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LHCb-CONF-2012-021July 6, 2012

First observation ofB−→ D0K−π+π− Decays to CP

even final states

The LHCb collaboration †

Abstract

We report a study of the suppressed B− → D0K−π+π− decays, where D0 →K−π+, D0 → K−K+ and D0 → π−π+. These decays are interesting because ofthe potential sensitivity to the weak phase γ, when the D0 decays to a final statethat is also accessible to D0. Here, we report first observations of this decay, wherethe neutral D meson is observed to decay into the CP even eigenstates, K+K−

and π+π−. The corresponding B− → D0π−π+π− decays provide a normalizationin which many systematic uncertainties cancel. From these rates, we measure thefollowing CP-sensitive relative decay rate

RCP+ = 0.95± 0.11(stat)± 0.02(syst).

We also measure several B± decay rate asymmetries and find,

ACP+s = −0.14 ± 0.10 (stat)± 0.01 (syst)

AK−π+

s = −0.009± 0.028(stat)± 0.013(syst)

ACP+d = −0.018± 0.018(stat)± 0.007(syst)

AK−π+

d = −0.006± 0.006(stat)± 0.010(syst),

where the subscripts d and s refer to the favored B− → D0π−π+π− and suppressedB− → D0K−π+π− final states, respectively. The largest sensitivity to γ amongstthese modes is expected in ACP+

s .

†Conference report prepared for the 36th international conference on high energy physics Melbourne,Australia, 4-11 July 2012. Contact authors: Justin Garofoli, justing@physics.syr.edu and Steven Blusk,sblusk@syr.edu

1 Introduction

A core part of the LHCb physics program is to search for new physics in the CKM[1, 2] sector. One goal is to make a theoretically clean measurement of the weak phaseγ using tree-level decays, which is expected to be free from New Physics (NP). Anydeviation of the value found in these decays with the value determined from loop-sensitivequantities would constitute evidence for NP. Sensitivity to γ is obtained via interferencebetween B− → D0K− and B− → D0K− decays, where the D0 and D0 mesons decayto a common final state. Significant CP asymmetries in these decay modes have alreadybeen observed [3]. An extension of this technique is to use B− → D0K−π+π− decays [4].The B− → D0K−π+π− decay has recently been observed in the favored D0 → K−π+

decay mode [5], but greater sensitivity is expected when analyzing CP eigenstates [6], thedoubly-Cabibbo suppressed (ADS) D0 → K+π− decay [7] or multi-body final (GGSZ)states [8] such as K0

Sπ+π−. Here, we present first observations of the B− → D0K−π+π−

decay modes, where the D0 meson is reconstructed in either the K+K− or π+π− CPeigenstate. The corresponding B− → D0π−π+π− decays serve as a normalization modein which many of the systematic uncertainties cancel. We use these decays to measurequantities that are sensitive to the weak phase γ. The ADS and GGSZ final states arealso of great use and will be sought in the near future.

The yields in the Cabibbo-favored (CF) and CP modes are given by

N(B− → D(K−π+)X−s ) = NKπ(1 + (rBrD)2 + 2κrBrD cos(δB − δD − γ))

N(B+ → D(K+π−)X+s ) = NKπ(1 + (rBrD)2 + 2κrBrD cos(δB − δD + γ))

N(B− → D(h−h+)X−s ) = Nhh(1 + r2B + 2κrB cos(δB − γ))

N(B+ → D(h−h+)X+s ) = Nhh(1 + r2B + 2κrB cos(δB + γ)). (1)

Here, for brevity, X±s refers to the K±π∓π± three-particle state. Similarly, we use thenotation X±d for the π±π∓π± system. The parameters rB and δB are the amplitude ra-tio and strong phase difference between the B− → D0K−π+π− and B− → D0K−π+π−

decays, respectively. The factor κ, sometimes referred to as the coherence factor, repre-sents a potential dilution due to the interference between the strong decay amplitudesacross the Dalitz plot. Its value is bound between 0 and 1, and can be determined froma fit, once additional decay modes are included. The quantities rD and δD represent therelative amplitude and strong phase difference between D0 → K+π− and D0 → K−π+,respectively. Each expression is preceded by a normalization factor.

1

To expose the sensitivity to γ, two CP observables are defined,

RCP± = 2Γ(B− → DCP±X

−s ) + Γ(B+ → DCP±X

+s )

Γ(B− → D0X−s ) + Γ(B+ → D0X+s )

= 1 + r2B ± 2κrB cos δB cos γ (2)

ACP± = 2Γ(B− → DCP±X

−s )− Γ(B+ → DCP±X

+s )

Γ(B− → DCP±X−s ) + Γ(B+ → DCP±X+s )

= ±2κrB sin δB sin γ/RCP±, (3)

where DCP± refers to a CP eigenstate. It can be shown that RCP± is well approximatedusing

RCP± ' RCPK/π/R

K−π+

K/π , (4)

where

RCPK/π = Γ(B± → DCP±X

±s )/Γ(B± → DCP±X

±d ),

RK−π+

K/π = Γ(B± → DKπX±s )/Γ(B± → DKπX

±d ). (5)

The use of this double ratio is motivated by the resulting cancellation of various exper-imental systematic uncertainties. Measurements of these relative decay rates and B±

decay rate asymmetries are presented. Charge conjugate modes are implied throughoutthis note, unless otherwise noted.

2 Data Selection

The analysis presented here is based on Lint = 1.0 fb−1 of√s = 7 TeV pp collision data

sample collected with the LHCb detector [9]. Candidate D0 mesons are reconstructed viatheir decays to K−π+, K+K− and π+π−. The kaon and pion candidates are required tohave a transverse momentum (pT ) in excess of 100 MeV/c and be significantly detachedfrom any primary vertex (PV) in the event. Particles are identified using the difference inlog-likelihoods (DLL) between kaon and pion hypotheses obtained from the Ring ImagingCherenkov (RICH) detector. The DLLKπ requirements on each of the final state particlesare given in Table 1. The more stringent requirement on the π+ particle in Xs is usedto suppress peaking backgrounds from the decays B− → D0D−s (D−s → K−K+π−) andB− → D0K∗0K−, where the K+ particle is misidentified as π+.

To suppress charmless backgrounds, we require that the reconstructed D0 decay pointis well-separated and downstream of the B− decay vertex. Background from partiallyor fully reconstructed B → DX decays are identified by searching for peaks from knownparticles amongst all 2, 3, or 4-body invariant mass combinations (apart from the intended2-body D0 decay); in a few instances, we find specific combinations that give pronouncedpeaks at one of the D0, D+, D+

s or D∗+ meson masses. Candidates that have a masscombination within 15 MeV/c2 of the D0, D+ or D+

s mass are removed from the sample.

2

Table 1: Summary of selections requirement on DLLKπ applied to the daughters in thesignal decays for each of the six decay modes under study.

Decay D0 daughters Xs,d daughtersK π K−/π− π+ π−

B → DXs, D → Kπ > 5 < 8 > 12 < 2 < 8B → DXd, D → Kπ > 5 < 8 < 8 < 8 < 8B → DXs, D → KK > 10 - > 12 < 2 < 8B → DXd, D → KK > 10 - < 8 < 8 < 8B → DXs, D → ππ - < 0 > 12 < 2 < 8B → DXd, D → ππ - < 0 < 8 < 8 < 8

These vetoes remove about 1% of the signal, and a correction is included for each byinterpolating from the regions on either side of the veto region. We also remove D∗+

candidates by requiring the difference in invariant mass m(hh′π+)−m(hh′) > 150 MeV/c2.This requirement also removes decays such as B− → D1(2420)0π−, with D1(2420) →D∗+π− and D∗+ → D0π+. As this decay mode is flavor specific, it does not interfere withthe decay B− → D1(2420)0π−, and hence only dilutes any interference effects.

Combinatorial background is suppressed using a NeuroBayes (NB) [10] multi-variatediscriminant. We use ∼10% of the decay B− → D0π−π+π−, D0 → K−π+ data samplewith sWeights [11] based on the B− meson invariant mass for the signal training, and thehigh B− mass sidebands in data for background. The 12 variables used in the trainingare: (1) the maximum angle between the Xs,d daughter particles flight direction and theD0 meson flight direction, (2-3) the transverse momenta of the D0 and B− mesons, (4-5)the minimum pT of the Xs,d daughter particles and the minimum pT of the D0 daughterparticles, (6-7) the minimum impact parameter (IP) χ2 of the D0 daughter particles andthe Xs,d daughter particles with respect to the associated PV1, (8) the maximum IP χ2

of the D0 daughter particles, (9) the Xs,d flight distance χ2 from the associated primaryvertex), (10) the B− meson vertex fit χ2/ndf, (11) the B− meson IP χ2 to the associatedPV, and (12) a pT asymmetry variable [3] between the B− candidate and other tracksfrom the same PV. We select the optimal cut value of 0.45 by optimizing S/

√S +B,

where S is the expected signal yield in the decay B− → D0K−π+π−, D0 → K+K− finalstate, and B meson is the expected background in that mode, obtained by scaling theupper B− mass sideband. With this requirement, we obtain a signal efficiency of ∼85%with a background rejection of 93%. The results of the optimization are shown in Fig. 1.To improve the mass resolution, selected B− candidates are refit using both D0 mass andvertex constraints.

1The associated primary vertex is the one that has the smallest impact parameter χ2.

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B2D0A1_pik NeuroBayesfull BKG Rejection (upper side band)Figure 1: Signal significance versus the neurobayes cut value, as described in the text.

3 Fits to Data

We perform a simultaneous binned maximum likelihood fit to the 12 invariant massspectra, namely the decays B− → D0π−π+π− and B− → D0K−π+π−, each withD0 → K−π+, K+K− and π+π−, and their charge conjugates. Each distribution is fittedfor a B− signal component, specific peaking background contributions, and a combina-toric background shape. The signal component is described by the sum of a Crystal Ball(CB) [12] function and a Gaussian signal shape. The CB shape is used to describe thesmall radiative tail that extends toward lower invariant mass. The signal shape param-eters are fixed from simulation, except for their common mean and the Gaussian width,which are floated in the fit.

Specific peaking background shapes are obtained by simulating the background decaysand reconstructing them in the signal modes. The shapes are then parameterized usingsmooth functions and included in the mass fits. For backgrounds that involve a particlemisidentification, we use D∗± → D0π±s calibration data to measure the misidentificationrates. The calibration technique exploits the knowledge of the particles’ identities withoutthe use of the RICH using the charge of the πs. Expected yields are then readily computedusing the observed yields of correctly reconstructed background events and the computedfake rates.

For the B− → D0π−π+π− decay mass fits, we include background shapes from par-tially reconstructed B− → D∗π−π+π− decay and fully reconstructed B− → D0K−π+π−

decay. The B− → D0K−π+π− decay fit includes background components from the de-cays B− → D0π−π+π−, B− → D∗π−π+π−, B− → D∗−K−π+π−, B− → D∗π−π+π−,B− → D0D+

s , and B− → D0K∗0K−.

4

For the D0 → K+K− final state (in both B− → D0π−π+π− and B− → D0K−π+π−

decays), we also include a small background contribution from Λ0b → Λ+

c π−π+π− and

Λ0b → Λ+

c K−π+π− decays, where the proton (from the Λ+

c → pK−π+ decay) is misidenti-fied as a kaon, and the pion from the Λ+

c is not included in the reconstructed decay. Thecombinatorial background is described by a single exponential function.

The 12 signal yields are expressed in terms of (a) three B± → Dπ±π∓π± correctedsignal yields, N f

d,corr (sum of B+ and B−), where D = (D0, D0), (b) three ratios RfK/π

(see Eq. 5), and (c) six asymmetries, Afd and Afs , where the asymmetries are given by

A ≡ NB−−NB+

NB−+NB+. Here, the d and s subscripts refer to the quark content in Xd and Xs, and

the f superscript represents one of the three D0 decay modes (K−π+, K+K− or π+π−).With these definitions, we express the six B± → Dπ±π∓π±, where D = (D0, D0), fittedyields, N f

d,B∓ in terms of the parameters of interest as

N fd,B∓ =

1

2

(1

lcorr

N fd,corr

Cf,DXd

(1± Afd

)+ Cf,sb

d

), (6)

where the factor Cf,DXd is a correction for the events removed by the B → DX vetoes, and

Cf,sbd accounts for the charmless background contribution, estimated from the D0 mass

sidebands. The number lcorr = 1.11 is a correction factor, applied only for f = K−π+, toaccount for the events that are used in the NB training, and discarded from the rest ofthe analysis. With these definitions, a positive asymmetry implies a larger number of B−

signal decays than B+. Similarly, the six B− → D0K−π+π− yields, N fs,B∓,fit, are given

by

N fs,B∓ =

1

2

(RfK/π

N fd,corr

Cf,DXs

(1± Afs ) + Cf,sbs

), (7)

where RfK/π was defined in Eq. 5. The other factors are analogous to the ones defined in

Eq. 6. Table 2 lists the fitted signal yields, the correction factors and the corrected signalyields obtained from the fit.

Table 2: Fitted signal yields, correction factors and the corrected yields, as described inthe text.

f N fd/s,B+ N f

d/s,B− Cf,sbd/s Cf,DX

d/s lcorr N fd,corr

Xd, Kπ 15604± 131 15019± 129 13± 11 1.008 1.11 34330± 210Xd, KK 1226± 37 1154± 36 39± 10 1.010 1 2364± 53Xd, ππ 532± 24 513± 24 0± 1 1.011 1 1056± 35Xs, Kπ 839± 36 795± 35 4± 5 1.014 1 -Xs, KK 60± 10 51± 9 9± 5 1.031 1 -Xs, ππ 35± 7 21± 6 6± 3 1.038 1 -

5

The invariant mass spectra and resulting fits are shown in Figs. 2 and 3 for thedecays B− → D0π−π+π− and B− → D0K−π+π−, respectively. The left columns showB+ candidates and the right columns display B− candidates. The points are data andthe filled curves show the various signal and background components.

From the fit, we find

RK+K−

K/π = 0.045± 0.006(stat)

Rπ+π−

K/π = 0.048± 0.010(stat)

RK−π+

K/π = 0.048± 0.002(stat). (8)

The CP modes are statistically consistent with each other. The weighted average is foundto be

RCP+K/π = 0.046± 0.005(stat). (9)

Dividing through by RK−π+

K/π , we find

RCP+ = 0.95± 0.11(stat) (10)

The physical asymmetries in the B− → D0π−π+π− decay modes are found to be

AK−π+

d = −0.006± 0.006

AK+K−

d = −0.022± 0.022

Aπ+π−

d = −0.011± 0.032. (11)

For the suppressed B− → D0K−π+π− decays, we find

AK−π+

s = −0.009± 0.028

AK+K−

s = −0.08 ± 0.12

Aπ+π−

s = −0.28 ± 0.18, (12)

where the uncertainties are statistical only. These asymmetries include corrections forthe production asymmetry of Aprod = (−0.8 ± 0.7)%, and the kaon and pion detectionasymmetries of AK = (−0.5 ± 0.7)% and Aπ = (0.0 ± 0.2)% [13], respectively. The left-right asymmetries due to the magnet polarity cancel due to approximately equal samplesizes of magnet up and magnet down data.

Weighted averages of the asymmetries for the CP eigenstates yields the followingresults,

ACP+d = −0.018± 0.018

ACP+s = −0.14 ± 0.10. (13)

In the double ratio used to determine RCP+ almost all the uncertainties cancel to firstorder. Systematic uncertainties that do not cancel in the computation of RCP+ include

6

(i) 1% from the approximation in Eq. 4, (ii) 2% from modeling of the background shapesand (iii) 1% from the estimated yields of peaking backgrounds in the B− → D0K−π+π−,which are fixed in the nominal fits. For the asymmetries, we incur uncertainty from theB± production asymmetry (0.7%), the π± detection asymmetry (0.2% per pion) and thekaon detection asymmetry (0.7% per kaon). The total uncertainty on RCP+ is 2.4%. Onthe asymmetries, the systematic uncertainty varies from 0.7 to 1.3%.

The final results for the relative rate RCP+ and the asymmetries are

RCP+ = 0.95 ± 0.11 (stat)± 0.02 (syst)

ACP+s = −0.14 ± 0.10 (stat)± 0.01 (syst)

AK−π+

s = −0.009± 0.028(stat)± 0.013(syst) (14)

We also measure asymmetries in the corresponding Cabibbo-favored decays, and find:

ACP+d = −0.018± 0.018(stat)± 0.007(syst)

AK−π+

d = −0.006± 0.006(stat)± 0.010(syst) (15)

4 Conclusion

In summary, we report first observations of the CP modes in the decay B− → D0K−π+π−

and combined them with the rates from B− → D0π−π+π− final states to measurethe CP-sensitive parameters RCP+ and the B± decay rate asymmetries. We measurea central value of RCP+ that is about 0.5σ below unity. The CP asymmetry in theB− → D0K−π+π− decay mode with D0 → fCP is less than zero by about 1.5 standarddeviations. The other asymmetries are smaller and compatible with zero within 1 stan-dard deviation. Constraints on the weak phase γ will become possible with the inclusionof the ADS suppressed D0 → K+π− decay mode. Clearly a larger data sample will berequired to perform this measurement. Additional decay modes of the D0 meson can alsobe included, such as D0 → K−π+π−π+ and D0 → K0

Sπ−π+, which provide additional

constraints on the CP parameters.

References

[1] N. Cabibbo, Unitary symmetry and leptonic Decays, Phys. Rev. Lett. 10 (1963)531.

[2] M. Kobayashi and T. Maskawa, CP Violation in the renormalizable theory of weakinteraction, Prog. Theor. Phys. 49 (1973) 652.

[3] LHCb collaboration, R. Aaij et al., Observation of CP violation in B+ → DK+

decays, Phys. Lett. B712 (2012) 203, arXiv:1203.3662.

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[4] M. Gronau, Improving bounds on γ in B± → DK± and B±,0 → DX±,0s , Phys. Lett.B557 (2003) 198, arXiv:hep-ph/0211282.

[5] LHCb Collaboration, R. Aaij et al., First observation of the decays B̄0 →D+K−π+π− and B− → D0K−π+π−, Phys. Rev. Lett. 108 (2012) 161801,arXiv:1201.4402.

[6] M. Gronau and D. Wyler, On determining a weak phase from charged B decay asym-metries, Phys. Lett. B265 (1991) 172.

[7] D. Atwood, I. Dunietz, and A. Soni, Enhanced CP violation with B → KD0 (D0)modes and extraction of the Cabibbo-Kobayashi-Maskawa angle γ, Phys. Rev. Lett.78 (1997) 3257, arXiv:hep-ph/9612433.

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[9] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST3 (2008) S08005.

[10] M. Feindt and U. Kerzel, The NeuroBayes neural network package, Nucl. Instrum.Meth. A559 (2006) 190.

[11] M. Pivk and F. R. Le Diberder, SPlot: A statistical tool to unfold data distributions,Nucl. Instrum. Meth. A555 (2005) 356, arXiv:physics/0402083.

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metry in 7 TeV pp collisions, arXiv:1205.0897.

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ππ →0, DππK0D→-B

LHCb DataSignal

±π0D→±D*0π0D→D*γ0D→0D*

reflπππD*K*K refl0, DsD0D

reflπππ0DComb Bkg

LHCb Preliminary

ππ →0, DππK0D→-B

Figure 3: Invariant mass distributions for the decays B+ → D0K+π−π+ (left column)and B− → D0K−π+π− (right column). The rows correspond to the D0 → K−π+ (top),D0 → K+K− (middle) and D0 → π+π− (bottom) decays. Points with error bars are dataand the filled curves show the fitted components.

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