A closer look at the R D and R D* anomalies

Journal of High Energy Physics, Jan 2017

The measurement of R D (R D*), the ratio of the branching fraction of \( \overline{B}\to D\tau {\overline{\nu}}_{\tau}\left(\overline{B}\to {D}^{\ast}\tau {\overline{\nu}}_{\tau}\right) \) to that of \( \overline{B}\to Dl{\overline{\nu}}_l\left(\overline{B}\to {D}^{\ast }l{\overline{\nu}}_l\right) \), shows 1.9σ (3.3σ) deviation from its Standard Model (SM) prediction. The combined deviation is at the level of 4σ according to the Heavy Flavour Averaging Group (HFAG). In this paper, we perform an effective field theory analysis (at the dimension 6 level) of these potential New Physics (NP) signals assuming SU(3)C × SU(2)L × U(1)Y gauge invariance. We first show that, in general, R D and R D* are theoretically independent observables and hence, their theoretical predictions are not correlated. We identify the operators that can explain the experimental measurements of R D and R D* individually and also together. Motivated by the recent measurement of the τ polarisation in \( \overline{B}\to {D}^{\ast}\tau {\overline{\nu}}_{\tau } \) decay, P τ (D *) by the Belle collaboration, we study the impact of a more precise measurement of P τ (D *) (and a measurement of P τ (D)) on the various possible NP explanations. Furthermore, we show that the measurement of R D* in bins of q 2, the square of the invariant mass of the lepton-neutrino system, along with the information on τ polarisation and the forward-backward asymmetry of the τ lepton, can completely distinguish the various operator structures. We also provide the full expressions of the double differential decay widths for the individual τ helicities in the presence of all the 10 dimension-6 operators that can contribute to these decays.

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A closer look at the R D and R D* anomalies

Received: October closer look at the Debjyoti Bardhan 0 1 2 5 6 7 Pritibhajan Byakti 0 1 2 3 6 7 Diptimoy Ghosh 0 1 2 4 6 7 0 Rehovot 76100 , Israel 1 2A & 2B , Raja S.C. Mullick Road, Jadavpur, Kolkata 700 032 , India 2 1 Homi Bhabha Road , Mumbai 400005 , India 3 Department of Theoretical Physics, Indian Association for the Cultivation of Science 4 Department of Particle Physics and Astrophysics, Weizmann Institute of Science 5 Department of Theoretical Physics, Tata Institute of Fundamental Research 6 Open Access , c The Authors 7 Munich , Germany (2016) The measurement of RD (RD ), the ratio of the branching fraction of predictions are not correlated. We identify the operators that can explain the experimental measurements of RD and RD individually and also together. Motivated by the recent ment of RD in bins of q2, the square of the invariant mass of the lepton-neutrino system, ArXiv ePrint: 1610.03038 Beyond Standard Model; Heavy Quark Physics - (B ! D ) to that of B ! Dl l(B ! D l l), shows 1:9 (3:3 ) deviation e ective (NP) signals assuming SU(3)C SU(2)L U(1)Y gauge invariance. We rst show that, in polarisation in B ! D decay, P (D ) by the Belle collaboraalong with the information on helicities in the Contents 1 Introduction 2 Operator basis 3 Observables 4 B ! D form factors 5 B ! D form factors 6 Expressions for a`D, b`D and c`D for B ! D` ` 8 Results 9 Summary 8.1 8.2 8.3 Explaining RD alone Explaining RD alone Explaining RD and RD together A Full expressions for a`D, b`D and c`D B Full expressions for a`D , b`D and c`D C Contribution of the Tensor operator OTcbL` C.1 B ! D C.2 B ! D D SU(3)C SU(2)L U(1)Y gauge invariance E RG running of Wilson coe cients Introduction B B ! D( )l l B ! D( )` ` decay processes. List of Observables Experimental Results Measured value HFAG average 0.397 HFAG average 0.316 Experiment Our average HFAG average HFAG average 0.042 [20, 21] 0.028 [17] 0.015 [18] 0.011 [25] 0.018 [20, 21] 0.030 [26] 0.010 [17] 0.11 % 0.12 % 0.09 % 0.11 % SM Prediction 0.011 [19] 0.008 [22] 0:003 [23] 0.003 [24] 0:09 % 2:11+00::1120 % 5:04+00::4442% 0:009 [28] 0:013 [27, 29] 0:360+00::000021 Observable RD B B ! D B B ! D B B ! Dl l B B ! D l l section 5 for more details. or ) and l to denote only the light leptons, e and . explanations have been proposed. helicities for all the can be explained together. Very recently, the Belle collaboration reported the rst measurement of the -polarisation in the decay B ! D [27]. While the uncertainty in this measurement is polarisation in both the B ! D and B ! D decays can completely distinguish of the lepton (in the NP Lorentz structures. we summarise our ndings in section 9. Operator basis The e ective Lagrangian for the b ! c ` process at the dimension 6 level is given by, cb` 0 + Ccb` cb` + Ccb` 0 cb` 0 s + Cpcb`Opcb` + Cpcb` 0 cb` 0 + CTcb`OTcb` + CTcb5` OT 5 cb` Op C cb` = responding Wilson coe cients de ned at the renormalization scale mb. In the SM, The other possible tensor structures are related to cb` and cb` in the following way, = [c = [c PR b][` PR b][` = [c PR b][` ] = [c PR b][[` = [c = [c = [c PL b][` PL b][` = [c PL b][` ] = [c PL b][[` = [c = [c b][` PL = [c = [c = [c = [c 5 b][[` PL cb` +C cb` +C ] = ] = ] = The Wilson coe = [c = [c = [c = [c 5 b][[` PR = [c b][` PR cb` +C cb` +C +C10 +C10 + CT 5 WCs in eq. (2.1) satisfy the following relations, C9cb` = C9cb` 0 = CTcb` = CTcb5` : only in the appendix (see appendix C). in appendices A and B. Observables be written as dq2 d(cos ) = N jpD( ) j a`D( ) + b`D( ) cos + c`D( ) cos2 are given by, 2(ab + bc + ca). The angle is de ned as the angle The total branching fraction is given by, N = jpD( ) j = B G2F jVcbj2q2 256 3MB2 (MB2 ; M D2( ) ; q2) binned RD( ) in the following way, For the decays with lepton in the nal state, the polarisation of the also constitutes polarisation fraction is de ned in the following way, D( ) (+) and leptons respectively. forward-backward asymmetry, AFDB( ) is de ned as RD( ) [q2 bin] = B D( ) [q2 bin] P (D( )) = D( ) (+) + AF B = R =2 d D( ) R bD( ) (q2)dq2 D( ) is the total decay width of D( ) and the angle has already been de ned information on the nature of the short distance physics. D form factors hD(pD; MD)jc 5bjB(pB; MB)i = 0 hD(pD; MD)jc bjB(pB; MB)i = i(pBpD hD(pD; MD)jc 5bjB(pB; MB)i = " pBpD) MB + MD 2FT (q2) 2FT (q2) MB + MD r:h:s: = F0(q2)(MB2 M D2): 5 = hD(pD; MD)jc 5bjB(pB; MB)i = hD(pD; MD)jc bjB(pB; MB)i = " i(pB pD 2FT (q2) MB + MD 2FT (q2) MB + MD in [19].3 They are given by the following expressions, = (mb mc)hD(pD; MD)jcbjB(pB; MB)i multiplication by q and gives F+(z) = F0(z) = +(z) k=0 0(z) k=0 z(q2) = p(MB + MD)2 p(MB + MD)2 4MBMD 4MBMD q2(GeV2) q2(GeV2) 2(x) = (x for F0 and F+ correspond to a 1:646 where the 2 is computed using the expression 10% uncertainty on the central value. The functions +(z) and 0(z) are given by, +(z) = 1:1213 0(z) = 0:5299 (1 + z)2(1 z)1=2 [(1 + r (...truncated)


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Debjyoti Bardhan, Pritibhajan Byakti, Diptimoy Ghosh. A closer look at the R D and R D* anomalies, Journal of High Energy Physics, 2017, pp. 125, Volume 2017, Issue 1, DOI: 10.1007/JHEP01(2017)125