [154]19 BaBar [167]12 BESIII [168]11 CLEO [141]

πminusmicro+micro+ 870 E687 [166]170 E791 [154]48 Focus [169]20 BaBar [167]0022 LHCb [144]

πminuse+micro+ 1100 E687 [166]500 E791 [154]

ρminusmicro+micro+ 5600 E653 [157]Kminuse+e+ 1200 E687 [166]

35 CLEO [141]09 BaBar [167]

41

Table 20 continued from previous pageDecay Limit times106 Experiment Reference

06 BESIII [168]Kminusmicro+micro+ 3200 E653 [157]

1200 E687 [166]130 Focus [169]100 BaBar [167]

Kminuse+micro+ 1300 E687 [166]Klowastminus(892)micro+micro+ 8500 E653 [157]

Table 21 Upper limits at 90 CL for D+s decays

Decay Limit times106 Experiment Referenceπ+e+eminus 2700 E791 [154]

220 CLEO [141]130 BaBar [167]

π+micro+microminus 4300 E653 [157]1400 E791 [154]430 BaBar [167]260 Focus [169]041 LHCb [144]

K+e+eminus 16000 E791 [154]520 CLEO [141]37 BaBar [167]

K+micro+microminus 1400 E791 [154]360 Focus [169]210 BaBar [167]

Klowast+(892)micro+microminus 14000 E653 [157]π+eplusmnmicro∓ 6100 E791 [154]π+e+microminus 120 BaBar [167]π+micro+eminus 200 BaBar [167]K+eplusmnmicro∓ 6300 E791 [154]K+e+microminus 140 BaBar [167]K+micro+eminus 97 BaBar [167]πminuse+e+ 6900 E791 [154]

180 CLEO [141]41 BaBar [167]

πminusmicro+micro+ 4300 E653 [157]820 E791 [154]290 Focus [169]140 BaBar [167]012 LHCb [144]

πminuse+micro+ 7300 E791 [154]Kminuse+e+ 6300 E791 [154]

170 CLEO [141]

42

Table 21 continued from previous pageDecay Limit times106 Experiment Reference

52 BaBar [167]Kminusmicro+micro+ 5900 E653 [157]

1800 E791 [154]130 BaBar [167]

Kminuse+micro+ 6800 E791 [154]Klowastminus(892)micro+micro+ 14000 E653 [157]

Table 22 Upper limits at 90 CL for Λ+c decays

Decay Limit times106 Experiment Referencepe+eminus 55 BaBar [167]pmicro+microminus 3400 E653 [157]

440 BaBar [167]σ+micro+microminus 7000 E653 [157]pe+microminus 99 BaBar [167]pmicro+eminus 190 BaBar [167]p e+e+ 27 BaBar [167]p micro+micro+ 94 BaBar [167]

43

References

[1] N Cabibbo Phys Rev Lett 10 531533 (1963)

[2] M Kobayashi and T Maskawa Prog Theor Phys 49 652657 (1973)

[3] D Abbaneo et al (ALEPH CDF DELPHI L3 OPAL and SLD collaborations)arXivhep-ex0009052 (2000) CERN-EP-2000-096 arXivhep-ex0112028 (2001)CERN-EP-2001-050

[4] Y Amhis et al (Heavy Flavor Averaging Group) (2012) arXiv12071158 [hep-ex]

[5] K Olive et al (Particle Data Group) Chin Phys C38 090001 (2014)

[6] A L Kagan and M D Sokolo Phys Rev D80 076008 (2009) arXiv09073917 [hep-ph]

[7] Y Grossman A L Kagan and Y Nir Phys Rev D75 036008 (2007)arXivhep-ph0609178 [hep-ph]

[8] M Gersabeck M Alexander S Borghi V Gligorov and C Parkes J Phys G39 045005(2012) arXiv11116515 [hep-ex]

[9] J P Lees et al (BABAR collaboration) Phys Rev D87 012004 (2013) arXiv12093896[hep-ex]

[10] R Aaij et al (LHCb collaboration) Phys Rev Lett 112 041801 (2014) arXiv13107201[hep-ex]

[11] T A Aaltonen et al (CDF collaboration) Phys Rev D90 no 11 111103 (2014)arXiv14105435 [hep-ex]

[12] R Aaij et al (LHCb collaboration) JHEP 04 043 (2015) arXiv150106777 [hep-ex]

[13] M Staripound et al (Belle collaboration) Phys Lett B753 412418 (2016) arXiv150908266[hep-ex]

[14] B Aubert et al (BABAR collaboration) Phys Rev Lett 100 061803 (2008)arXiv07092715 [hep-ex]

[15] B Ko (Belle collaboration) PoS ICHEP2012 353 (2013) arXiv12121975

[16] T Aaltonen et al (CDF collaboration) Phys Rev Lett 109 111801 (2012)arXiv12072158 [hep-ex]

[17] R Aaij et al (LHCb collaboration) JHEP 07 041 (2014) arXiv14052797 [hep-ex]

[18] R Aaij et al (LHCb collaboration) Phys Rev Lett 116 no 19 191601 (2016)arXiv160203160 [hep-ex]

[19] T Becher and R J Hill Phys Lett B633 6169 (2006) arXivhep-ph0509090 [hep-ph]

[20] F J Gilman and R L Singleton Phys Rev D41 142 (1990)

[21] R J Hill eConf C060409 027 (2006) arXivhep-ph0606023 [hep-ph]

[22] D Becirevic and A B Kaidalov Phys Lett B478 417423 (2000) arXivhep-ph9904490[hep-ph]

44

[23] C G Boyd B Grinstein and R F Lebed Phys Rev Lett 74 46034606 (1995)arXivhep-ph9412324 [hep-ph]

[24] C G Boyd and M J Savage Phys Rev D56 303311 (1997) arXivhep-ph9702300[hep-ph]

[25] M C Arnesen B Grinstein I Z Rothstein and I W Stewart Phys Rev Lett 95 071802(2005)

[26] C Bourrely B Machet and E de Rafael Nucl Phys B189 157 (1981)

[27] D Becirevic A L Yaouanc A Oyanguren P Roudeau and F Sanlippo (2014)arXiv14071019 [hep-ph]

[28] J P Lees et al (BABAR collaboration) Phys Rev D88 052003 (2013) arXiv13045009[hep-ex]

[29] P del Amo Sanchez et al (BaBar Collaboration collaboration) PhysRev D82 111101(2010) arXiv10092076 [hep-ex]

[30] R Aaij et al (LHCb collaboration) JHEP 1309 145 (2013) arXiv13074556

[31] G Burdman and J Kambor Phys Rev D55 28172826 (1997) arXivhep-ph9602353[hep-ph]

[32] D Becirevic A Le Yaouanc L Oliver J-C Raynal P Roudeau and J Serrano Phys RevD87 no 5 054007 (2013) arXiv12065869 [hep-ph]

[33] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052022 (2015)arXiv14125502 [hep-ex]

[34] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 7 072012 (2015)arXiv150807560 [hep-ex]

[35] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 11 112008 (2015)arXiv151000308 [hep-ex]

[36] L Widhalm et al (Belle collaboration) Phys Rev Lett 97 061804 (2006)arXivhep-ex0604049 [hep-ex]

[37] B Aubert et al (BABAR collaboration) Phys Rev D76 052005 (2007) arXiv07040020[hep-ex]

[38] D Besson et al (CLEO collaboration) Phys Rev D80 032005 (2009) arXiv09062983[hep-ex]

[39] S Dobbs et al (CLEO collaboration) Phys Rev D77 112005 (2008) arXiv07121020[hep-ex]

[40] G Huang et al (CLEO collaboration) Phys Rev Lett 94 011802 (2005)arXivhep-ex0407035 [hep-ex]

[41] J Link et al (FOCUS collaboration) Phys Lett B607 233242 (2005)arXivhep-ex0410037 [hep-ex]

[42] J Adler et al (MARK-III collaboration) Phys Rev Lett 62 1821 (1989)

45

[43] K Kodama et al (Fermilab E653 collaboration) Phys Rev Lett 66 18191822 (1991)

[44] K Kodama et al (E653 collaboration) Phys Lett B336 605613 (1994)

[45] P L Frabetti et al (E687 collaboration) Phys Lett B364 127136 (1995)

[46] P L Frabetti et al (E687 collaboration) Phys Lett B315 203208 (1993)

[47] J C Anjos et al (Tagged Photon Spectrometer collaboration) Phys Rev Lett 6215871590 (1989)

[48] M Ablikim et al (BES collaboration) Phys Lett B597 3946 (2004)arXivhep-ex0406028 [hep-ex]

[49] M Ablikim et al (BES collaboration) (2006) arXivhep-ex0610019 [hep-ex]

[50] A Bean et al (CLEO collaboration) Phys Lett B317 647654 (1993)

[51] BESIII collaboration presented at ICHEP 2014 conference 2014httpindicoificuvesindicogetFilepyaccesscontribId=69ampsessionId=25ampresId=

0ampmaterialId=slidesampconfId=2025

[52] J G Korner and G A Schuler Z Phys C46 93 (1990)

[53] FLAG collaboration httpitpwikiunibechagimages44bFLAGpdf 2014httpitpwikiunibechflagimages44bFLAGpdf

[54] J Anjos et al (Fermilab E691 collaboration) Phys Rev Lett 65 26302633 (1990)

[55] K Kodama et al (Fermilab E653 collaboration) Phys Lett B274 246252 (1992)

[56] P Frabetti et al (Fermilab E687 collaboration) Phys Lett B307 262268 (1993)

[57] E Aitala et al (E791 collaboration) Phys Rev Lett 80 13931397 (1998)arXivhep-ph9710216 [hep-ph]

[58] E Aitala et al (E791 collaboration) Phys Lett B440 435441 (1998)arXivhep-ex9809026 [hep-ex]

[59] M Adamovich et al (BEATRICE collaboration) Eur Phys J C6 3541 (1999)

[60] J Link et al (FOCUS collaboration) Phys Lett B544 8996 (2002)arXivhep-ex0207049 [hep-ex]

[61] J Link et al (FOCUS collaboration) Phys Lett B607 6777 (2005)arXivhep-ex0410067 [hep-ex]

[62] P del Amo Sanchez et al (BABAR collaboration) Phys Rev D83 072001 (2011)arXiv10121810 [hep-ex]

[63] B Aubert et al (BABAR collaboration) Phys Rev D78 051101 (2008) arXiv08071599[hep-ex]

[64] H Mahlke eConf C0610161 014 (2006) arXivhep-ex0702014 [hep-ex]

[65] J Link et al (FOCUS collaboration) Phys Lett B535 4351 (2002)arXivhep-ex0203031 [hep-ex]

46

[66] K M Ecklund et al (CLEO collaboration) Phys Rev D80 052009 (2009)arXiv09073201 [hep-ex]

[67] R A Briere et al (CLEO collaboration) Phys Rev D81 112001 (2010) arXiv10041954[hep-ex]

[68] P Estabrooks R Carnegie A D Martin W Dunwoodie T Lasinski et al Nucl PhysB133 490 (1978)

[69] D Aston et al Nucl Phys B296 493 (1988)

[70] B Aubert et al (BABAR collaboration) Phys Rev Lett 90 242001 (2003)arXivhep-ex0304021 [hep-ex]

[71] D Besson et al (CLEO Collaboration collaboration) PhysRev D68 032002 (2003)arXivhep-ex0305100 [hep-ex]

[72] K Abe et al (Belle Collaboration collaboration) PhysRevLett 92 012002 (2004)arXivhep-ex0307052 [hep-ex]

[73] B Aubert et al (BaBar Collaboration collaboration) PhysRev D69 031101 (2004)arXivhep-ex0310050 [hep-ex]

[74] K Abe et al (Belle collaboration) Phys Rev D69 112002 (2004) arXivhep-ex0307021[hep-ex]

[75] J M Link et al (FOCUS Collaboration collaboration) PhysLett B586 1120 (2004)arXivhep-ex0312060 [hep-ex]

[76] S Godfrey and N Isgur Phys Rev D32 189231 (1985)

[77] S Godfrey and R Kokoski Phys Rev D43 16791687 (1991)

[78] N Isgur and M B Wise Phys Rev Lett 66 11301133 (1991)

[79] P Schweitzer S Bo and M Radici Phys Rev D66 114004 (2002)arXivhep-ph0207230 [hep-ph]

[80] F Jugeau A Le Yaouanc L Oliver and J-C Raynal Phys Rev D72 094010 (2005)arXivhep-ph0504206 [hep-ph]

[81] P Colangelo F De Fazio and R Ferrandes ModPhysLett A19 20832102 (2004)arXivhep-ph0407137 [hep-ph]

[82] R N Cahn and J D Jackson Phys Rev D68 037502 (2003) arXivhep-ph0305012[hep-ph]

[83] T Barnes F E Close and H J Lipkin PhysRev D68 054006 (2003)arXivhep-ph0305025 [hep-ph]

[84] H Lipkin PhysLett B580 5053 (2004) arXivhep-ph0306204 [hep-ph]

[85] W A Bardeen E J Eichten and C T Hill Phys Rev D68 054024 (2003)arXivhep-ph0305049 [hep-ph]

[86] B Aubert et al (BaBar Collaboration collaboration) PhysRev D80 092003 (2009)arXiv09080806 [hep-ex]

47

[87] R Aaij et al (LHCb Collaboration collaboration) JHEP 1210 151 (2012) arXiv12076016[hep-ex]

[88] R Aaij et al (LHCb collaboration) Phys Rev Lett 113 162001 (2014) arXiv14077574[hep-ex]

[89] R Aaij et al (LHCb collaboration) JHEP 02 133 (2016) arXiv160101495 [hep-ex]

[90] T Matsuki T Morii and K Sudoh EurPhysJ A31 701704 (2007)arXivhep-ph0610186 [hep-ph]

[91] N Isgur and M B Wise PhysLett B232 113117 (1989)

[92] M Neubert PhysRept 245 259396 (1994) arXivhep-ph9306320 [hep-ph]

[93] B Aubert et al (BaBar Collaboration collaboration) PhysRev D74 032007 (2006)arXivhep-ex0604030 [hep-ex]

[94] V M Abazov et al (D0 Collaboration collaboration) PhysRevLett 102 051801 (2009)arXiv07123789 [hep-ex]

[95] B Aubert et al (BABAR collaboration) Phys Rev D77 011102 (2008) arXiv07081565[hep-ex]

[96] P L Frabetti et al (E687 Collaboration collaboration) PhysRevLett 72 324327 (1994)

[97] J P Alexander et al (CLEO Collaboration collaboration) PhysLett B303 377384 (1993)

[98] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B297 425431 (1992)

[99] P Avery et al (CLEO Collaboration collaboration) PhysRev D41 774 (1990)

[100] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B230 162 (1989)

[101] J P Lees et al (BaBar Collaboration collaboration) PhysRev D83 072003 (2011)arXiv11032675 [hep-ex]

[102] R Aaij et al (LHCb collaboration) Phys Rev D90 no 7 072003 (2014) arXiv14077712[hep-ex]

[103] R Aaij et al (LHCb collaboration) PhysLett B698 1420 (2011) arXiv11020348[hep-ex]

[104] B Aubert et al (BaBar Collaboration collaboration) PhysRevLett 97 222001 (2006)arXivhep-ex0607082 [hep-ex]

[105] H Albrecht et al (ARGUS Collaboration collaboration) ZPhys C69 405408 (1996)

[106] Y Kubota et al (CLEO Collaboration collaboration) PhysRevLett 72 19721976 (1994)arXivhep-ph9403325 [hep-ph]

[107] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052002 (2015)arXiv14126751 [hep-ex]

[108] J Brodzicka et al (Belle collaboration) Phys Rev Lett 100 092001 (2008)arXiv07073491 [hep-ex]

48

[109] B Aubert et al (BABAR collaboration) Phys Rev D79 112004 (2009) arXiv09011291[hep-ex]

[110] R Aaij et al (LHCb collaboration) Phys Rev D92 no 3 032002 (2015)arXiv150501710 [hep-ex]

[111] R Aaij et al (LHCb collaboration) Phys Rev D92 no 1 012012 (2015)arXiv150501505 [hep-ex]

[112] A Kuzmin et al (Belle Collaboration collaboration) PhysRev D76 012006 (2007)arXivhep-ex0611054 [hep-ex]

[113] H Abramowicz et al (ZEUS Collaboration collaboration) NuclPhys B866 229254 (2013)arXiv12084468 [hep-ex]

[114] A Abulencia et al (CDF Collaboration collaboration) PhysRev D73 051104 (2006)arXivhep-ex0512069 [hep-ex]

[115] K Abe et al (Belle collaboration) Phys Rev Lett 94 221805 (2005)arXivhep-ex0410091 [hep-ex]

[116] P Avery et al (CLEO Collaboration collaboration) PhysLett B331 236244 (1994)arXivhep-ph9403359 [hep-ph]

[117] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B232 398 (1989)

[118] J C Anjos et al (Tagged Photon Spectrometer Collaboration collaboration) PhysRevLett62 1717 (1989)

[119] T Bergfeld et al (CLEO Collaboration collaboration) PhysLett B340 194204 (1994)

[120] R Aaij et al (LHCb collaboration) Phys Rev D91 no 9 092002 (2015)arXiv150302995 [hep-ex] [Erratum Phys RevD93no11119901(2016)]

[121] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B221 422 (1989)

[122] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B231 208 (1989)

[123] P Abreu et al (DELPHI Collaboration collaboration) PhysLett B426 231242 (1998)

[124] D Matvienko et al (Belle collaboration) Phys Rev D92 no 1 012013 (2015)arXiv150503362 [hep-ex]

[125] P Krokovny et al (Belle collaboration) Phys Rev Lett 91 262002 (2003)arXivhep-ex0308019 [hep-ex]

[126] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 181801 (2004)arXivhep-ex0408041 [hep-ex]

[127] S K Choi et al (Belle collaboration) Phys Rev D91 no 9 092011 (2015)arXiv150402637 [hep-ex] [Addendum Phys RevD92no3039905(2015)]

[128] A Drutskoy et al (Belle collaboration) Phys Rev Lett 94 061802 (2005)arXivhep-ex0409026 [hep-ex]

[129] B Aubert et al (BABAR collaboration) Phys Rev D74 031103 (2006)arXivhep-ex0605036 [hep-ex]

49

[130] S Chekanov et al (ZEUS Collaboration collaboration) EurPhysJ C60 2545 (2009)arXiv08071290 [hep-ex]

[131] A Heister et al (ALEPH Collaboration collaboration) PhysLett B526 3449 (2002)arXivhep-ex0112010 [hep-ex]

[132] B Aubert et al (BABAR collaboration) Phys Rev Lett 103 051803 (2009)arXiv08080333 [hep-ex]

[133] G Burdman E Golowich J L Hewett and S Pakvasa Phys Rev D66 014009 (2002)arXivhep-ph0112235 [hep-ph]

[134] S Fajfer A Prapotnik S Prelovsek P Singer and J Zupan Nucl Phys Proc Suppl 1159397 (2003) arXivhep-ph0208201 [hep-ph]

[135] S Fajfer N Kosnik and S Prelovsek Phys Rev D76 074010 (2007) arXiv07061133[hep-ph]

[136] E Golowich J Hewett S Pakvasa and A A Petrov Phys Rev D79 114030 (2009)arXiv09032830 [hep-ph]

[137] A Paul I I Bigi and S Recksiegel Phys Rev D82 094006 (2010) arXiv10083141[hep-ph]

[138] A Borisov (2011) arXiv11123269 [hep-ph]

[139] R-M Wang J-H Sheng J Zhu Y-Y Fan and Y Gao Int J Mod Phys A29 no 291450169 (2014)

[140] S de Boer and G Hiller Phys Rev D93 no 7 074001 (2016) arXiv151000311 [hep-ph]

[141] P Rubin et al (CLEO collaboration) Phys Rev D82 092007 (2010) arXiv10091606[hep-ex]

[142] V Abazov et al (D0 collaboration) Phys Rev Lett 100 101801 (2008) arXiv07082094[hep-ex]

[143] R Aaij et al (LHCb collaboration) Phys Lett B728 234243 (2014) arXiv13102535[hep-ex]

[144] R Aaij et al (LHCb collaboration) Phys Lett B724 203212 (2013) arXiv13046365[hep-ex]

[145] T Coan et al (CLEO collaboration) Phys Rev Lett 90 101801 (2003)arXivhep-ex0212045 [hep-ex]

[146] M Ablikim et al (BESIII collaboration) Phys Rev D91 no 11 112015 (2015)arXiv150503087 [hep-ex]

[147] J P Lees et al (BABAR collaboration) Phys Rev D85 091107 (2012) arXiv11106480[hep-ex]

[148] N K Nisar et al (Belle collaboration) Phys Rev D93 no 5 051102 (2016)arXiv151202992 [hep-ex]

[149] P Haas et al (CLEO collaboration) Phys Rev Lett 60 1614 (1988)

50

[150] H Albrecht et al (ARGUS collaboration) Phys Lett B209 380 (1988)

[151] J Adler et al (MARK-III collaboration) Phys Rev D37 2023 (1988) Erratum ibid D40(1989) 3788

[152] A Freyberger et al (CLEO collaboration) Phys Rev Lett 76 30653069 (1996)

[153] D Pripstein et al (E789 collaboration) Phys Rev D61 032005 (2000)arXivhep-ex9906022 [hep-ex]

[154] E Aitala et al (E791 collaboration) Phys Lett B462 401409 (1999)arXivhep-ex9906045 [hep-ex]

[155] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 191801 (2004)arXivhep-ex0408023 [hep-ex]

[156] M Petric et al (Belle collaboration) Phys Rev D81 091102 (2010) arXiv10032345[hep-ex]

[157] K Kodama et al (E653 collaboration) Phys Lett B345 8592 (1995)

[158] I Abt et al (HERA-B collaboration) Phys Lett B596 173183 (2004)arXivhep-ex0405059 [hep-ex]

[159] T Aaltonen et al (CDF collaboration) Phys Rev D82 091105 (2010) arXiv10085077[hep-ex]

[160] R Aaij et al (LHCb collaboration) Phys Lett B725 1524 (2013) arXiv13055059[hep-ex]

[161] E Aitala et al (E791 collaboration) Phys Rev Lett 86 39693972 (2001)arXivhep-ex0011077 [hep-ex]

[162] J Adler et al (MARK-III collaboration) Phys Rev D40 906 (1989)

[163] J Becker et al (MARK-III collaboration) Phys Lett B193 147 (1987)

[164] R Aaij et al (LHCb collaboration) Phys Lett B754 167175 (2016) arXiv151200322[hep-ex]

[165] P Rubin et al (CLEO collaboration) Phys Rev D79 097101 (2009) arXiv09041619[hep-ex]

[166] P Frabetti et al (E687 collaboration) Phys Lett B398 239244 (1997)

[167] J P Lees et al (BABAR collaboration) Phys Rev D84 072006 (2011) arXiv11074465[hep-ex]

[168] (BESIII collaboration) M-G Zhao D rareforbidden decays at BESIII in 7th International

Workshop on Charm Physics (Charm 2015) Detroit MI USA May 18-22 2015 2016arXiv160508952 [hep-ex]httpinspirehepnetrecord1466292filesarXiv160508952pdf

[169] J Link et al (FOCUS collaboration) Phys Lett B572 2131 (2003)arXivhep-ex0306049 [hep-ex]

51

  • Introduction
  • D decays
    • Interplay of direct and indirect CP violation
    • Semileptonic decays
      • Introduction
      • DP decays
      • Form factor parameterizations
      • Simple pole
      • z expansion
      • Three-pole formalism
      • Experimental techniques and results
      • Combined results for the DK channel
      • Combined results for the D channel
      • Vcs and Vcd determination
      • DV decays
      • Form factor measurements
        • Excited D(s) mesons
        • Rare and forbidden decays
          • References
Page 9: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

22 Semileptonic decays

221 Introduction

Semileptonic decays of D mesons involve the interaction of a leptonic current with a hadroniccurrent The latter is nonperturbative and cannot be calculated from rst principles thus it isusually parameterized in terms of form factors The transition matrix element is written

M = minusi GFradic2Vcq L

microHmicro (7)

where GF is the Fermi constant and Vcq is a CKM matrix element The leptonic current Lmicro isevaluated directly from the lepton spinors and has a simple structure this allows one to extractinformation about the form factors (in Hmicro) from data on semileptonic decays [19] Converselybecause there are no strong nal-state interactions between the leptonic and hadronic systemssemileptonic decays for which the form factors can be calculated allow one to determine Vcq [2]

222 DrarrP`ν` decays

When the nal state hadron is a pseudoscalar the hadronic current is given by

Hmicro = 〈P (p)|qγmicroc|D(pprime)〉 = f+(q2)

[(pprime + p)micro minus

m2D minusm2

P

q2qmicro

]+ f0(q2)

m2D minusm2

P

q2qmicro (8)

where mD and pprime are the mass and four momentum of the parent D meson mP and p are thoseof the daughter meson f+(q2) and f0(q2) are form factors and q = pprime minus p Kinematics requirethat f+(0) = f0(0) The contraction qmicroL

micro results in terms proportional to m` [20] and thus for` = e the terms proportionals to qmicro in Eq (8) are negligible For light leptons only the f+(q2)vector form factor is relevant and the dierential partial width is

dΓ(D rarr P`ν`)

dq2 d cos θ`=

G2F |Vcq|2

32π3plowast 3|f+(q2)|2 sin θ2

` (9)

where plowast is the magnitude of the momentum of the nal state hadron in the D rest frame andθ` is the angle of the lepton in the `ν rest frame with respect to the direction of the pseudoscalarmeson in the D rest frame

223 Form factor parameterizations

The form factor is traditionally parameterized with an explicit pole and a sum of eective poles

f+(q2) =f+(0)

(1minus α)

[(1

1minus q2m2pole

)+

Nsumk=1

ρk1minus q2(γkm2

pole)

] (10)

where ρk and γk are expansion parameters and α is a parameter that normalizes the formfactor at q2 = 0 f+(0) The parameter mpole is the mass of the lowest-lying cq resonance withthe vector quantum numbers this is expected to provide the largest contribution to the formfactor for the crarr q transition The sum over N gives the contribution of higher mass statesFor example for D rarr π transitions the dominant resonance is expected to be Dlowast(2010) andthus mpole = mDlowast(2010) For D rarr K transitions the dominant contribution is expected from

Dlowasts(2112) with mpole = mDlowasts (2112)

9

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Comparison between CLEO-c and BABAR results for the quantities q2H20 (q2) and

q2h0(q2)H0(q2)

Table 11 Results for rV and r2 from various experiments

Experiment Ref rV r2

D+ rarr Klowast0l+ν

E691 [54] 20plusmn 06plusmn 03 00plusmn 05plusmn 02E653 [55] 200plusmn 033plusmn 016 082plusmn 022plusmn 011E687 [56] 174plusmn 027plusmn 028 078plusmn 018plusmn 011

E791 (e) [57] 190plusmn 011plusmn 009 071plusmn 008plusmn 009E791 (micro) [58] 184plusmn011plusmn009 075plusmn008plusmn009Beatrice [59] 145plusmn 023plusmn 007 100plusmn 015plusmn 003FOCUS [60] 1504plusmn0057plusmn0039 0875plusmn0049plusmn0064

D0 rarr K0πminusmicro+ν

FOCUS [61] 1706plusmn0677plusmn0342 0912plusmn0370plusmn0104BABAR [62] 1493plusmn 0014plusmn 0021 0775plusmn 0011plusmn 0011

D+s rarr φ e+νBABAR [63] 1849plusmn0060plusmn0095 0763plusmn0071plusmn0065

D0 D+ rarr ρ eνCLEO [64] 140plusmn025plusmn003 057plusmn018plusmn006

23

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

Experiment

V

r2r

-4

-3

-2

-1

0

1

2

3

eν +

e0

K rarr +

E69

1

D

microν + micro

0K

rarr +E

653

D

microν + micro

0K

rarr+

E68

7

D

ν + micro

+ e

0K

rarr+

E79

1

D

microν + micro

0K

rarr +

BE

AT

RIC

E D

microν + micro

0K

rarr +

FO

CU

S

D

eν +

e+ π

- K

rarr +

BaB

ar

D

eν + eφ

rarr s+

BaB

ar

D

microν+ micro - π

0K

rarr 0

FO

CU

S

D

HFLAV())+-amp

Figure 7 A comparison of r2 (lled inverted triangles) and rV (open triangles) values fromvarious experiments The rst seven measurements are for D+ rarr Kminusπ+l+νl decays Alsoshown as a line with 1-σ limits is the average of these The last two points are D+

s and D0

decays

24

23 Excited D(s) mesons

Excited charm meson states have received increased attention since the rst observation ofstates that could not be accommodated by QCD predictions [70 71 72 73] Tables 12 13and 14 summarize recent measurements of the masses and widths of excited D and Ds mesonsrespectively If a preferred assignment of spin and parity was measured it is listed in the columnJP where the label natural denotes JP = 0minus 1+ 2minus and unnatural JP = 0+ 1minus 2+ Ifpossible an average mass and width was calculated which is listed in the gray shaded rowThe calculation of the averages assumes no correlation between individual measurements Asummary of the averaged masses and widths is shown in Figure 8

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

0+ 1+ 2+ 1minus 1 3minus

unnatu

ral

Dlowast s0

(2317)plusmn

Ds1

(2460)plusmn

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn D

sJ(3

040)plusmn

HFAG-charmAugust 2016

(a)

Mas

s[M

eVc

2]

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

0+ 1+ 2+ 0minus 1minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ralDlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn

D(2

550)0

D(2

580)0

D(2

600)0

D(2

600)plusmn

Dlowast (

2640)plusmn

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(b)

Mas

s[M

eVc

2]

0

50

100

150

200

250

300

350

400

450

500

550

1+ 2+ 1minus 1 3minus

unnatu

ral

Ds1

(2536)plusmn

Dlowast s2

(2573)plusmn

Dlowast s1

(2700)plusmn

Dlowast s1

(2860)plusmn

Dlowast s3

(2860)plusmn

DsJ

(3040)plusmn

HFAG-charmAugust 2016

(c)

Wid

th[M

eV]

50100150200250300350400450500550600650700

0+ 1+ 2+ 0minus 1+ 3minus

unnatu

ral

natu

ral

natu

ral

unnatu

ral

Dlowast 0

(2400)0

Dlowast 0

(2400)plusmn

D1(2

420)0

D1(2

420)plusmn

D1(2

430)0

Dlowast 2

(2460)0

Dlowast 2

(2460)plusmn D(2

550)0

D(2

580)0

D(2

600)0

Dlowast (

2650)0

D(2

740)0

D(2

750)0

Dlowast 1

(2760)0

Dlowast 3

(2760)plusmn

HFAG-charmAugust 2016

(d)

Wid

th[M

eV]

Figure 8 Averaged masses for Ds mesons are shown in subgure (a) and for D mesons insubgure (b) The average widths for Ds mesons are shown in subgure (c) and for D mesonsin subgure (d) The vertical shaded regions distinguish between dierent spin parity states

The masses and widths of narrow (Γ lt 50 MeV) orbitally excited D mesons (denotedDlowastlowast) both neutral and charged are well established Measurements of broad states (Γ sim200400 MeV) are less abundant as identifying the signal is more challenging There is aslight discrepancy between the Dlowast0(2400)0 masses measured by the Belle [74] and FOCUS [75]experiments No data exist yet for the D1(2430)plusmn state Dalitz plot analyses of B rarr D(lowast)ππ

25

decays strongly favor the assignments 0+ and 1+ for the spin-parity quantum numbers of theDlowast0(2400)0Dlowast0(2400)plusmn and D1(2430)0 states respectively The measured masses and widthsas well as the JP values are in agreement with theoretical predictions based on potentialmodels [76777879]

Tables 15 and 16 summarizes the branching fractions of B mesons decays to excited D andDs states respectively It can be noted that the branching fractions for B mesons decaying to anarrow Dlowastlowast state and a pion are similar for charged and neutral B initial states the branchingfractions to a broad Dlowastlowast state and π+ are much larger for B+ than for B0 This may be dueto the fact that color-suppressed amplitudes contribute only to the B+ decay and not to theB0 decay (for a theoretical discussion see Ref [8081]) Measurements of individual branchingfractions of D mesons are dicult due to the unknown fragmentation of cc rarr Dlowastlowast or due tothe unknown B rarr DlowastlowastX branching fractions

The discoveries of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn have triggered increased interest in prop-erties of and searches for excited Ds mesons (here generically denoted D

lowastlowasts ) While the masses

and widths of Ds1(2536)plusmn and Ds2(2573)plusmn states are in relatively good agreement with po-tential model predictions the masses of Dlowasts0(2317)plusmn and Ds1(2460)plusmn states are signicantlylower than expected (see Ref [82] for a discussion of cs models) Moreover the mass splittingbetween these two states greatly exceeds that between the Ds1(2536)plusmn and Ds2(2573)plusmn Theseunexpected properties have led to interpretations of the Dlowasts0(2317)plusmn and Ds1(2460)plusmn as exoticfour-quark states [8384]

While there are few measurements of the JP values of Dlowasts0(2317)plusmn andDs1(2460)plusmn the avail-able data favor 0+ and 1+ respectively A molecule-like (DK) interpretation of the Dlowasts0(2317)plusmn

and Ds1(2460)plusmn [8384] that can account for their low masses and isospin-breaking decay modesis tested by searching for charged and neutral isospin partners of these states thus far suchsearches have yielded negative results Therefore the subset of models that predict equal pro-duction rates for dierent charged states is excluded The molecular picture can also be testedby measuring the rates for the radiative processes Dlowasts0(2317)plusmnDs1(2460)plusmn rarr D

(lowast)s γ and com-

paring to theoretical predictions The predicted rates however are below the sensitivity ofcurrent experiments

Another model successful in explaining the total widths and the Dlowasts0(2317)plusmn Ds1(2460)plusmn

mass splitting is based on the assumption that these states are chiral partners of the groundstates D+

s and Dlowasts [85] While some measured branching fraction ratios agree with predictedvalues further experimental tests with better sensitivity are needed to conrm or refute thisscenario A summary of the mass dierence measurements is given in Table 17

Measurements by BABAR [86] and LHCb [87] rst indicated the existence of a strange-charm DlowastsJ(2860)plusmn meson An LHCb study of B0

s rarr D0Kminusπ+ decays in which they searchedfor excited Ds mesons [88] showed with 10σ signicance that this state is comprised of twodierent particles one of spin 1 and one of spin 3 This represents the rst measurement of aheavy avored spin-3 particle and the rst observation B mesons decays to spin 3 particlesA subsequent study of DsJ mesons by the LHCb collaboration [89] supports the natural parityassignment for this state (JP = 3minus) This study also shows weak evidence for a further structureat a mass around 3040 MeVc2 with unnatural parity which was rst hinted at by a Babaranalysis [86]

Recent evidence shows that the 1D family of charm resonances can be explored in the Dalitzplot analyses of B-meson decays in the same way as seen for the charm-strange resonances TheLHCb collaboration performed an analysis of B0 rarr D0π+πminus decays in which they measured

26

the spin-parity assignment of the stateDlowast3(2760)plusmn which was observed previously by BABAR [29]and LHCb [30] to be JP = 3minus The measurement suggests a spectroscopic assignment of 3D3This is the second observation of a spin-3 charm meson

Other observed excited Ds states include Ds1(2700)plusmn and Ds2(2573)plusmn The properties ofboth (mass width JP ) have been measured and determined in several analyses A theoreticaldiscussion [90] investigates the possibility that theDs1(2700)plusmn could represent radial excitationsof the Dlowastplusmns Similarly the Ds1(2860)plusmn and DsJ(3040)plusmn could be excitations of Dlowasts0(2317)plusmn andDs1(2460)plusmn or Ds1(2536)plusmn respectively

Table 18 summarizes measurements of the polarization amplitude AD (sometimes also re-ferred as helicity parameter) which describes the initial polarization of the D meson In Dlowastlowast

meson decay the helicity distribution varies like 1 + AD cos2 θH where θH is the angle in theDlowast rest frame between the two pions emitted by decay Dlowastlowast rarr Dlowastπ and the Dlowast rarr Dπ Theparameter is sensitive to possible S-wave contributions in the decay In the case of an unpolar-ized D meson decay decaying purely via D-wave the polarization amplitude is predicted to giveAD = 3 Studies of the D1(2420)0 meson by the ZEUS and BABAR collaborations suggest thatthere is an S-wave admixture in the decay which is contrary to Heavy Quark Eective Theorycalculations [9192]

27

Table 12 Recent measurements of mass and width for dierent excited Ds mesons Thecolumn JP list the most signicant assignment of spin and parity If possible an average massor width is calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowasts0(2317)plusmn 0+

D+s π

0 23196plusmn 02plusmn 14 BABAR [93]D+s π

0 23173plusmn 04plusmn 08 BABAR [73]

23180plusmn 08 Our average

Ds1(2460)plusmn 1+

D+s π

0γD+s γD

+s π

+πminus 24601plusmn 02plusmn 08 BABAR [93]D+s π

0γ 2458plusmn 10plusmn 10 BABAR [73]

24596plusmn 07 Our average

Ds1(2536)plusmn 1+

Dlowast+K0S 25357plusmn 06plusmn 05 DOslash [94]

Dlowast+K0S D

lowast0K+ 253478plusmn 031plusmn 040 BABAR [95]D+s π

+πminus 25346plusmn 03plusmn 07 BABAR [93]Dlowast+K0

S Dlowast0K+ 25350plusmn 06plusmn 10 E687 [96]

Dlowast0K+ 25353plusmn 02plusmn 05 CLEO [97]Dlowast+K0

S 25348plusmn 06plusmn 06 CLEO [97]Dlowast0K+ 25352plusmn 05plusmn 15 ARGUS [98]Dlowast+K0

S 25356plusmn 07plusmn 04 CLEO [99]Dlowast+K0

S 25359plusmn 06plusmn 20 ARGUS [100]Dlowast+K0

S 092plusmn 003plusmn 004 BABAR [101]

253510plusmn 026 092plusmn 005 Our average

Dlowasts2(2573)plusmn 2+

D0K+ Dlowast+K0S 256839plusmn 029plusmn 026 169plusmn 05plusmn 06 LHCb [102]

D+K0S D

0K+ 25694plusmn 16plusmn 05 121plusmn 45plusmn 16 LHCb [103]D+K0

S D0K+ 25722plusmn 03plusmn 10 271plusmn 06plusmn 56 BABAR [104]

D0K+ 257425plusmn 33plusmn 16 104plusmn 83plusmn 30 ARGUS [105]D0K+ 25732+17

minus16 plusmn 09 16+5minus4 plusmn 3 CLEO [106]

256908plusmn 035 169plusmn 08 Our average

Dlowasts1(2700)plusmn 1minus

Dlowast+K0S D

lowast0K+ 27323plusmn 43plusmn 58 136plusmn 19plusmn 24 LHCb [89]D0K+ 2699+14

minus7 127+24minus19 BABAR [107]

Dlowast+K0S D

lowast0K+ 27092plusmn 19plusmn 45 1158plusmn 73plusmn 121 LHCb [87]DKDlowastK 2710plusmn 2+12

minus7 149plusmn 7+39minus52 BABAR [86]

D0K+ 2708plusmn 9+11minus10 108plusmn 2+36

minus31 Belle [108]

27120plusmn 15 1215plusmn 102 Our average

Dlowasts1(2860)plusmn 1 D0K+ 2859plusmn 12plusmn 24 159plusmn 23plusmn 77 LHCb [88]

Dlowasts3(2860)plusmn 3minusDlowast+K0

S Dlowast0K+ 28671plusmn 43plusmn 19 50plusmn 11plusmn 13 LHCb [89]

D0K+ 28605plusmn 26plusmn 65 53plusmn 7plusmn 7 LHCb [88]

28650plusmn 39 522plusmn 86 Our average

DsJ(3040)plusmn Unnatural DlowastK 3044plusmn 8+30minus5 239plusmn 35+46

minus42 BABAR (m amp Γ) + LHCb(JP ) [86]+ [89]

28

Table 13 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast0(2400)0 0+

D+πminus 2297plusmn 8plusmn 20 273plusmn 12plusmn 48 BABAR [109]D+πminus 2308plusmn 17plusmn 32 276plusmn 21plusmn 63 Belle [74]D+πminus 2407plusmn 21plusmn 35 240plusmn 55plusmn 59 Focus [75]

23182plusmn 169 2674plusmn 356 Our average

Dlowast0(2400)plusmn 0+

D0π+ 2349plusmn 6plusmn 1plusmn 4 217plusmn 13plusmn 5plusmn 12 LHCb [110]D0π+ 2360plusmn 15plusmn 12plusmn 28 255plusmn 26plusmn 20plusmn 47 LHCb [111]D0π+ 2403plusmn 14plusmn 35 283plusmn 24plusmn 34 Focus(m ampΓ) + Belle(JP ) [75] + [112]

23506plusmn 59 2337plusmn 155 Our average

D1(2420)0 1+

Dlowast+πminus 24196plusmn 01plusmn 07 352plusmn 04plusmn 09 LHCb [30]Dlowast+πminus 24231plusmn 15+04

minus10 388plusmn 5+19minus54 Zeus [113]

Dlowast+πminus 24201plusmn 01plusmn 08 314plusmn 05plusmn 13 BABAR [29]Dlowast+πminus 200plusmn 17plusmn 13 CDF [114]D0π+πminus 2426plusmn 3plusmn 1 24plusmn 7plusmn 8 Belle [115]Dlowast+πminus 24214plusmn 15plusmn 09 237plusmn 27plusmn 40 Belle [74]Dlowast+πminus 2421+1

minus2 plusmn 2 20+6minus5

+3minus3 CLEO [116]

Dlowast+πminus 2422plusmn 2plusmn 2 15plusmn 8plusmn 4 E687 [96]Dlowast+πminus 2428plusmn 3plusmn 2 23+8

minus6+10minus4 CLEO [99]

Dlowast+πminus 2414plusmn 2plusmn 5 13plusmn 6+10minus5 ARGUS [117]

Dlowast+πminus 2428plusmn 8plusmn 5 58plusmn 14plusmn 10 TPS [118]

24205plusmn 05 317plusmn 07 Our average

D1(2420)plusmn 1+

Dlowast0π+ 24219plusmn 47+34minus12 Zeus [113]

D+πminusπ+ 2421plusmn 2plusmn 1 21plusmn 5plusmn 8 Belle [115]Dlowast0π+ 2425plusmn 2plusmn 2 26+8

minus7 plusmn 4 CLEO [119]Dlowast0π+ 2443plusmn 7plusmn 5 41plusmn 19plusmn 8 TPS [118]

24232plusmn 16 252plusmn 60 Our average

D1(2430)0 1+ Dlowast+πminus 2427plusmn 26plusmn 25 384+107minus75 plusmn 74 Belle [74]

Dlowast2(2460)0 2+

Dlowast+πminus 24640plusmn 14plusmn 05plusmn 02 438plusmn 29plusmn 17plusmn 06 LHCb [120]Dlowast+πminus 24604plusmn 04plusmn 12 432plusmn 12plusmn 30 LHCb [30]D+πminus 24604plusmn 01plusmn 01 456plusmn 04plusmn 11 LHCb [30]

Dlowast+πminus D+πminus 24625plusmn 24+13minus11 466plusmn 81+59

minus38 Zeus [113]D+πminus 24622plusmn 01plusmn 08 505plusmn 06plusmn 07 BABAR [29]D+πminus 24604plusmn 12plusmn 22 418plusmn 25plusmn 29 BABAR [109]D+πminus 492plusmn 23plusmn 13 CDF [114]D+πminus 24616plusmn 21plusmn 33 456plusmn 44plusmn 67 Belle [74]D+πminus 24645plusmn 11plusmn 19 387plusmn 53plusmn 29 Focus [75]D+πminus 2465plusmn 3plusmn 3 28+8

minus7 plusmn 6 CLEO [116]D+πminus 2453plusmn 3plusmn 2 25plusmn 10plusmn 5 E687 [96]Dlowast+πminus 2461plusmn 3plusmn 1 20+9

minus12+9minus10 CLEO [99]

D+πminus 2455plusmn 3plusmn 5 15+13minus10

+5minus10 ARGUS [121]

D+πminus 2459plusmn 3plusmn 2 20plusmn 10plusmn 5 TPS [118]

246049plusmn 017 4752plusmn 065 Our average

29

Table 14 Recent measurements of mass and width for dierent excited D mesons The columnJP list the most signicant assignment of spin and parity If possible an average mass or widthis calculated

Resonance JP Decay mode Mass [MeVc2] Width [MeV] Measured by Reference

Dlowast2(2460)plusmn 2+

D0π+ 24686plusmn 06plusmn 00plusmn 03 473plusmn 15plusmn 03plusmn 06 LHCb [110]D0π+ 24656plusmn 18plusmn 05plusmn 12 460plusmn 34plusmn 14plusmn 29 LHCb [111]D0π+ 24631plusmn 02plusmn 06 486plusmn 13plusmn 19 LHCb [30]

Dlowast0π+ D0π+ 24606plusmn 44+36minus08 Zeus [113]

D0π+ 24654plusmn 02plusmn 11 BABAR [29]D0π+ 24657plusmn 18+14

minus48 497plusmn 38plusmn 64 Belle [112]D0π+ 24676plusmn 15plusmn 08 341plusmn 65plusmn 42 Focus [75]D0π+ 2463plusmn 3plusmn 3 27+11

minus8 plusmn 5 CLEO [119]D0π+ 2453plusmn 3plusmn 2 23plusmn 9plusmn 5 E687 [96]D0π+ 2469plusmn 4plusmn 6 ARGUS [122]

246555plusmn 040 467plusmn 12 Our average

D(2550)0 0minus Dlowast+πminus 25394plusmn 45plusmn 68 130plusmn 12plusmn 13 BABAR [29]

D(2580)0 Unnatural Dlowast+πminus 25795plusmn 34plusmn 55 1175plusmn 178plusmn 460 LHCb [30]

D(2600)0 Natural D+πminus 26087plusmn 24plusmn 25 93plusmn 6plusmn 13 BABAR [29]

D(2600)plusmn Natural D0π+ 26213plusmn 37plusmn 42 BABAR [29]

Dlowast(2640)plusmn 1minus Dlowast+π+πminus 2637plusmn 2plusmn 6 Delphi [123]

Dlowast(2650)0 Natural Dlowast+πminus 26492plusmn 35plusmn 35 1402plusmn 171plusmn 186 LHCb [30]

D(2740)0 Unnatural Dlowast+πminus 27370plusmn 35plusmn 112 732plusmn 134plusmn 250 LHCb [30]

D(2750)0 Dlowast+πminus 27524plusmn 17plusmn 27 71plusmn 6plusmn 11 BABAR [29]

Dlowast1(2760)0 1+

D+πminus 2781plusmn 18plusmn 11plusmn 6 177plusmn 32plusmn 20plusmn 7 LHCb [120]Dlowast+πminus 27611plusmn 51plusmn 65 744plusmn 34plusmn 370 LHCb [30]D+πminus 27601plusmn 11plusmn 37 744plusmn 34plusmn 191 LHCb [30]D+πminus 27633plusmn 23plusmn 23 609plusmn 51plusmn 36 BABAR [29]

27621plusmn 24 651plusmn 58 Our average

Dlowast3(2760)plusmn 3minus

D0π+ 2798plusmn 7plusmn 1plusmn 7 105plusmn 18plusmn 6plusmn 23 LHCb [110]D0π+ 27717plusmn 17plusmn 38 667plusmn 66plusmn 105 LHCb [30]D0π+ 27697plusmn 38plusmn 15 BABAR [29]

27739plusmn 33 723plusmn 115 Our average

30

Table 15 Product of B meson branching fraction and (daughter) excited D meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowast0(2400)0

Bminus rarr Dlowast0(2400)0(rarr D+π+)πminus61plusmn 06plusmn 18 Belle [74]68plusmn 03plusmn 20 BABAR [109]

64plusmn 14 Our average

Bminus rarr Dlowast0(2400)0(rarr D+π+)Kminus 0061plusmn 0019plusmn 0005plusmn 0014plusmn 0004 LHCb [120]

Dlowast0(2400)plusmnB0 rarr Dlowast0(2400)+(rarr D0π+)πminus

077plusmn 005plusmn 003plusmn 003plusmn 004 LHCb [110]060plusmn 013plusmn 027 Belle [112]

076plusmn 007 Our average

B0 rarr Dlowast0(2400)+(rarr D0π+)Kminus 0177plusmn 0026plusmn 0019plusmn 0067plusmn 020 LHCb [111]

D1(2420)0

Bminus rarr D1(2420)0(rarr Dlowast+πminus)πminus 68plusmn 07plusmn 13 Belle [74]

Bminus rarr D1(2420)0(rarr D0π+πminus)πminus 185plusmn 029plusmn 027plusmn 041 Belle [115]

B0 rarr D1(2420)0(rarr Dlowast+πminus)ω 07plusmn 02+01minus00 plusmn 01 Belle [124]

D1(2420)plusmn B0 rarr D1(2420)+(rarr D+πminusπ+)πminus 089plusmn 015plusmn 022 Belle [115]

D1(2430)0Bminus rarr D1(2430)0(rarr Dlowast+πminus)πminus 50plusmn 04plusmn 108 Belle [74]

B0 rarr D1(2430)0(rarr Dlowast+πminus)ω 25plusmn 04+07minus02

+04minus01 Belle [124]

Dlowast2(2460)0

Bminus rarr Dlowast2(2460)0(rarr D+πminus)πminus34plusmn 03plusmn 07 Belle [74]35plusmn 02plusmn 05 BABAR [109]

34plusmn 03 Our average

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)πminus 18plusmn 03plusmn 04 Belle [74]

Bminus rarr Dlowast2(2460)0(rarr Dlowast+πminus)ω 04plusmn 01+00minus01 plusmn 01 Belle [124]

Bminus rarr Dlowast2(2460)0(rarr D+π+)Kminus 0232plusmn 0011plusmn 0006plusmn 0010plusmn 0016 LHCb [120]

Dlowast2(2460)plusmnB0 rarr Dlowast2(2460)+(rarr D0π+)πminus

244plusmn 007plusmn 010plusmn 004plusmn 012 LHCb [110]215plusmn 017plusmn 031 Belle [112]

238plusmn 016 Our average

B0 rarr Dlowast2(2460)+(rarr D0π+)Kminus 0212plusmn 0010plusmn 0011plusmn 0011plusmn 025 LHCb [111]

Dlowast1(2760)0 Bminus rarr Dlowast1(2760)0(rarr D+π+)Kminus 0036plusmn 0009plusmn 0003plusmn 0007plusmn 0002 LHCb [120]

Dlowast3(2760)plusmn B0 rarr Dlowast3(2760)0(rarr D0π+)πminus 0103plusmn 0016plusmn 0007plusmn 0008plusmn 0005 LHCb [110]

31

Table 16 Product of B meson branching fraction and (daughter) excited Ds meson branchingfraction

Resonance Decay Br[10minus4] Measured by Reference

Dlowasts0(2317)plusmnB0 rarr Dlowasts0(2317)+(rarr D+

s π0)Dminus

86+33minus26 plusmn 26 Belle [125]

180plusmn 40+67minus50 BABAR [126]

101+13minus12 plusmn 10plusmn 04 Belle [127]

102plusmn 15 Our average

B+ rarr Dlowasts0(2317)+(rarr D+s π

0)D0 80+13minus12 plusmn 10plusmn 04 Belle [127]

B0 rarr Dlowasts0(2317)+(rarr D+s π

0)Kminus 053+015minus013 plusmn 016 Belle [128]

Ds1(2460)plusmn

B0 rarr Ds1(2460)+(rarr Dlowast+s π0)Dminus227+73

minus62 plusmn 68 Belle [125]280plusmn 80+112

minus78 BABAR [126]

247plusmn 76 Our average

B0 rarr Ds1(2460)+(rarr Dlowast+s γ)Dminus82+22minus19 plusmn 25 Belle [125]

80plusmn 20+32minus23 BABAR [126]

81plusmn 23 Our average

Ds1(2460)+ rarr Dlowast+s π0 (56plusmn 13plusmn 9) BABAR [129]

Ds1(2460)+ rarr Dlowast+s γ (16plusmn 4plusmn 3) BABAR [129]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dminus 171plusmn 048plusmn 032 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast+K0)Dminus 261plusmn 103plusmn 031 BABAR [95]

B0 rarr Ds1(2536)+(rarr Dlowast0K+)Dlowastminus 332plusmn 088plusmn 066 BABAR [95]

Ds1(2536)plusmnB0 rarr Ds1(2536)+(rarr Dlowast+K0)Dlowastminus 500plusmn 151plusmn 067 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)D0 216plusmn 052plusmn 045 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)D0 230plusmn 098plusmn 043 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast0K+)Dlowast0 546plusmn 117plusmn 104 BABAR [95]

B+ rarr Ds1(2536)+(rarr Dlowast+K0)Dlowast0 392plusmn 246plusmn 083 BABAR [95]

Ds2(2573)plusmnB0 rarr Ds2(2573)(rarr D0K+)Dminus 034plusmn 017plusmn 005 BABAR [107]

B+ rarr Ds2(2573)(rarr D0K+)D0 008plusmn 14plusmn 005 BABAR [107]

Ds1(2700)plusmn B+ rarr Ds1(2700)+(rarr D0K+)D0

113plusmn 22+14minus28 Belle [108]

502plusmn 071plusmn 093 BABAR [107]

583plusmn 109 Our average

B0 rarr Ds1(2700)+(rarr D0K+)Dminus 714plusmn 096plusmn 069 BABAR [107]

32

Table 17 Mass dierence measurements for excited D mesons

Resonance Relative to ∆m [MeVc2] Measured by Reference

Dlowast1(2420)0 Dlowast+4102plusmn 21plusmn 09 Zeus [130]4117plusmn 07plusmn 04 CDF [114]

4115plusmn 08 Our average

D1(2420)plusmn Dlowast1(2420)0 4+2minus3 plusmn 3 CLEO [119]

Dlowast2(2460)0 D+ 5939plusmn 06plusmn 05 CDF [114]

Dlowast+ 4588plusmn 37+12minus13 Zeus [130]

Dlowast2(2460)plusmn Dlowast2(2460)0

31plusmn 19plusmn 09 Focus [75]minus2plusmn 4plusmn 4 CLEO [119]14plusmn 5plusmn 8 ARGUS [122]

30plusmn 19 Our average

Dlowasts0(2317)plusmn Dplusmns

3487plusmn 05plusmn 07 Belle [72]3500plusmn 12plusmn 10 CLEO [71]3513plusmn 21plusmn 19 Belle [125]

3492plusmn 07 Our average

Ds1(2460)plusmn

Dlowastplusmns

3441plusmn 13plusmn 11 Belle [72]3512plusmn 17plusmn 10 CLEO [71]3468plusmn 16plusmn 19 Belle [125]

3471plusmn 11 Our average

Dplusmns

4910plusmn 13plusmn 19 Belle [72]4914plusmn 09plusmn 15 Belle [72]

4913plusmn 14 Our average

Ds1(2536)plusmnDlowast(2010)plusmn

52483plusmn 001plusmn 004 BABAR [101]52530+044

minus041 plusmn 010 Zeus [130]5253plusmn 06plusmn 01 ALEPH [131]

52484plusmn 004 Our average

Dlowast(2007)0 5287plusmn 19plusmn 05 ALEPH [131]

Dlowasts2(2573)plusmn D0 704plusmn 3plusmn 1 ALEPH [131]

33

Table 18 Measurements of polarization amplitudes for excited D mesons

Resonance AD Measured by Reference

D1(2420)0

78+67minus27

+46minus18 ZEUS [113]

572plusmn 025 BABAR [29]59+30minus17

+24minus10 ZEUS [130]

38plusmn 06plusmn 08 BABAR [132]

561plusmn 024 Our average

D1(2420)plusmn 38plusmn 06plusmn 08 BABAR [132]

Dlowast2(2460)0 minus116plusmn 035 ZEUS [113]

D(2750)0 minus033plusmn 028 BABAR [29]

34

24 Rare and forbidden decays

This section provides a summary of rare and forbidden charm decays in tabular form The decaymodes can be categorized as avor-changing neutral currents lepton-avor-violating lepton-number-violating and both baryon- and lepton-number-violating decays Figures 9-11 plot theupper limits for D0 D+ D+

s and Λ+c decays Tables 19-22 give the corresponding numerical

results Some theoretical predictions are given in Refs [133134135136137138139140]In several cases the rare-decay nal states have been observed with the di-lepton pair being

the decay product of a hadronic resonance For these measurements the quoted limits are thoseexpected for the non-resonant di-lepton spectrum For the extrapolation to the full spectruma phase-space distribution of the non-resonant component has been assumed This applies tothe CLEO measurement of the decays D+

(s) rarr (K+π+)e+eminus [141] to the D0 measurements

of the decays D+(s) rarr π+micro+microminus [142] and to the BABAR measurements of the decays D+

(s) rarr(K+π+)e+eminus and D+

(s) rarr (K+π+)micro+microminus where the contribution from φ rarr l+lminus (l = e micro) has

been excluded In the case of the LHCb measurements of the decays D0 rarr π+πminusmicro+microminus [143]as well as the decays D+

(s) rarr π+micro+microminus [144] the contributions from φ rarr l+lminus as well as from

ρ ω rarr l+lminus (l = e micro) have been excluded

Table 19 Upper limits at 90 CL for D0 decays

Decay Limit times106 Experiment Referenceγγ 260 CLEO II [145]

38 BESIII [146]22 BaBar [147]085 Belle [148]

e+eminus 2200 CLEO [149]1700 Argus [150]1300 Mark3 [151]130 CLEO II [152]819 E789 [153]62 E791 [154]12 BaBar [155]0079 Belle [156]

micro+microminus 700 Argus [150]440 E653 [157]340 CLEO II [152]156 E789 [153]52 E791 [154]20 HERAb [158]13 BaBar [155]021 CDF [159]014 Belle [156]00062 LHCb [160]

π0e+eminus 450 CLEO II [152]π0micro+microminus 5400 CLEO II [152]

1800 E653 [157]

35

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceη e+eminus 1100 CLEO II [152]η micro+microminus 5300 CLEO II [152]π+πminuse+eminus 3700 E791 [161]ρ0e+eminus 4500 CLEO [149]

1240 E791 [161]1000 CLEO II [152]

π+πminusmicro+microminus 300 E791 [161]055 LHCb [143]

ρ0micro+microminus 8100 CLEO [149]4900 CLEO II [152]2300 E653 [157]220 E791 [161]

ω e+eminus 1800 CLEO II [152]ω micro+microminus 8300 CLEO II [152]K+Kminuse+eminus 3150 E791 [161]φ e+eminus 590 E791 [161]

520 CLEO II [152]K+Kminusmicro+microminus 330 E791 [161]φmicro+microminus 4100 CLEO II [152]

310 E791 [161]

K0e+eminus 17000 Mark3 [162]

1100 CLEO II [152]

K0micro+microminus 6700 CLEO II [152]

2600 E653 [157]Kminusπ+e+eminus 3850 E791 [161]

Klowast0

(892)e+eminus 1400 CLEO II [152]470 E791 [161]

Kminusπ+micro+microminus 3600 E791 [161]

Klowast0

(892)micro+microminus 11800 CLEO II [152]240 E791 [161]

π+πminusπ0micro+microminus 8100 E653 [157]microplusmne∓ 2700 CLEO [149]

1200 Mark3 [163]1000 Argus [150]190 CLEO II [152]172 E789 [153]81 E791 [154]081 BaBar [155]026 Belle [156]0016 LHCb [164]

π0eplusmnmicro∓ 860 CLEO II [152]η eplusmnmicro∓ 1000 CLEO II [152]

36

Table 19 continued from previous pageDecay Limit times106 Experiment Referenceπ+πminuseplusmnmicro∓ 150 E791 [161]ρ0eplusmnmicro∓ 660 E791 [161]

490 CLEO II [152]ω eplusmnmicro∓ 1200 CLEO II [152]K+Kminuseplusmnmicro∓ 1800 E791 [161]φ eplusmnmicro∓ 470 E791 [161]

340 CLEO II [152]

K0eplusmnmicro∓ 1000 CLEO II [152]

Kminusπ+eplusmnmicro∓ 5500 E791 [161]Klowast0(892)eplusmnmicro∓ 1000 CLEO II [152]

830 E791 [161]π∓π∓eplusmneplusmn 1120 E791 [161]π∓π∓microplusmnmicroplusmn 290 E791 [161]K∓π∓eplusmneplusmn 2060 E791 [161]K∓π∓microplusmnmicroplusmn 3900 E791 [161]K∓K∓eplusmneplusmn 1520 E791 [161]K∓K∓microplusmnmicroplusmn 940 E791 [161]π∓π∓eplusmnmicroplusmn 790 E791 [161]K∓π∓eplusmnmicroplusmn 2180 E791 [161]K∓K∓eplusmnmicroplusmn 570 E791 [161]p eminus 100 CLEO [165]p e+ 110 CLEO [165]

37

γγ

ρ0micro

+microminus

π+πminusπ

0micro

+microminus

K+K

minuse

+eminus

ηe

+eminus

φmicro

+microminus

π0e

+eminus

φe

+eminus

ωmicro

+microminus

Kminusπ

+micro

+microminus

ρ0e

+eminus

K0micro

+microminus

Klowast0

(892

)e+eminus

π+πminusmicro

+microminus

micro+microminus

π+πminuse

+eminus

e+eminus

Klowast0

(892

)micro+microminus

K+K

minusmicro

+microminus

Kminusπ

+e

+eminus

π0micro

+microminus

K0e

+eminus

ωe

+eminus

ηmicro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

HFAG-charm

Belle

BESIII

CLEO II

BaBar

E791

CLEO

E653

LHCb

E789

HERAB

CDF

Argus

Mark3

June 16

K∓π∓microplusmnmicroplusmn

ωeplusmnmicro∓

Kminusπ

+eplusmnmicro∓

K∓K∓eplusmnmicroplusmn

π∓π∓eplusmnmicroplusmn

peminus

K∓π∓eplusmnmicroplusmn

π∓π∓eplusmneplusmn

ηeplusmnmicro∓

π∓π∓microplusmnmicroplusmn

K∓K∓eplusmneplusmn

K0eplusmnmicro∓

π+πminuseplusmnmicro∓

K∓K∓microplusmnmicroplusmn

ρ0eplusmnmicro∓

pe

+

φeplusmnmicro∓

microplusmne∓

K+K

minuseplusmnmicro∓

Klowast0

(892

)eplusmnmicro∓

π0eplusmnmicro∓

K∓π∓eplusmneplusmn

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

L BLHFAG-charm

E791

CLEO II

CLEO

Belle

E789

Mark3

Argus

LHCb

BaBar

June 16

Figure 9 Upper limits at 90 CL for D0 decays The top plot shows avor-changing neu-tral current decays and the bottom plot shows lepton-avor-changing (LF) lepton-number-changing (L) and both baryon- and lepton-number-changing (BL) decays38

Kminuse

+micro

+

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminusmicro

+micro

+

K+e

+eminus

π+e

+eminus

πminuse

+micro

+

Kminuse

+e

+

K+micro

+eminus

ρminusmicro

+micro

+

K+e

+microminus

K+eplusmnmicro∓

π+micro

+eminus

π+e

+microminus

πminusmicro

+micro

+

πminuse

+e

+

π+micro

+microminus

ρ+micro

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E687

E653

E791

BaBar

Focus

CLEO

BESIII

LHCb

D0

June 16

Klowastminus

(892

)micro+micro

+

π+eplusmnmicro∓

Kminuse

+micro

+

K+e

+eminus

π+e

+eminus

K+eplusmnmicro∓

Kminuse

+e

+

K+micro

+eminus

K+e

+microminus

Klowast+

(892

)micro+microminus

π+micro

+eminus

Kminusmicro

+micro

+

πminusmicro

+micro

+

πminuse

+e

+

πminuse

+micro

+

π+micro

+microminus

K+micro

+microminus

π+e

+microminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF LHFAG-charm

E653

E791

CLEO

BaBar

Focus

LHCb

June 16

Figure 10 Upper limits at 90 CL for D+ (top) and D+s (bottom) decays Each plot shows

avor-changing neutral current decays lepton-avor-changing decays (LF) and lepton-number-changing (L) decays 39

pmicro

+microminus

pe

+microminus

σ+micro

+microminus

pe

+e

+

pe

+eminus

pe

+micro

+

pmicro

+micro

+

pmicro

+eminus

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

90

C

L

LF

LHFAG-charm

BaBar E653

June 16

Figure 11 Upper limits at 90 CL for Λ+c decays Shown are avor-changing neutral current

decays lepton-avor-changing (LF) decays and lepton-number-changing (L) decays

40

Table 20 Upper limits at 90 CL for D+ decays

Decay Limit times106 Experiment Referenceπ+e+eminus 1100 E687 [166]

520 E791 [154]59 CLEO [141]11 BaBar [167]03 BESIII [168]

π+micro+microminus 2200 E653 [157]890 E687 [166]150 E791 [154]88 Focus [169]65 BaBar [167]39 D0 [142]0073 LHCb [144]

ρ+micro+microminus 5600 E653 [157]K+e+eminus 2000 E687 [166]

30 CLEO [141]12 BESIII [168]10 BaBar [167]

π+eplusmnmicro∓ 340 E791 [154]π+e+microminus 1100 E687 [166]

29 BaBar [167]π+micro+eminus 1300 E687 [166]

36 BaBar [167]K+eplusmnmicro∓ 680 E791 [154]K+e+microminus 1300 E687 [166]

12 BaBar [167]K+micro+eminus 1200 E687 [166]

28 BaBar [167]πminuse+e+ 1100 E687 [166]

960 E791 [154]19 BaBar [167]12 BESIII [168]11 CLEO [141]

πminusmicro+micro+ 870 E687 [166]170 E791 [154]48 Focus [169]20 BaBar [167]0022 LHCb [144]

πminuse+micro+ 1100 E687 [166]500 E791 [154]

ρminusmicro+micro+ 5600 E653 [157]Kminuse+e+ 1200 E687 [166]

35 CLEO [141]09 BaBar [167]

41

Table 20 continued from previous pageDecay Limit times106 Experiment Reference

06 BESIII [168]Kminusmicro+micro+ 3200 E653 [157]

1200 E687 [166]130 Focus [169]100 BaBar [167]

Kminuse+micro+ 1300 E687 [166]Klowastminus(892)micro+micro+ 8500 E653 [157]

Table 21 Upper limits at 90 CL for D+s decays

Decay Limit times106 Experiment Referenceπ+e+eminus 2700 E791 [154]

220 CLEO [141]130 BaBar [167]

π+micro+microminus 4300 E653 [157]1400 E791 [154]430 BaBar [167]260 Focus [169]041 LHCb [144]

K+e+eminus 16000 E791 [154]520 CLEO [141]37 BaBar [167]

K+micro+microminus 1400 E791 [154]360 Focus [169]210 BaBar [167]

Klowast+(892)micro+microminus 14000 E653 [157]π+eplusmnmicro∓ 6100 E791 [154]π+e+microminus 120 BaBar [167]π+micro+eminus 200 BaBar [167]K+eplusmnmicro∓ 6300 E791 [154]K+e+microminus 140 BaBar [167]K+micro+eminus 97 BaBar [167]πminuse+e+ 6900 E791 [154]

180 CLEO [141]41 BaBar [167]

πminusmicro+micro+ 4300 E653 [157]820 E791 [154]290 Focus [169]140 BaBar [167]012 LHCb [144]

πminuse+micro+ 7300 E791 [154]Kminuse+e+ 6300 E791 [154]

170 CLEO [141]

42

Table 21 continued from previous pageDecay Limit times106 Experiment Reference

52 BaBar [167]Kminusmicro+micro+ 5900 E653 [157]

1800 E791 [154]130 BaBar [167]

Kminuse+micro+ 6800 E791 [154]Klowastminus(892)micro+micro+ 14000 E653 [157]

Table 22 Upper limits at 90 CL for Λ+c decays

Decay Limit times106 Experiment Referencepe+eminus 55 BaBar [167]pmicro+microminus 3400 E653 [157]

440 BaBar [167]σ+micro+microminus 7000 E653 [157]pe+microminus 99 BaBar [167]pmicro+eminus 190 BaBar [167]p e+e+ 27 BaBar [167]p micro+micro+ 94 BaBar [167]

43

References

[1] N Cabibbo Phys Rev Lett 10 531533 (1963)

[2] M Kobayashi and T Maskawa Prog Theor Phys 49 652657 (1973)

[3] D Abbaneo et al (ALEPH CDF DELPHI L3 OPAL and SLD collaborations)arXivhep-ex0009052 (2000) CERN-EP-2000-096 arXivhep-ex0112028 (2001)CERN-EP-2001-050

[4] Y Amhis et al (Heavy Flavor Averaging Group) (2012) arXiv12071158 [hep-ex]

[5] K Olive et al (Particle Data Group) Chin Phys C38 090001 (2014)

[6] A L Kagan and M D Sokolo Phys Rev D80 076008 (2009) arXiv09073917 [hep-ph]

[7] Y Grossman A L Kagan and Y Nir Phys Rev D75 036008 (2007)arXivhep-ph0609178 [hep-ph]

[8] M Gersabeck M Alexander S Borghi V Gligorov and C Parkes J Phys G39 045005(2012) arXiv11116515 [hep-ex]

[9] J P Lees et al (BABAR collaboration) Phys Rev D87 012004 (2013) arXiv12093896[hep-ex]

[10] R Aaij et al (LHCb collaboration) Phys Rev Lett 112 041801 (2014) arXiv13107201[hep-ex]

[11] T A Aaltonen et al (CDF collaboration) Phys Rev D90 no 11 111103 (2014)arXiv14105435 [hep-ex]

[12] R Aaij et al (LHCb collaboration) JHEP 04 043 (2015) arXiv150106777 [hep-ex]

[13] M Staripound et al (Belle collaboration) Phys Lett B753 412418 (2016) arXiv150908266[hep-ex]

[14] B Aubert et al (BABAR collaboration) Phys Rev Lett 100 061803 (2008)arXiv07092715 [hep-ex]

[15] B Ko (Belle collaboration) PoS ICHEP2012 353 (2013) arXiv12121975

[16] T Aaltonen et al (CDF collaboration) Phys Rev Lett 109 111801 (2012)arXiv12072158 [hep-ex]

[17] R Aaij et al (LHCb collaboration) JHEP 07 041 (2014) arXiv14052797 [hep-ex]

[18] R Aaij et al (LHCb collaboration) Phys Rev Lett 116 no 19 191601 (2016)arXiv160203160 [hep-ex]

[19] T Becher and R J Hill Phys Lett B633 6169 (2006) arXivhep-ph0509090 [hep-ph]

[20] F J Gilman and R L Singleton Phys Rev D41 142 (1990)

[21] R J Hill eConf C060409 027 (2006) arXivhep-ph0606023 [hep-ph]

[22] D Becirevic and A B Kaidalov Phys Lett B478 417423 (2000) arXivhep-ph9904490[hep-ph]

44

[23] C G Boyd B Grinstein and R F Lebed Phys Rev Lett 74 46034606 (1995)arXivhep-ph9412324 [hep-ph]

[24] C G Boyd and M J Savage Phys Rev D56 303311 (1997) arXivhep-ph9702300[hep-ph]

[25] M C Arnesen B Grinstein I Z Rothstein and I W Stewart Phys Rev Lett 95 071802(2005)

[26] C Bourrely B Machet and E de Rafael Nucl Phys B189 157 (1981)

[27] D Becirevic A L Yaouanc A Oyanguren P Roudeau and F Sanlippo (2014)arXiv14071019 [hep-ph]

[28] J P Lees et al (BABAR collaboration) Phys Rev D88 052003 (2013) arXiv13045009[hep-ex]

[29] P del Amo Sanchez et al (BaBar Collaboration collaboration) PhysRev D82 111101(2010) arXiv10092076 [hep-ex]

[30] R Aaij et al (LHCb collaboration) JHEP 1309 145 (2013) arXiv13074556

[31] G Burdman and J Kambor Phys Rev D55 28172826 (1997) arXivhep-ph9602353[hep-ph]

[32] D Becirevic A Le Yaouanc L Oliver J-C Raynal P Roudeau and J Serrano Phys RevD87 no 5 054007 (2013) arXiv12065869 [hep-ph]

[33] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052022 (2015)arXiv14125502 [hep-ex]

[34] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 7 072012 (2015)arXiv150807560 [hep-ex]

[35] M Ablikim et al (BESIII collaboration) Phys Rev D92 no 11 112008 (2015)arXiv151000308 [hep-ex]

[36] L Widhalm et al (Belle collaboration) Phys Rev Lett 97 061804 (2006)arXivhep-ex0604049 [hep-ex]

[37] B Aubert et al (BABAR collaboration) Phys Rev D76 052005 (2007) arXiv07040020[hep-ex]

[38] D Besson et al (CLEO collaboration) Phys Rev D80 032005 (2009) arXiv09062983[hep-ex]

[39] S Dobbs et al (CLEO collaboration) Phys Rev D77 112005 (2008) arXiv07121020[hep-ex]

[40] G Huang et al (CLEO collaboration) Phys Rev Lett 94 011802 (2005)arXivhep-ex0407035 [hep-ex]

[41] J Link et al (FOCUS collaboration) Phys Lett B607 233242 (2005)arXivhep-ex0410037 [hep-ex]

[42] J Adler et al (MARK-III collaboration) Phys Rev Lett 62 1821 (1989)

45

[43] K Kodama et al (Fermilab E653 collaboration) Phys Rev Lett 66 18191822 (1991)

[44] K Kodama et al (E653 collaboration) Phys Lett B336 605613 (1994)

[45] P L Frabetti et al (E687 collaboration) Phys Lett B364 127136 (1995)

[46] P L Frabetti et al (E687 collaboration) Phys Lett B315 203208 (1993)

[47] J C Anjos et al (Tagged Photon Spectrometer collaboration) Phys Rev Lett 6215871590 (1989)

[48] M Ablikim et al (BES collaboration) Phys Lett B597 3946 (2004)arXivhep-ex0406028 [hep-ex]

[49] M Ablikim et al (BES collaboration) (2006) arXivhep-ex0610019 [hep-ex]

[50] A Bean et al (CLEO collaboration) Phys Lett B317 647654 (1993)

[51] BESIII collaboration presented at ICHEP 2014 conference 2014httpindicoificuvesindicogetFilepyaccesscontribId=69ampsessionId=25ampresId=

0ampmaterialId=slidesampconfId=2025

[52] J G Korner and G A Schuler Z Phys C46 93 (1990)

[53] FLAG collaboration httpitpwikiunibechagimages44bFLAGpdf 2014httpitpwikiunibechflagimages44bFLAGpdf

[54] J Anjos et al (Fermilab E691 collaboration) Phys Rev Lett 65 26302633 (1990)

[55] K Kodama et al (Fermilab E653 collaboration) Phys Lett B274 246252 (1992)

[56] P Frabetti et al (Fermilab E687 collaboration) Phys Lett B307 262268 (1993)

[57] E Aitala et al (E791 collaboration) Phys Rev Lett 80 13931397 (1998)arXivhep-ph9710216 [hep-ph]

[58] E Aitala et al (E791 collaboration) Phys Lett B440 435441 (1998)arXivhep-ex9809026 [hep-ex]

[59] M Adamovich et al (BEATRICE collaboration) Eur Phys J C6 3541 (1999)

[60] J Link et al (FOCUS collaboration) Phys Lett B544 8996 (2002)arXivhep-ex0207049 [hep-ex]

[61] J Link et al (FOCUS collaboration) Phys Lett B607 6777 (2005)arXivhep-ex0410067 [hep-ex]

[62] P del Amo Sanchez et al (BABAR collaboration) Phys Rev D83 072001 (2011)arXiv10121810 [hep-ex]

[63] B Aubert et al (BABAR collaboration) Phys Rev D78 051101 (2008) arXiv08071599[hep-ex]

[64] H Mahlke eConf C0610161 014 (2006) arXivhep-ex0702014 [hep-ex]

[65] J Link et al (FOCUS collaboration) Phys Lett B535 4351 (2002)arXivhep-ex0203031 [hep-ex]

46

[66] K M Ecklund et al (CLEO collaboration) Phys Rev D80 052009 (2009)arXiv09073201 [hep-ex]

[67] R A Briere et al (CLEO collaboration) Phys Rev D81 112001 (2010) arXiv10041954[hep-ex]

[68] P Estabrooks R Carnegie A D Martin W Dunwoodie T Lasinski et al Nucl PhysB133 490 (1978)

[69] D Aston et al Nucl Phys B296 493 (1988)

[70] B Aubert et al (BABAR collaboration) Phys Rev Lett 90 242001 (2003)arXivhep-ex0304021 [hep-ex]

[71] D Besson et al (CLEO Collaboration collaboration) PhysRev D68 032002 (2003)arXivhep-ex0305100 [hep-ex]

[72] K Abe et al (Belle Collaboration collaboration) PhysRevLett 92 012002 (2004)arXivhep-ex0307052 [hep-ex]

[73] B Aubert et al (BaBar Collaboration collaboration) PhysRev D69 031101 (2004)arXivhep-ex0310050 [hep-ex]

[74] K Abe et al (Belle collaboration) Phys Rev D69 112002 (2004) arXivhep-ex0307021[hep-ex]

[75] J M Link et al (FOCUS Collaboration collaboration) PhysLett B586 1120 (2004)arXivhep-ex0312060 [hep-ex]

[76] S Godfrey and N Isgur Phys Rev D32 189231 (1985)

[77] S Godfrey and R Kokoski Phys Rev D43 16791687 (1991)

[78] N Isgur and M B Wise Phys Rev Lett 66 11301133 (1991)

[79] P Schweitzer S Bo and M Radici Phys Rev D66 114004 (2002)arXivhep-ph0207230 [hep-ph]

[80] F Jugeau A Le Yaouanc L Oliver and J-C Raynal Phys Rev D72 094010 (2005)arXivhep-ph0504206 [hep-ph]

[81] P Colangelo F De Fazio and R Ferrandes ModPhysLett A19 20832102 (2004)arXivhep-ph0407137 [hep-ph]

[82] R N Cahn and J D Jackson Phys Rev D68 037502 (2003) arXivhep-ph0305012[hep-ph]

[83] T Barnes F E Close and H J Lipkin PhysRev D68 054006 (2003)arXivhep-ph0305025 [hep-ph]

[84] H Lipkin PhysLett B580 5053 (2004) arXivhep-ph0306204 [hep-ph]

[85] W A Bardeen E J Eichten and C T Hill Phys Rev D68 054024 (2003)arXivhep-ph0305049 [hep-ph]

[86] B Aubert et al (BaBar Collaboration collaboration) PhysRev D80 092003 (2009)arXiv09080806 [hep-ex]

47

[87] R Aaij et al (LHCb Collaboration collaboration) JHEP 1210 151 (2012) arXiv12076016[hep-ex]

[88] R Aaij et al (LHCb collaboration) Phys Rev Lett 113 162001 (2014) arXiv14077574[hep-ex]

[89] R Aaij et al (LHCb collaboration) JHEP 02 133 (2016) arXiv160101495 [hep-ex]

[90] T Matsuki T Morii and K Sudoh EurPhysJ A31 701704 (2007)arXivhep-ph0610186 [hep-ph]

[91] N Isgur and M B Wise PhysLett B232 113117 (1989)

[92] M Neubert PhysRept 245 259396 (1994) arXivhep-ph9306320 [hep-ph]

[93] B Aubert et al (BaBar Collaboration collaboration) PhysRev D74 032007 (2006)arXivhep-ex0604030 [hep-ex]

[94] V M Abazov et al (D0 Collaboration collaboration) PhysRevLett 102 051801 (2009)arXiv07123789 [hep-ex]

[95] B Aubert et al (BABAR collaboration) Phys Rev D77 011102 (2008) arXiv07081565[hep-ex]

[96] P L Frabetti et al (E687 Collaboration collaboration) PhysRevLett 72 324327 (1994)

[97] J P Alexander et al (CLEO Collaboration collaboration) PhysLett B303 377384 (1993)

[98] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B297 425431 (1992)

[99] P Avery et al (CLEO Collaboration collaboration) PhysRev D41 774 (1990)

[100] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B230 162 (1989)

[101] J P Lees et al (BaBar Collaboration collaboration) PhysRev D83 072003 (2011)arXiv11032675 [hep-ex]

[102] R Aaij et al (LHCb collaboration) Phys Rev D90 no 7 072003 (2014) arXiv14077712[hep-ex]

[103] R Aaij et al (LHCb collaboration) PhysLett B698 1420 (2011) arXiv11020348[hep-ex]

[104] B Aubert et al (BaBar Collaboration collaboration) PhysRevLett 97 222001 (2006)arXivhep-ex0607082 [hep-ex]

[105] H Albrecht et al (ARGUS Collaboration collaboration) ZPhys C69 405408 (1996)

[106] Y Kubota et al (CLEO Collaboration collaboration) PhysRevLett 72 19721976 (1994)arXivhep-ph9403325 [hep-ph]

[107] J P Lees et al (BaBar collaboration) Phys Rev D91 no 5 052002 (2015)arXiv14126751 [hep-ex]

[108] J Brodzicka et al (Belle collaboration) Phys Rev Lett 100 092001 (2008)arXiv07073491 [hep-ex]

48

[109] B Aubert et al (BABAR collaboration) Phys Rev D79 112004 (2009) arXiv09011291[hep-ex]

[110] R Aaij et al (LHCb collaboration) Phys Rev D92 no 3 032002 (2015)arXiv150501710 [hep-ex]

[111] R Aaij et al (LHCb collaboration) Phys Rev D92 no 1 012012 (2015)arXiv150501505 [hep-ex]

[112] A Kuzmin et al (Belle Collaboration collaboration) PhysRev D76 012006 (2007)arXivhep-ex0611054 [hep-ex]

[113] H Abramowicz et al (ZEUS Collaboration collaboration) NuclPhys B866 229254 (2013)arXiv12084468 [hep-ex]

[114] A Abulencia et al (CDF Collaboration collaboration) PhysRev D73 051104 (2006)arXivhep-ex0512069 [hep-ex]

[115] K Abe et al (Belle collaboration) Phys Rev Lett 94 221805 (2005)arXivhep-ex0410091 [hep-ex]

[116] P Avery et al (CLEO Collaboration collaboration) PhysLett B331 236244 (1994)arXivhep-ph9403359 [hep-ph]

[117] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B232 398 (1989)

[118] J C Anjos et al (Tagged Photon Spectrometer Collaboration collaboration) PhysRevLett62 1717 (1989)

[119] T Bergfeld et al (CLEO Collaboration collaboration) PhysLett B340 194204 (1994)

[120] R Aaij et al (LHCb collaboration) Phys Rev D91 no 9 092002 (2015)arXiv150302995 [hep-ex] [Erratum Phys RevD93no11119901(2016)]

[121] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B221 422 (1989)

[122] H Albrecht et al (ARGUS Collaboration collaboration) PhysLett B231 208 (1989)

[123] P Abreu et al (DELPHI Collaboration collaboration) PhysLett B426 231242 (1998)

[124] D Matvienko et al (Belle collaboration) Phys Rev D92 no 1 012013 (2015)arXiv150503362 [hep-ex]

[125] P Krokovny et al (Belle collaboration) Phys Rev Lett 91 262002 (2003)arXivhep-ex0308019 [hep-ex]

[126] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 181801 (2004)arXivhep-ex0408041 [hep-ex]

[127] S K Choi et al (Belle collaboration) Phys Rev D91 no 9 092011 (2015)arXiv150402637 [hep-ex] [Addendum Phys RevD92no3039905(2015)]

[128] A Drutskoy et al (Belle collaboration) Phys Rev Lett 94 061802 (2005)arXivhep-ex0409026 [hep-ex]

[129] B Aubert et al (BABAR collaboration) Phys Rev D74 031103 (2006)arXivhep-ex0605036 [hep-ex]

49

[130] S Chekanov et al (ZEUS Collaboration collaboration) EurPhysJ C60 2545 (2009)arXiv08071290 [hep-ex]

[131] A Heister et al (ALEPH Collaboration collaboration) PhysLett B526 3449 (2002)arXivhep-ex0112010 [hep-ex]

[132] B Aubert et al (BABAR collaboration) Phys Rev Lett 103 051803 (2009)arXiv08080333 [hep-ex]

[133] G Burdman E Golowich J L Hewett and S Pakvasa Phys Rev D66 014009 (2002)arXivhep-ph0112235 [hep-ph]

[134] S Fajfer A Prapotnik S Prelovsek P Singer and J Zupan Nucl Phys Proc Suppl 1159397 (2003) arXivhep-ph0208201 [hep-ph]

[135] S Fajfer N Kosnik and S Prelovsek Phys Rev D76 074010 (2007) arXiv07061133[hep-ph]

[136] E Golowich J Hewett S Pakvasa and A A Petrov Phys Rev D79 114030 (2009)arXiv09032830 [hep-ph]

[137] A Paul I I Bigi and S Recksiegel Phys Rev D82 094006 (2010) arXiv10083141[hep-ph]

[138] A Borisov (2011) arXiv11123269 [hep-ph]

[139] R-M Wang J-H Sheng J Zhu Y-Y Fan and Y Gao Int J Mod Phys A29 no 291450169 (2014)

[140] S de Boer and G Hiller Phys Rev D93 no 7 074001 (2016) arXiv151000311 [hep-ph]

[141] P Rubin et al (CLEO collaboration) Phys Rev D82 092007 (2010) arXiv10091606[hep-ex]

[142] V Abazov et al (D0 collaboration) Phys Rev Lett 100 101801 (2008) arXiv07082094[hep-ex]

[143] R Aaij et al (LHCb collaboration) Phys Lett B728 234243 (2014) arXiv13102535[hep-ex]

[144] R Aaij et al (LHCb collaboration) Phys Lett B724 203212 (2013) arXiv13046365[hep-ex]

[145] T Coan et al (CLEO collaboration) Phys Rev Lett 90 101801 (2003)arXivhep-ex0212045 [hep-ex]

[146] M Ablikim et al (BESIII collaboration) Phys Rev D91 no 11 112015 (2015)arXiv150503087 [hep-ex]

[147] J P Lees et al (BABAR collaboration) Phys Rev D85 091107 (2012) arXiv11106480[hep-ex]

[148] N K Nisar et al (Belle collaboration) Phys Rev D93 no 5 051102 (2016)arXiv151202992 [hep-ex]

[149] P Haas et al (CLEO collaboration) Phys Rev Lett 60 1614 (1988)

50

[150] H Albrecht et al (ARGUS collaboration) Phys Lett B209 380 (1988)

[151] J Adler et al (MARK-III collaboration) Phys Rev D37 2023 (1988) Erratum ibid D40(1989) 3788

[152] A Freyberger et al (CLEO collaboration) Phys Rev Lett 76 30653069 (1996)

[153] D Pripstein et al (E789 collaboration) Phys Rev D61 032005 (2000)arXivhep-ex9906022 [hep-ex]

[154] E Aitala et al (E791 collaboration) Phys Lett B462 401409 (1999)arXivhep-ex9906045 [hep-ex]

[155] B Aubert et al (BABAR collaboration) Phys Rev Lett 93 191801 (2004)arXivhep-ex0408023 [hep-ex]

[156] M Petric et al (Belle collaboration) Phys Rev D81 091102 (2010) arXiv10032345[hep-ex]

[157] K Kodama et al (E653 collaboration) Phys Lett B345 8592 (1995)

[158] I Abt et al (HERA-B collaboration) Phys Lett B596 173183 (2004)arXivhep-ex0405059 [hep-ex]

[159] T Aaltonen et al (CDF collaboration) Phys Rev D82 091105 (2010) arXiv10085077[hep-ex]

[160] R Aaij et al (LHCb collaboration) Phys Lett B725 1524 (2013) arXiv13055059[hep-ex]

[161] E Aitala et al (E791 collaboration) Phys Rev Lett 86 39693972 (2001)arXivhep-ex0011077 [hep-ex]

[162] J Adler et al (MARK-III collaboration) Phys Rev D40 906 (1989)

[163] J Becker et al (MARK-III collaboration) Phys Lett B193 147 (1987)

[164] R Aaij et al (LHCb collaboration) Phys Lett B754 167175 (2016) arXiv151200322[hep-ex]

[165] P Rubin et al (CLEO collaboration) Phys Rev D79 097101 (2009) arXiv09041619[hep-ex]

[166] P Frabetti et al (E687 collaboration) Phys Lett B398 239244 (1997)

[167] J P Lees et al (BABAR collaboration) Phys Rev D84 072006 (2011) arXiv11074465[hep-ex]

[168] (BESIII collaboration) M-G Zhao D rareforbidden decays at BESIII in 7th International

Workshop on Charm Physics (Charm 2015) Detroit MI USA May 18-22 2015 2016arXiv160508952 [hep-ex]httpinspirehepnetrecord1466292filesarXiv160508952pdf

[169] J Link et al (FOCUS collaboration) Phys Lett B572 2131 (2003)arXivhep-ex0306049 [hep-ex]

51

  • Introduction
  • D decays
    • Interplay of direct and indirect CP violation
    • Semileptonic decays
      • Introduction
      • DP decays
      • Form factor parameterizations
      • Simple pole
      • z expansion
      • Three-pole formalism
      • Experimental techniques and results
      • Combined results for the DK channel
      • Combined results for the D channel
      • Vcs and Vcd determination
      • DV decays
      • Form factor measurements
        • Excited D(s) mesons
        • Rare and forbidden decays
          • References
Page 10: Averages of b-hadron, c-hadron, and -lepton …ific.uv.es/~oyangur/tempo/Summer16.pdfAverages of b-hadron, c-hadron, and ˝-lepton properties as of summer 2016 Heavy Flavor Averaging

224 Simple pole

Equation (10) can be simplied by neglecting the sum over eective poles leaving only theexplicit vector meson pole This approximation is referred to as nearest pole dominance orvector-meson dominance The resulting parameterization is

f+(q2) =f+(0)

(1minus q2m2pole)

(11)

However values of mpole that give a good t to the data do not agree with the expected vectormeson masses [21] To address this problem the modied pole or Becirevic-Kaidalov (BK)parameterization [22] was introduced mpole

radicαBK is interpreted as the mass of an eective

pole higher than mpole thus it is expected that αBK lt 1The parameterization takes the form

f+(q2) =f+(0)

(1minus q2m2pole)

1(1minus αBK

q2

m2pole

) (12)

These parameterizations are used by several experiments to determine form factor parametersMeasured values of mpole and αBK are listed in Tables 2 and 3 for D rarr K`ν` and D rarr π`ν`decays respectively

225 z expansion

An alternative series expansion around some value q2 = t0 to parameterize f+(q2) can beused [23 24 25 19] This parameterization is model independent and satises general QCDconstraints being suitable for tting experimental data The expansion is given in terms of acomplex parameter z which is the analytic continuation of q2 into the complex plane

z(q2 t0) =

radict+ minus q2 minus

radict+ minus t0radic

t+ minus q2 +radict+ minus t0

(13)

where tplusmn equiv (mDplusmnmP )2 and t0 is the (arbitrary) q2 value corresponding to z = 0 The physical

region corresponds to plusmn|z|max = plusmn0051 for D rarr K`ν` and = plusmn017 for D rarr π`ν` usingt0 = t+(1minus

radic1minus tminust+)

The form factor is expressed as

f+(q2) =1

P (q2)φ(q2 t0)

infinsumk=0

ak(t0)[z(q2 t0)]k (14)

where the P (q2) factor accommodates sub-threshold resonances via

P (q2) equiv

1 (D rarr π)

z(q2M2Dlowasts

) (D rarr K) (15)

The outer function φ(t t0) can be any analytic function but a preferred choice (see eg

Refs [23 2426]) obtained from the Operator Product Expansion (OPE) is

φ(q2 t0) = α(radic

t+ minus q2 +radict+ minus t0

)times

t+ minus q2

(t+ minus t0)14

(radict+ minus q2 +

radict+ minus tminus)32

(radict+ minus q2 +

radict+)5

(16)

10

with α =radicπm2

c3 The OPE analysis provides a constraint upon the expansion coecientssumNk=0 a

2k le 1 These coecients receive 1MD corrections and thus the constraint is only ap-

proximate However the expansion is expected to converge rapidly since |z| lt 0051 (017) forDrarrK (Drarrπ) over the entire physical q2 range and Eq (14) remains a useful parameteriza-tion The main disadvantage as compared to phenomenological approaches is that there is nophysical interpretation of the tted coecients aK

226 Three-pole formalism

An update of the vector pole dominance model has been developed for the D rarr π`ν` channel[27] It uses information of the residues of the semileptonic form factor at its rst two polesthe Dlowast(2010) and Dlowast

prime(2600) resonances The form factor is expressed as an innite sum of

residues from JP = 1minus states with masses mDlowastn

f+(q2) =infinsumn=0

Resq2=m2

Dlowastn

f+(q2)

m2Dlowastnminus q2

(17)

with the residues given by

Resq2=m2

Dlowastn

f+(q2) =1

2mDlowastnfDlowastngDlowastnDπ (18)

Values of the fDlowast and fDlowastprime decay constants have been obtained by lattice QCD calculationsrelative to fD with 2 and 28 precision respectively [27] The couplings to the Dπ stategDlowastDπ and gDlowastprimeDπ are extracted from measurements of the Dlowast(2010) and Dlowast

prime(2600) widths by

BABAR and LHCb experiments [28 29 30] Thus the contribution from the rst pole is knownwith a 3 accuracy The contribution from the Dlowast

prime(2600) is determined with poorer accuracy

sim 30 mainly due to lattice uncertainties A superconvergence condition [31] is applied

infinsumn=0

Resq2=m2

Dlowastn

f+(q2) = 0 (19)

protecting the form factor behavior at large q2 Within this model the rst two poles are notsucient to describe the data and a third eective pole needs to be included

One of the advantages of this phenomenological model is that it can be extrapolated outsidethe charm physical region providing a method to extract the CKM matrix element Vub usingthe ratio of the form factors of the D rarr π`ν and B rarr π`ν decay channels It will be used oncelattice calculations provide the form factor ratio f+

Bπ(q2)f+Dπ(q2) at the same pion energy

This form factor description can be extended to the D rarr K`ν decay channel consideringthe contribution of several cs resonances with JP = 1minus The rst two pole masses contributingto the form factor correspond to the Dlowasts(2112) and Dlowasts1(2700) resonant states [5] A constrainton the rst residue can be obtained using information of the fK decay constant [5] and theg coupling extracted from the Dlowast+ width [28] The contribution from the second pole can beevaluated using the decay constants from [32] the measured total width and the ratio of DlowastKand DK decay branching fractions [5]

11

227 Experimental techniques and results

Dierent techniques by several experiments are used to measure D meson semileptonic decayswith a pseudoscalar particle in the nal state The most recent results are provided by theBABAR [33] and BES III [34 35] collaborations Belle [36] BABAR [37] and CLEO-c [38 39]collaborations have previously reported results The Belle collaboration fully reconstructs thee+eminus rarr DDX events from the continuum under the Υ (4S) resonance achieving a very goodq2 resolution (15 MeV2) and low background level but having a low eciency Using 282 fbminus1about 1300 and 115 signal semileptonic decays are isolated for each lepton avor (e and micro) forthe Cabibbo-favoured and suppressed modes respectively The BABAR experiment uses a partialreconstruction technique where the semileptonic decays are tagged through the Dlowast+ rarr D0π+

decay The D direction and neutrino energy is obtained using information from the rest of theevent With 75 fbminus1 74000 signal events in theD0 rarr Kminuse+ν mode are obtained This techniqueprovides larger statistics but a higher background level and poorer q2 resolution (ranging from66 to 219 MeV2) In this case the measurement of the branching fraction is obtained bynormalizing to the D0 rarr Kminusπ+ decay channel and will benet from future improvements inthe determination of this reference channel The measurement of the Cabibbo suppressed modehas been recently obtained using the same technique and 350 fbminus1 data 5000 D0 rarr πminuse+νsignal events are reconstructed using this method [33]

The CLEO-c experiment uses two dierent methods to measure charm semileptonic decaysTagged analyses [38] rely on the full reconstruction of Ψ(3770) rarr DD events One of the Dmesons is reconstructed in a hadronic decay mode the other in the semileptonic channel Theonly missing particle is the neutrino so the q2 resolution is very good and the background levelvery low With the entire CLEO-c data sample 818 pbminus1 14123 and 1374 signal events arereconstructed for the D0 rarr Kminuse+ν and D0 rarr πminuse+ν channels and 8467 and 838 for the

D+ rarr K0e+ν and D+ rarr π0e+ν decays respectively Another technique without tagging the

D meson in a hadronic mode (untagged in the following) has been also used by CLEO-c [39]In this method the entire missing energy and momentum in an event are associated with theneutrino four momentum with the penalty of larger background as compared to the taggedmethod Using the tagged method the BES III experiment measures the D0 rarr Kminuse+ν andD0 rarr πminuse+ν decay channels With 29 fbminus1 they fully reconstruct 70700 and 6300 signal eventsfor each channel respectively [34] In a separated analysis the BES III experiment measuresalso the D+ decay mode into D+ rarr K0

Le+ν [35] Using several tagged hadronic events they

reconstruct 20100 semileptonic candidates

Previous measurements were also performed by several experiments Events registeredat the Υ (4S) energy corresponding to an integrated luminosity of 7 fbminus1 were analyzed byCLEO III [40] Fixed targed photo-production experiments performed also measurements ofthe normalized form factor distribution (FOCUS [41]) and total decay rates (Mark-III [42]E653 [43 44] E687 [45 46] E691 [47] BES II [48 49] CLEO II [50]) In the FOCUS xedtarget photo-production experiment D0 semimuonic events were obtained from the decay of aDlowast+ with a kaon or a pion detected

Results of the hadronic form factor parameters mpole and αBK obtained from the measure-ments discussed above are given in Tables 2 and 3

The z-expansion formalism has been used by BABAR [37 33] BES III [51] and CLEO-c [38] [39] Their ts use the rst three terms of the expansion and the results for the ratiosr1 equiv a1a0 and r2 equiv a2a0 are listed in Tables 4 and 5

12

Table 2 Results for mpole and αBK from various experiments for D0 rarr Kminus`+ν and D+ rarrK

0`+ν decays

D rarr K`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 189plusmn 005+004minus003 036plusmn 010+003

minus007

FOCUS (D0 ` = micro) [41] 193plusmn 005plusmn 003 028plusmn 008plusmn 007Belle (D0 ` = e micro) [36] 182plusmn 004plusmn 003 052plusmn 008plusmn 006BABAR (D0 ` = e) [37] 1889plusmn 0012plusmn 0015 0366plusmn 0023plusmn 0029

CLEO-c (tagged) (D0 D+ ` = e) [38] 193plusmn 002plusmn 001 030plusmn 003plusmn 001CLEO-c (untagged) (D0 ` = e) [39] 197plusmn 003plusmn 001 021plusmn 005plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 196plusmn 004plusmn 002 022plusmn 008plusmn 003

BESIII (D0 ` = e) [34] 1921plusmn 0010plusmn 0007 0309plusmn 0020plusmn 0013BESIII (D+ ` = e) [35] 1953plusmn 0044plusmn 0036 0239plusmn 0077plusmn 0065

Table 3 Results formpole and αBK from various experiments for D0 rarr πminus`+ν and D+ rarr π0`+νdecays

D rarr π`ν` Expt Mode Ref mpole (GeVc2) αBK

CLEO III (D0 ` = e micro) [40] 186+010+007minus006minus003 037+020

minus031 plusmn 015FOCUS (D0 ` = micro) [41] 191+030

minus015 plusmn 007 Belle (D0 ` = e micro) [36] 197plusmn 008plusmn 004 010plusmn 021plusmn 010

CLEO-c (tagged) (D0 D+ ` = e) [38] 191plusmn 002plusmn 001 021plusmn 007plusmn 002CLEO-c (untagged) (D0 ` = e) [39] 187plusmn 003plusmn 001 037plusmn 008plusmn 003CLEO-c (untagged) (D+ ` = e) [39] 197plusmn 007plusmn 002 014plusmn 016plusmn 004

BES III (D0 ` = e) [34] 1911plusmn 0012plusmn 0004 0279plusmn 0035plusmn 0011BABAR (D0 ` = e) [33] 1906plusmn 0029plusmn 0023 0268plusmn 0074plusmn 0059

Table 4 Results for r1 and r2 from various experiments for the D rarr K`ν` decay channel Thecorrelation coecient between these parameters is larger than 09

Expt D rarr K`ν` Mode Ref r1 r2

BABAR (D0 ` = e) [37] minus25plusmn 02plusmn 02 06plusmn 60plusmn 50CLEO-c (tagged) (D0 ` = e) [38] minus265plusmn 034plusmn 008 13plusmn 9plusmn 1CLEO-c (tagged) (D+ ` = e) [38] minus166plusmn 044plusmn 010 minus14plusmn 11plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus24plusmn 04plusmn 01 21plusmn 11plusmn 2CLEO-c (untagged) (D+ ` = e) [39] minus28plusmn 6plusmn 2 32plusmn 18plusmn 4

BES III (D0 ` = e) [34] minus2334plusmn 0159plusmn 0080 342plusmn 391plusmn 241BES III (D+ ` = e) [35] minus223plusmn 042plusmn 053 113plusmn 85plusmn 87

13

Table 5 Results for r1 and r2 from various experiments for D rarr π`ν` The correlationcoecient between these parameters is larger than 09

Expt D rarr π`ν` Mode Ref r1 r2

CLEO-c (tagged) (D0 ` = e) [38] minus280plusmn 049plusmn 004 6 plusmn 3 plusmn 0CLEO-c (tagged) (D+ ` = e) [38] minus137plusmn 088plusmn 024 -4 plusmn 5 plusmn 1CLEO-c (untagged) (D0 ` = e) [39] minus21plusmn 07plusmn 03 minus12plusmn 48plusmn 17CLEO-c (untagged) (D+ ` = e) [39] minus02plusmn 15plusmn 04 minus98plusmn 91plusmn 21

BES III (D0 ` = e) [34] minus185plusmn 022plusmn 007 minus14plusmn 15plusmn 05BABAR (D0 ` = e) [33] minus131plusmn 070plusmn 043 minus42plusmn 40plusmn 19

228 Combined results for the D rarr K`ν` channel

The q2 distribution provided by each individual measurement is used to determine a combinedresult by performing a t to the z-expansion formalism at second order Results for the formfactor normalization fK+ (0)|Vcs| and the shape parameters r1 and r2 for each individual mea-surement and for the combination are presented in Table 6 Measurements have been correctedwith respect to the original ones using recent values from PDG [5] This includes updatedbranching fractions of normalization channels corrected CKM matrix elements and the D me-son lifetime The BABAR measurement has been corrected accounting for nal-state radiationThe result for the D+ rarr K0

Le+νe decay channel from BES III [35] is included as a constraint

in the combined result since correlation matrices are not provided Correlation coecients ofthe parameters are quoted in the last column of Table 6 The χ2 per degree of freedom is1147101 Results are shown in Figure 4

In the combination of the electron and muon channels the measurements with muons arecorrected for the reduction of phase space and for the f0(q2) contribution [52] Channels witha D0 or a D+ are combined assuming isospin invariance and using physical meson and leptonmasses These combined results are noted as D rarr K`ν` in the following Hadronic formfactors are assumed to be the same for charged and neutral D mesons Separate results for the

D0 rarr Kminus`+ν` and D+ rarr K

0`+ν` decay channels are shown in Table 7 and Figure 3 Using the

tted parameters and integrating over the full q2 range the combined semileptonic branchingfraction expressed in terms of the D0 decay channel gives

B(D0 rarr Kminus`+ν`) = (3490plusmn 0011plusmn 0020) (20)

Data from the dierent experiments are also tted within the three-pole form factor formal-ism Constraints on the rst and second poles are imposed using information of the Dlowasts(2112)and Dlowasts1(2700) resonances Results are presented in Table 8 Fitted parameters are the rsttwo residues γK0 = Res

q2=m2Dlowasts (2112)

fK+ (q2) and γπ1 = Resq2=m2

Dlowasts1(2700)

fK+ (q2) and an eective mass mDlowastprimeprimes eff

accounting for higher mass hadronic contributions It is found that the tted eective thirdpole mass is larger than the mass of the second radial excitation around 32 GeV as expectedThe contribution to the form factor by only the Dlowasts resonance is disfavoured by the dataFigure 2 (left) shows the result of the tted form factors for the z-expansion and three-poleparametrizations

14

Table 6 Results of the ts to D rarr K`ν` measurements from several experiments using thez-expansion External inputs have been updated to PDG [5] The correlation coecients listedin the last column refer to ρ12 equiv ρ|Vcs|fK+ (0)r1 ρ13 equiv ρ|Vcs|fK+ (0)r2 and ρ23 equiv ρr1r2 and are for the

total uncertainties (statistical oplus systematic) The result for the D+ rarr K0Le

+νe decay channelfrom BES III [35] is included in the combined results as a constraint on the normalization|Vcs|fK+ (0) The entry others refers to total decay rates measured by Mark-III [42] E653 [4344]E687 [4546] E691 [47] BES II [4849] and CLEO II [50]

Expt D rarr K`ν` Mode |Vcs|fK+ (0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 07195(35)(43) minus233(16)(8) 34(40)(25) minus021058minus081CLEO-c (tagged) [38] (D0 D+) 07189(64)(48) minus229(28)(27) 30(70)(10) minus019058minus081CLEO-c (untagged) [39] (D0 D+) 07436(76)(79) minus257(33)(18) 239(89)(43) minus034066minus084

BABAR [37] (D0) 07241(64)(60) minus245(20)(18) minus06(60)(38) minus036059minus082Belle [36] (D0) 0700(19) minus306(71) minus33(179) minus020066minus081

FOCUS [41] and others 0724(29) minus254(75) 70(128) minus002002minus097Combined (D0 D+) 07226(22)(26) minus238(11)(6) 47(26)(14) minus019051minus084

Table 7 Results for the D0 rarr Kminus`+ν` and D+ rarr K0`+ν` decays channels using the z-

expansion formalism at second order

Fit value D0 rarr Kminus`+ν` D+ rarr K0`+ν`

|Vcs|fK+ (0) 07219 plusmn 00024 plusmn 00027 0726 plusmn 0005 plusmn 0007r1 minus241 plusmn 011 plusmn 007 minus207 plusmn 038 plusmn 010r2 47 plusmn 27 plusmn 14 54 plusmn 82 plusmn 46

ρ12ρ13ρ23 minus019051minus084 minus010039minus084

Table 8 Results of the three-pole model form factors obtained from a t to all measurementsFitted parameters are the rst two residues γK0 and γK1 which are constrained using presentmeasurements of masses and widths of the Dlowasts and Dlowasts1 mesons and lattice computations ofdecay constants and the eective mass mDlowast

primeprimes eff

accounting for higher mass hadronic contribu-tions

Parameter Combined result (D rarr K`ν`)

γK0 485 plusmn 008 GeV2

γK1 minus12 plusmn 030 GeV2

mDlowastprimeprimes eff

446 plusmn 026 GeV

15

Table 9 Results of the ts to D rarr π`ν` measurements from several experiments using thez-expansion External inputs are updated to PDG [5] The correlation coecients listed in thelast column refer to ρ12 equiv ρ|Vcd|fπ+(0)r1 ρ13 equiv ρ|Vcd|fπ+(0)r2 and ρ23 equiv ρr1r2 and are for the totaluncertainties (statistical oplus systematic)

Expt D rarr π`ν` mode |Vcd|fπ+(0) r1 r2 ρ12ρ13ρ23

BES III (tagged) [34] (D0) 01422(25)(10) minus186(23)(7) minus124(151)(47) minus037064minus093CLEO-c (tagged) [38] (D0 D+) 01507(42)(11) minus245(43)(9) 38(28)(6) minus043067minus094CLEO-c (untagged) [39] (D0 D+) 01394(58)(25) minus171(62)(25) minus28(40)(16) minus050069minus096

BABAR [37] (D0) 01381(36)(22) minus142(66)(45) minus35(37)(20) minus040057minus097Belle [36] (D0) 0142(11) minus183(100) 15(65) minus030059minus091Combined (D0 D+) 01426(17)(8) minus195(18)(1) minus052(117)(32) minus037063minus094

229 Combined results for the D rarr π`ν` channel

The combined result for the D rarr π`ν` decay channel is obtained from a t to BABAR BelleBES III and CLEO-c data with updated input values from [5] The available measurementsare tted in bins of q2 to the z-expansion model at second order Results of the individualts for each experiment and the combined result are shown in Table 9 The χ2 per degree offreedom of the combined t is 5155

Using the tted parameters and integrating over the full q2 range the combined semileptonicbranching fraction expressed in terms of the D0 decay channel gives

B(D0 rarr πminus`+ν`) = (2891plusmn 0030plusmn 0022)times 10minus3 (21)

Results of the three-pole model to the D rarr π`ν` data are shown in Table 10 Fittedparameters are the rst two residues γπ0 = Res

q2=m2Dlowastfπ+(q2) and γπ1 = Res

q2=m2

Dlowastprime

fπ+(q2) (which are

constrained using present measurements of masses and widths of the Dlowast(2010) and Dlowastprime(2600)

mesons and lattice computations of decay constants following [27]) and an eective massmDlowast

primeprimeeff accounting for higher mass hadronic contributions The Vcd value entering in the t is

given in Eq 22 The χ2 per degree of freedom of the combined t is 57557The eective mass mDlowast

primeprimeeff

is larger than the predicted mass of the second radially excited

state with JP = 1minus (sim 311 GeV) indicating that more contributions are needed to explain theform factor Figure 2 (right) shows the result of the combined form factor for the z-expansionand three-pole parameterizations

2210 Vcs and Vcd determination

Assuming unitarity of the CKM matrix the values of the CKM matrix elements entering incharm semileptonic decays are evaluated from the Vud Vtd and Vcb elements [5]

Vcs = 097343plusmn 000015

Vcd = 022521plusmn 000061 (22)

Using the combined values of fK+ (0)|Vcs| and fπ+(0)|Vcd| in Tables 6 and 9 leads to the formfactor values

fK+ (0) = 07423plusmn 00035

fπ+(0) = 06327plusmn 00086

16

-

15

1

05

z-expansion fit

Effective 3-pole fit

05 1

HFLAV

Summer 2016

15

q2 [GeV2]

3

2

1

- z-expansion fit

bull bull bull Effective 3-pole fit

HFLAVSummer 2016

o

1

Figure 2 Form factors as function of q2 for the D rarr K`ν` (left) and D rarr π`ν` (right) channelsobtained from a t to all experimental data Central values (central lines) and uncertainties(one σ deviation) are shown for the z-expansion and the 3-pole parameterization

Table 10 Results of the three-pole model to BABAR Belle BES III and CLEO-c (tagged anduntagged) data Fitted parameters are the rst two residues γπ0 and γπ1 which are constrainedusing present measurements of masses and widths of the Dlowast and Dlowast

primemesons and lattice

computations of decay constants and the eective mass mDlowastprimeprime

eff accounting for higher mass

hadronic contributions

Parameter Combined result (D rarr π`ν`)

γπ0 3881 plusmn 0093 GeV2

γπ1 -118 plusmn 030 GeV2

mDlowastprimeprime

eff417 plusmn 042 GeV

17

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5minus

4minus

3minus

2minus

1minus

0

1

ν + K lrarrDν + l- Krarr0D

ν + l0

K rarr+D

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ K lD + l- K0D

+ l0

K +D

Average

Figure 3 Results of the combined t shown separately for the D0 rarr Kminus`+ν and D+ rarr K0`+ν

decay channels Ellipses are shown for 68 CL

18

|cs

(0)|V+f06 065 07 075 08 085 09

1r

5

4

3

2

1

0

1

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

1r

4

3

2

1

0 + l- 0D BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

|cs

(0)|V+f06 065 07 075 08 085 09

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

|cd

(0)|V+f01 011 012 013 014 015 016 017 018 019 02

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

1r5 4 3 2 1 0 1

2r

40

20

0

20

40

60

+ l-

K0DE691 E687 E653 CLEOIIFOCUS MARK3 BESII

CLEO-c untagged

CLEO-c tagged

BaBar

BELLE

BES III

Average

1r4 3 2 1 0

2r

15

10

5

0

5

10

15

20

+ l- 0D

BELLE

CLEO-c untagged

CLEO-c tagged

BaBar

BES III

Average

Figure 4 The D0 rarr Kminus`+ν (left) and D0 rarr πminus`+ν (right) 68 CL error ellipses from theaverage t of the 3-parameter z-expansion results

19

which are in agreement with present lattice QCD computations [] fK+ (0) = 0747 plusmn 0019and fπ+(0) = 0666plusmn 0029 The experimental accuracy is at present higher than the one fromlattice calculations If instead one assumes the lattice QCD form factor values one obtains forthe CKM matrix elements using the combined results in Tables 6 and 9

Vcs = 0967plusmn 0025

Vcd = 02140plusmn 00097

still compatible with unitarity of the CKM matrix

2211 DrarrV `ν` decays

When the nal state hadron is a vector meson the decay can proceed through both vector andaxial vector currents and four form factors are needed The hadronic current is Hmicro = Vmicro +Amicrowhere [20]

Vmicro = 〈V (p ε)|qγmicroc|D(pprime)〉 =2V (q2)

mD +mV

εmicroνρσεlowastνpprimeρpσ (23)

Amicro = 〈V (p ε)| minus qγmicroγ5c|D(pprime)〉 = minusi (mD +mV )A1(q2)εlowastmicro

+ iA2(q2)

mD +mV

(εlowast middot q)(pprime + p)micro (24)

+ i2mV

q2

(A3(q2)minus A0(q2)

)[εlowast middot (pprime + p)]qmicro

In this expression mV is the daughter meson mass and

A3(q2) =mD +mV

2mV

A1(q2) minus mD minusmV

2mV

A2(q2) (25)

Kinematics require that A3(0) = A0(0) Terms proportional to qmicro are only important for thecase of τ leptons Thus only three form factors are relevant in the decays involving micro or eA1(q2) A2(q2) and V (q2) The dierential partial width is

dΓ(D rarr V `ν`)

dq2 d cos θ`=

G2F |Vcq|2

128π3m2D

plowast q2 times[(1minus cos θ`)

2

2|Hminus|2 +

(1 + cos θ`)2

2|H+|2 + sin2 θ`|H0|2

] (26)

where Hplusmn and H0 are helicity amplitudes corresponding to helicities of the V meson or virtualW given by

Hplusmn =1

mD +mV

[(mD +mV )2A1(q2) ∓ 2mD p

lowastV (q2)]

(27)

H0 =1

|q|m2D

2mV (mD +mV )times[(

1minus m2V minus q2

m2D

)(mD +mV )2A1(q2) minus 4plowast2A2(q2)

] (28)

20

plowast is the magnitude of the three-momentum of the V system measured in the D rest frameand θ` is the angle of the lepton momentum in the W rest frame with respect to the oppositedirection of the D meson (see Figure 5 for the electron case (θe)) The left-handed nature ofthe quark current manifests itself as |Hminus| gt |H+| The dierential decay rate for Drarr V `νfollowed by the vector meson decaying into two pseudoscalars is

dΓ(DrarrV `ν V rarrP1P2)

dq2d cos θV d cos θ`dχ=

3G2F

2048π4|Vcq|2

plowast(q2)q2

m2D

B(V rarr P1P2) times(1 + cos θ`)

2 sin2 θV |H+(q2)|2

+ (1minus cos θ`)2 sin2 θV |Hminus(q2)|2

+ 4 sin2 θ` cos2 θV |H0(q2)|2

minus 4 sin θ`(1 + cos θ`) sin θV cos θV cosχH+(q2)H0(q2)

+ 4 sin θ`(1minus cos θ`) sin θV cos θV cosχHminus(q2)H0(q2)

minus 2 sin2 θ` sin2 θV cos 2χH+(q2)Hminus(q2) (29)

where the helicity angles θ` θV and acoplanarity angle χ are dened in Fig 5

Figure 5 Decay angles θV θ` and χ Note that the angle χ between the decay planes is denedin the D-meson reference frame whereas the angles θV and θ` are dened in the V meson andW reference frames respectively

Ratios between the values of the hadronic form factors expressed at q2 = 0 are usuallyintroduced

rV equiv V (0)A1(0) r2 equiv A2(0)A1(0) (30)

2212 Form factor measurements

In 2002 FOCUS reported [65] an asymmetry in the observed cos(θV ) distribution in D+ rarrKminusπ+micro+ν decays This is interpreted as evidence for an S-wave Kminusπ+ component in thedecay amplitude Since H0 typically dominates over Hplusmn the distribution given by Eq (29)is after integration over χ roughly proportional to cos2 θV Inclusion of a constant S-waveamplitude of the form Aeiδ leads to an interference term proportional to |AH0 sin θ` cos θV |this term causes an asymmetry in cos(θV ) When FOCUS t their data including this S-wave

21

amplitude they obtained A = 0330 plusmn 0022 plusmn 0015 GeVminus1 and δ = 068 plusmn 007 plusmn 005 [60]Both BABAR [63] and CLEO-c [66] have also found evidence for an f0 rarr K+Kminus component insemileptonic Ds decays

The CLEO-c collaboration extracted the form factors H+(q2) Hminus(q2) and H0(q2) from11000 D+ rarr Kminusπ+`+ν` events in a model-independent fashion directly as functions of q2 [67]They also determined the S-wave form factor h0(q2) via the interference term despite the factthat the Kπ mass distribution appears dominated by the vector Klowast(892) state It is observedthat H0(q2) dominates over a wide range of q2 especially at low q2 The transverse form factorHt(q

2) which can be related to A3(q2) is small compared to lattice gauge theory calculationsand suggests that the form factor ratio r3 equiv A3(0)A1(0) is large and negative

BABAR [62] selected a large sample of 244 times 103 D+ rarr Kminusπ+e+νe candidates with a ratioSB sim 23 from an analyzed integrated luminosity of 347 fbminus1 With four particles emittedin the nal state the dierential decay rate depends on ve variables In addition to the fourvariables dened in previous sections there is also m2 the mass squared of the Kπ systemTo analyze the D+ rarr Kminusπ+e+νe decay channel it is assumed that all form factors have aq2 variation given by the simple pole model and the eective pole mass value mA = (263 plusmn010 plusmn 013) GeVc2 is tted for the axial vector form factors This value is compatiblewith expectations when comparing with the mass of JP = 1+ charm mesons For the massdependence of the form factors a Breit-Wigner with a mass dependent width and a Blatt-Weisskopf damping factor is used For the S-wave amplitude considering what was measuredin D+ rarr Kminusπ+π+ decays a polynomial variation below the K

lowast0(1430) and a Breit-Wigner

distribution above are assumed For the polynomial part a linear term is sucient to tdata It is veried that the variation of the S-wave phase is compatible with expectations fromelastic Kπ [68 69] (after correcting for δ32) according to the Watson theorem At variancewith elastic scattering a negative relative sign between the S- and P-waves is measured this iscompatible with the previous theorem Contributions from other spin-1 and spin-2 resonancesdecaying into Kminusπ+ are considered

In Fig 6 measured values from CLEO-c of the products q2H20 (q2) and q2h0(q2)H0(q2) are

compared with corresponding results from BABAR illustrating the dierence in behavior of thescalar h0 component and the H0 form factor For this comparison the plotted values fromBABAR for the two distributions are xed to 1 at q2 = 0 The dierent behavior of h0(q2) andH0(q2) can be explained by their dierent dependence in the plowast variable

Table 11 lists measurements of rV and r2 from several experiments Most of the measure-ments assume that the q2 dependence of hadronic form factors is given by the simple poleansatz Some of these measurements do not consider a S-wave contribution and it is includedin the measured values The measurements are plotted in Fig 7 which shows that they are allconsistent

22

-05

0

05

1

15

2

0 02 04 06 08 1

q2(GeVc2)

q2 H02 (q

2 )

CLEOc ---- BaBar q2H02(q2)

CLEOc BaBar q2H02h0(q

2)

HFLAVamp ())+-amp

Figure 6 Compar