1 2 University of Rajasthan, Jaipur 302004, India · 3University of Rajasthan, Jaipur 302004, India...

5
D * polarization as a probe to discriminate new physics in B D * τ ¯ ν Ashutosh Kumar Alok, 1, * Dinesh Kumar, 2, 3, Suman Kumbhakar, 2, and S Uma Sankar 2, § 1 Indian Institute of Technology Jodhpur, Jodhpur 342011, India 2 Indian Institute of Technology Bombay, Mumbai 400076, India 3 University of Rajasthan, Jaipur 302004, India (Dated: February 18, 2020) The confirmation of excess in RD * at the LHCb is an indication of lepton flavor non-universality. In order to identify the Lorentz structure of new physics responsible for this excess, one requires measurements of angular observables in B D * τ ¯ ν . But with the present methodology used at LHCb, BaBar and Belle, it would not be possible to measure most of the angular observables. We point out that it is possible to measure the distribution in polar angle θD, the angle between directions of B and D mesons in the rest frame, using the same data set which measured R * D . Therefore D * polarization fraction fL(q 2 ) can be measured fairly accurately. We find that D * polarization fraction can be a good discriminant of new physics operators provided their Lorentz structure is different from the standard model operator. We also find that other asymmetries, based on yet to be measured angles, do not have additional capability to discriminate between new physics operators. For the values of new physics couplings which provide good fit to RD/RD * and q 2 spectra, fL(q 2 ) provides good discrimination for half the allowed solutions. I. INTRODUCTION The currently running LHC has not only provided new smoking gun signatures of possible physics beyond the Standard Model (SM) but also confirmed some of the prevailing tensions in the SM. The most striking exam- ple of the confirmation of previously observed anomaly is the 3.5σ deviation from the SM expectation of the ra- tio R D * = Γ(B D * τ ¯ ν )/Γ(B D * l ¯ ν )(l = e, μ)[1–6]. This is an indication towards lepton flavor non universal- ity, in disagreement with the SM predictions. The idea of lepton flavour non universality is further bolstered by the measurement that R K = Γ(B + μ - )/Γ(B Ke + e - ) 6= 1 [7]. The four fermion interaction b ¯ ν , which induces the decays B (D, D * ) τ ¯ ν , occurs at the tree level within the SM. Note that the situation in the case of b + μ - is quite different because this transition oc- curs only at one loop level in SM. Relatively large new physics (NP) contributions are required to explain the anomaly in the measurement of R D * . Such large contri- butions are more likely to occur in NP models where the four fermion interaction occurs at tree level. However such models must also be consistent with the measure- ment of other observables which are in agreement with their SM predictions. As a result there are only a limited a set of NP models which can explain the R D * anomaly, see for example [8–20]. In particular, ref. [17] listed all the four fermion operators contributing to B D * τ ¯ ν and derived the values of various NP couplings which satisfy the measurement of R D /R D * and the q 2 spectra. * Electronic address: [email protected] Electronic address: [email protected] Electronic address: [email protected] § Electronic address: [email protected] The next step is to discriminate between various NP operators which can explain the excess in R D * . This can be achieved if we have a handle on various angular observables in B D * τ ¯ ν similar to the ones we have in B K * μ + μ - decay. In the semileptonic decays of pseudoscalar mesons to vector mesons, it is possible to measure differential distributions with respect to three angles, besides dΓ/dq 2 . These angles are usually defined in the vector meson rest frame. For the decay B D * τ ¯ ν , these angles are (a) θ D , the angle between B and D where the D meson comes from D * decay, (b) θ τ , the angle between τ and B and (c) φ, the angle between D * decay plane and the plane defined by the lepton momenta [21]. A study of these angular distributions, in the case of B K * μ + μ - , has revealed significant discrepancies between the measurements and the predictions of SM [22]. Various authors have done theoretical analysis of similar angular distributions for B D * τ ¯ ν [23–27]. So far the τ lepton has not been reconstructed in any of the experiments which measured R D /R D * . Therefore θ τ and φ have not been measured. Hence it is not possible to measure the full differential distribution. However, it is possible to measure θ D from the same data used by BaBar and Belle to determine R D * . From the θ D distribution one can extract the D * polarization fraction f L (q 2 ). In this letter we study the capability of f L (q 2 ) to discriminate between various NP solutions which account for R D * excess. II. DISENTANGLING VARIOUS NEW PHYSICS CONTRIBUTIONS TO ¯ B D * τ ¯ ν First we summarize the results of ref. [17], which per- formed a fit of various NP models to the present R D * and R D data. These fits are also consistent with the q 2 distri- bution provided by BaBar [2] and Belle [6]. The effective Hamiltonian for the quark level transition b ¯ ν is arXiv:1606.03164v1 [hep-ph] 10 Jun 2016

Transcript of 1 2 University of Rajasthan, Jaipur 302004, India · 3University of Rajasthan, Jaipur 302004, India...

D∗ polarization as a probe to discriminate new physics in B → D∗τ ν̄

Ashutosh Kumar Alok,1, ∗ Dinesh Kumar,2, 3, † Suman Kumbhakar,2, ‡ and S Uma Sankar2, §

1Indian Institute of Technology Jodhpur, Jodhpur 342011, India2Indian Institute of Technology Bombay, Mumbai 400076, India

3University of Rajasthan, Jaipur 302004, India(Dated: February 18, 2020)

The confirmation of excess in RD∗ at the LHCb is an indication of lepton flavor non-universality.In order to identify the Lorentz structure of new physics responsible for this excess, one requiresmeasurements of angular observables in B → D∗ τ ν̄. But with the present methodology used atLHCb, BaBar and Belle, it would not be possible to measure most of the angular observables.We point out that it is possible to measure the distribution in polar angle θD, the angle betweendirections of B and D mesons in the Dπ rest frame, using the same data set which measuredR∗D. Therefore D∗ polarization fraction fL(q2) can be measured fairly accurately. We find that D∗

polarization fraction can be a good discriminant of new physics operators provided their Lorentzstructure is different from the standard model operator. We also find that other asymmetries, basedon yet to be measured angles, do not have additional capability to discriminate between new physicsoperators. For the values of new physics couplings which provide good fit to RD/RD∗ and q2 spectra,fL(q2) provides good discrimination for half the allowed solutions.

I. INTRODUCTION

The currently running LHC has not only provided newsmoking gun signatures of possible physics beyond theStandard Model (SM) but also confirmed some of theprevailing tensions in the SM. The most striking exam-ple of the confirmation of previously observed anomalyis the 3.5σ deviation from the SM expectation of the ra-tio RD∗ = Γ(B → D∗ τ ν̄)/Γ(B → D∗ lν̄) (l = e, µ)[1–6].This is an indication towards lepton flavor non universal-ity, in disagreement with the SM predictions. The ideaof lepton flavour non universality is further bolstered bythe measurement that RK = Γ(B → K µ+ µ−)/Γ(B →K e+ e−) 6= 1 [7].

The four fermion interaction b → c τ ν̄, which inducesthe decays B → (D, D∗) τ ν̄, occurs at the tree levelwithin the SM. Note that the situation in the case ofb→ s µ+ µ− is quite different because this transition oc-curs only at one loop level in SM. Relatively large newphysics (NP) contributions are required to explain theanomaly in the measurement of RD∗ . Such large contri-butions are more likely to occur in NP models where thefour fermion interaction occurs at tree level. Howeversuch models must also be consistent with the measure-ment of other observables which are in agreement withtheir SM predictions. As a result there are only a limiteda set of NP models which can explain the RD∗ anomaly,see for example [8–20]. In particular, ref. [17] listed allthe four fermion operators contributing to B → D∗τ ν̄and derived the values of various NP couplings whichsatisfy the measurement of RD/RD∗ and the q2 spectra.

∗Electronic address: [email protected]†Electronic address: [email protected]‡Electronic address: [email protected]§Electronic address: [email protected]

The next step is to discriminate between various NPoperators which can explain the excess in RD∗ . Thiscan be achieved if we have a handle on various angularobservables in B → D∗ τ ν̄ similar to the ones we havein B → K∗ µ+ µ− decay. In the semileptonic decays ofpseudoscalar mesons to vector mesons, it is possible tomeasure differential distributions with respect to threeangles, besides dΓ/dq2. These angles are usually definedin the vector meson rest frame. For the decay B →D∗τ ν̄, these angles are (a) θD, the angle between B andD where the D meson comes from D∗ decay, (b) θτ , theangle between τ and B and (c) φ, the angle between D∗

decay plane and the plane defined by the lepton momenta[21]. A study of these angular distributions, in the caseof B → K∗µ+ µ−, has revealed significant discrepanciesbetween the measurements and the predictions of SM[22]. Various authors have done theoretical analysis ofsimilar angular distributions for B → D∗τ ν̄ [23–27]. Sofar the τ lepton has not been reconstructed in any ofthe experiments which measured RD/RD∗ . Therefore θτand φ have not been measured. Hence it is not possibleto measure the full differential distribution. However,it is possible to measure θD from the same data usedby BaBar and Belle to determine RD∗ . From the θDdistribution one can extract the D∗ polarization fractionfL(q2). In this letter we study the capability of fL(q2) todiscriminate between various NP solutions which accountfor RD∗ excess.

II. DISENTANGLING VARIOUS NEWPHYSICS CONTRIBUTIONS TO B̄ → D∗τ ν̄

First we summarize the results of ref. [17], which per-formed a fit of various NP models to the present RD∗ andRD data. These fits are also consistent with the q2 distri-bution provided by BaBar [2] and Belle [6]. The effectiveHamiltonian for the quark level transition b → c τ ν̄ is

arX

iv:1

606.

0316

4v1

[he

p-ph

] 1

0 Ju

n 20

16

2

given by

Heff =4GF√

2Vcb

[OVL

+

√2

4GFVcb

1

Λ2

{∑i

(CiOi + C

iO′

i + C′′

i O′′

i

)}], (1)

where the scale Λ is assumed to be 1 TeV. The Lorentzstructures of the unprimed Oi and primed O′i and O′′ioperators are given in Table I. For each primed operator,this table also lists the corresponding Fierz transformedunprimed operator. The values of all operator coefficientswhich provide a good fit to the data are given in TableII.

In the fit with the operators O′′SRand O′′SL

, there arefour allowed values for C ′′SR

and C ′′SLcouplings. An at-

tempt is made in ref. [28] to distinguish between thesesolutions based on their predictions for the rate of thedecay B−c → τ−ν̄. They found that the two solutions(C ′′SR

, C ′′SL) = (0.96, 2.41) and (−6.34,−2.39) are ex-

cluded because the predicted partial decay width is largerthan the measured total decay width of Bc. This re-sult can be understood by noting that O′′SR

operator isequivalent to OVL

whereas O′′SLoperator is equivalent to

linear combination of OSLand OT . The two solutions

with (C ′′SR, C ′′SL

) = (0.35,−0.03) and (−5.74, 0.03) haveessentially OVL

Lorentz structure. Therefore their pre-diction for the pure leptonic decay of Bc is subject tohelicity suppression. For the other two cases, ruled outby [28], the coefficient of O′′SL

and hence OSLis quite

large. For this operator there is no helicity suppression

Operator Fierz identity

OVL (c̄γµPLb) (τ̄ γµPLν)

OVR (c̄γµPRb) (τ̄ γµPLν)

OSR (c̄PRb) (τ̄PLν)

OSL (c̄PLb) (τ̄PLν)

OT (c̄σµνPLb) (τ̄σµνPLν)

O′VL(τ̄ γµPLb) (c̄γµPLν) ←→ OVL

O′VR(τ̄ γµPRb) (c̄γµPLν) ←→ −2OSR

O′SR(τ̄PRb) (c̄PLν) ←→ − 1

2OVR

O′SL(τ̄PLb) (c̄PLν) ←→ − 1

2OSL − 1

8OT

O′T (τ̄σµνPLb) (c̄σµνPLν) ←→ −6OSL + 12OT

O′′VL(τ̄ γµPLc

c) (b̄cγµPLν) ←→ −OVR

O′′VR(τ̄ γµPRc

c) (b̄cγµPLν) ←→ −2OSR

O′′SR(τ̄PRc

c) (b̄cPLν) ←→ 12OVL

O′′SL(τ̄PLc

c) (b̄cPLν) ←→ − 12OSL + 1

8OT

O′′T (τ̄σµνPLcc) (b̄cσµνPLν) ←→ −6OSL − 1

2OT

TABLE I: All possible four-fermion operators that can con-tribute to B̄ → D(∗)τ ν̄.

which leads to the prediction of very large decay widthfor B−c → τ−ν̄.

The angular distribution in θD is given by [27]

d2Γ

dq2d cos θD=

1

4

dq2[2fL(q2) cos2 θD + (1− fL(q2)) sin2 θD

],

(2)where the fL(q2) is defined to be

fL(q2) =AL

AL +AT. (3)

The quantities AL and AT are defined in [21]. From theseformulae we compute fL(q2) for the allowed NP couplingslisted in Table II[17].

Fig. 1 depicts fL(q2) in different panels for differentNP operators given in Table I. In these panels, the bluecurve represents the SM and the red and the black curvesrepresent NP operators. Each curve is in the form ofa narrow band. The thickness of the band representsthe theoretical uncertainty in fL(q2), mainly due to formfactor [11], which is quite small. We discuss the form offL(q2) panel by panel:

• Only CVLpresent: This NP has the same Lorentz

structure of the SM operator. Hence fL(q2) for thiscase has a complete overlap with SM prediction.

• Only CT present: Here there are two soultions, onewith a large value of CT and the other with a smallvalue. It is difficult to distinguish the small CT casefrom SM but fL(q2), for the large CT case, is much

Coefficient(s) Best fit value(s)

CVL 0.18± 0.04, −2.88± 0.04

CT 0.52± 0.02, −0.07± 0.02

C′′SL−0.46± 0.09

(CSR , CSL) (1.25,−1.02), (−2.84, 3.08)

(C′VR, C′VL

) (−0.01, 0.18), (0.01,−2.88)

(C′′SR, C′′SL

) (0.35,−0.03), (0.96, 2.41),

(−5.74, 0.03), (−6.34,−2.39)

TABLE II: Best fit values of the new physics operator coef-ficients which provide a good fit to the present experimentaldata in b→ c τ ν̄ sector [17]. The values in the upper (lower)panel are obtained by considering one (two) new physics op-erator(s) at a time in the fit.

3

3 4 5 6 7 8 9 10

0.4

0.5

0.6

0.7

q2HGeV2L

f L

Only CVLpresent

3 4 5 6 7 8 9 10

0.2

0.3

0.4

0.5

0.6

0.7

q2HGeV2L

f L

Only CT present

3 4 5 6 7 8 9 10

0.4

0.5

0.6

0.7

q2HGeV2L

f L

Only CSL

'' present

3 4 5 6 7 8 9 10

0.4

0.5

0.6

0.7

0.8

0.9

q2HGeV2L

f L

CSLand CSR

present

3 4 5 6 7 8 9 10

0.4

0.5

0.6

0.7

q2HGeV2L

f L

CVR

' and CVL

' present

3 4 5 6 7 8 9 10

0.3

0.4

0.5

0.6

0.7

q2HGeV2L

f L

CSR

'' and CSL

'' present

FIG. 1: Plots of D∗ longitudinal polarization fraction fL(q2) as a function of the dilepton invariant mass q2 in the decayB̄ → D∗τ ν̄. The blue band in all the plots corresponds to the SM prediction. The band is due to theoretical uncertainties,mainly due to form factors, added in quadrature. The plot in the left panel of top row represents fL(q2) prediction in thepresence of NP couplings CVL = (0.18± 0.04) (black band) and CVL = (−2.88± 0.04) (red band). The black and red bands inthe middle panel of the top row are for fL(q2) with NP couplings CT = (0.52±0.02) and CT = (−0.07±0.02), respectively. The

red band in the right panel of top row corresponds to C′′SL

= (−0.46± 0.09). In the left panel of bottom row, the black and redbands correspond to NP coefficients (CSL , CSR) = (−1.02, 1.25) and (3.08,−2.84), respectively. In the bottom middle panel,

fL(q2) prediction for (C′VL, C′VR

) = (0.18,−0.01) and (−2.88, 0.01) are shown by black and red bands, respectively. fL(q2) for

NP couplings (C′′SR, C′′SL

) = (0.96, 2, 41) (black band) and (−6.34,−2.39) (red band) are shown in right panel of bottom row.(Color online)

smaller than SM prediction for the whole range ofq2.

• Only C ′′SLpresent: Here the Lorentz structure is

different from that of SM. But fL(q2) is nearly thesame as that of SM because the coupling constantis quite small.

• CSLand CSR

present: These Lorentz structures arequite different from SM and NP couplings are mod-erately large for both the allowed solutions. HencefL(q2) for both of them is significantly differentfrom SM.

• C ′VRand C ′VL

present: For both the allowed soul-

tions C ′VRis negligibly small. Therefore the NP

has the same Lorentz structure of SM and hencefL(q2) cannot distinguish it from SM.

• C ′′SRand C ′′SL

present: For the two solution allowed

by [28] C ′′SLis negligibly small, leaving a significant

coefficient only for O′′SRwhich has the same Lorentz

structure of SM. Hence fL(q2) cannot distinguishthese two solutions from SM. The two disallowedsolutions have large C ′′SL

values and can be dis-

tinguished by fL(q2) because O′′SLhas a different

Lorentz structure from SM.

It would be interesting to see the discrimination ca-pability of the asymmetries based on other angular ob-servables. One such example is the forward-backwardasymmetry of leptons, AFB(q2) in B̄ → D∗τ ν̄. The val-ues of AFB(q2) for the six different NP combinationslisted in Table II are plotted in various panels of fig .2. Here again the blue band represents the SM and thered and the black bands represent NP solutions. As inthe case of fL(q2), the plots of AFB(q2) distinguish theNP solutions from SM for the following cases:(i) OnlyCT present, (ii) CSL

and CSRpresent and (iii) the two

disallowed solutions of C ′′SRand C ′′SL

present. For thetwo cases, only CVL

present and C ′VRand C ′VL

present,

AFB(q2) is essentially the same as that of SM, which isalso true for fL(q2). The results for the sixth case, onlyC ′′SL

present, are quite interesting. This case could not

be distinguished from SM with fL(q2) but it can be withAFB(q2). This can be seen in the right panel of the toprow of fig. 2.

The angle θτ has to be measured to determineAFB(q2). As mentioned before, such a measurement isnot possible so far. It may be possible for LHCb to makethis measurement for those events where τ decays intomultiple hadrons, using the same technique they used toidentify the B meson in the decay B → D∗τ ν̄. But asdemonstrated in figs. 1 and 2 the only advantage of mak-ing this measurement is to distinguish the solution where

4

3 4 5 6 7 8 9 10

-0.2

-0.1

0.0

0.1

q2HGeV2L

AF

B

Only CVLpresent

3 4 5 6 7 8 9 10

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

q2HGeV2L

AF

B

Only CT present

3 4 5 6 7 8 9 10-0.3

-0.2

-0.1

0.0

0.1

q2HGeV2L

AF

B

Only CSL

'' present

3 4 5 6 7 8 9 10-0.3

-0.2

-0.1

0.0

0.1

0.2

q2HGeV2L

AF

B

CSLand CSR

present

3 4 5 6 7 8 9 10

-0.2

-0.1

0.0

0.1

q2HGeV2LA

FB

CVR

' and CVL

' present

3 4 5 6 7 8 9 10

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

q2HGeV2L

AF

B

CSR

'' and CSL

'' present

FIG. 2: Plots of lepton forward-backward asymmerty AFB(q2) as a function of the dilepton invariant mass q2 in the decayB̄ → D∗τ ν̄. The blue band in all the plots corresponds to the SM prediction. The band is due to theoretical uncertainties,mainly due to form factors, added in quadrature. The plot in the left panel of top row represents AFB(q2) prediction in thepresence of NP couplings CVL = (0.18± 0.04) (black band) and CVL = (−2.88± 0.04) (red band). The black and red bands inthe middle panel of the top row represent NP couplings CT = (0.52±0.02) and CT = (−0.07±0.02), respectively. The red band

in the right panel of top row corresponds to C′′SL

= (−0.46 ± 0.09). In the left panel of bottom row, the black and red bands

correspond to AFB(q2) with NP coefficients (CSL , CSR) = (−1.02, 1.25) and (3.08,−2.84), respectively. In the bottom middle

panel, AFB(q2) prediction for (C′VL, C′VR

) = (0.18,−0.01) and (−2.88, 0.01) are shown by black and red bands, respectively.

AFB(q2) with NP couplings (C′′SR, C′′SL

) = (0.96, 2.41) (black band) and (−6.34,−2.39) (red band) are shown in right panel ofbottom row. (Color online)

only C ′′SLis present.

III. fL(q2) IN LEPTOQUARK MODELS

As emphasized in ref. [17], a solution to RD∗/RDanomaly is possible only if the coefficients of NP opera-tors are moderately large. Such large coefficients occuronly if these operators arise at tree level. In certainmodels such operators arise due to the exchange of lep-toquarks at tree level. A number of leptoquark modelshave been constructed to account for RD∗/RD anomaly[17, 20, 28]. Here we consider the effective NP couplingsderived from leptoquark models in ref. [17]. For ascalar leptoquark S, with U(3)Q×U(3)u×U(3)d charge(1, 1, 3̄), the effective NP couplings are C ′′SL

≈ 0 and

C ′′SR/Λ2 = (0.35 ± 0.1)/(1 TeV)2. As discussed earlier,

the operator O′′SRhas the Fierz transformed form OVL

,

the SM operator. Hence neither fL(q2) nor AFB(q2) candistinguish this NP solution. For the case of a vectorleptoquark V µ, with U(3)Q × U(3)u × U(3)d charge

(1, 1, 3), the NP operator leading to B → D∗τ ν̄ decay isO′VL

which again has the Fierz transformation to OVL.

Hence this NP solution also cannot be distinguishedthrough either fL(q2) or AFB(q2).

IV. CONCLUSIONS

In this letter, we studied the possibility to distin-guish between various models which can explain the ob-served excess in RD∗ . The angular observables in thedecay B → D∗τ ν̄ can discriminate between NP oper-ators whose Lorentz structure is different from that ofSM. TheD∗ polarization, fL(q2), and the lepton forward-backward asymmetry, AFB(q2), are both capable of dis-tinguishing between three of the six allowed NP solutions.A measurement of AFB(q2) is not possible with presenttechniques. However, fL(q2) can be determined from thesame data which measured RD∗ . Therefore a measure-ment of this quantity will be of great value in narrowingdown the allowed NP models.

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