Y and ψ leptonic decays as probes of solutions to the R(D (*)) puzzle

Journal of High Energy Physics, Jun 2017

Experimental measurements of the ratios \( R\left({D}^{\left(\ast \right)}\right)\equiv \frac{\Gamma \left(B\to {D}^{\left(*\right)}\tau v\right)}{\Gamma \left(B\to {D}^{\left(*\right)}\ell v\right)}\left(\ell =e,\mu \right) \) show a 3.9σ deviation from the Standard Model prediction. In the absence of light right-handed neutrinos, a new physics contribution to b → cτν decays necessarily modifies also \( b\overline{b}\to {\tau}^{+}{\tau}^{-} \) and/or \( c\overline{c}\to {\tau}^{+}{\tau}^{-} \) transitions. These contributions lead to violation of lepton flavor universality in, respectively, Y and ψ leptonic decays. We analyze the constraints resulting from measurements of the leptonic vector-meson decays on solutions to the R(D (*)) puzzle. Available data from BaBar and Belle can already disfavor some of the new physics explanations of this anomaly. Further discrimination can be made by measuring Y(1S, 2S, 3S) → ττ in the upcoming Belle II experiment.

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Y and ψ leptonic decays as probes of solutions to the R(D (*)) puzzle

Received: March Published for SISSA by Springer Open Access 0 1 c The Authors. 0 1 0 decays necessarily modi es 1 Rehovot , 7610001 Israel 2 Department of Physics, LEPP, Cornell University 3 Department of Particle Physics and Astrophysics, Weizmann Institute of Science Experimental measurements of the ratios R(D( )) deviation from the Standard Model prediction. In the absence of light righthanded neutrinos, a new physics contribution to b ! c Beyond Standard Model; Heavy Quark Physics; Precision QED - ((BB!!DD(( ))` )) (` = e; ) transitions. These contributions lead to violation of lepton and/or cc ! avor universality in, respectively, leptonic decays. We analyze the (1S; 2S; 3S) ! in the upcoming Belle II experiment. Contents 1 Introduction V ! `` decay rate The e ective eld theory Numerical results (1; 3)0 (3; 1)+2=3 (3; 3)+2=3 (3; 1) 1=3 (3; 3) 1=3 (1; 2)+1=2 (3; 2)+7=6 (3; 2) 5=6 Discussion and future prospects Summary and conclusions A The leptonic width in the SM B Other EFT operators B.1 Z mediated operators B.2 Dipole operator Introduction R(D( )) ; (` = e; ): R(D) = 0:403 0:047; R(D ) = 0:310 result, R(D ) = 0:270 0:044 [6], is not included in the HFAG average [8].) The SM predictions are [9, 10] R(D) = 0:300 0:008; R(D ) = 0:252 works analyze the deviation in terms of e ective eld theory (EFT), construct explicit and/or cc ! purely left-handed, NP contributions to the b ! c in ref. [47] which analyze the high PT distribution of the are governed by the cc ! and bb ! quarkonia. Speci cally, we study the ratios transition imply that NP contributions transitions are unavoidable. This point was discussed signature at the LHC, transitions: non-universality in leptonic decays RV=` ; (V = ; ; ` = e; ); making two assumptions: e ective operators of dimension six. R(D( )) is modi ed by new physics that a ects only the B ! D( ) decays (and a ected (and not V ! ``). decays of vector-mesons. anomaly and those modifying the leptonic decays of is that all processes occur at mixing, as well as its compatibility with other relevant observables. Tests of LFU have been carried out for (2S) and (3S) [60, 61]. We collect RV=` ' (1 + 2x2)(1 4x2)1=2 BR( (2S) ! BR( (2S) ! ) = (3:1 ) = (7:9 BR( (2S) ! e+e ) = (7:89 threshold, respectively. lepton pairs obey [63] is below the We also do not consider (3770) and (4S) which have SM prediction Exp. value m (1S) = 9:46030 m (2S) = 10:02326 m (3S) = 10:3552 m (2S) = 3:686097 0:00026 GeV; 0:00031 GeV; 0:0005 GeV; 0:000025 GeV; 0:00012 GeV: as is evident from table 1. the formalism is similar. ! `` decay rate The most general V ! `+` decay amplitude can be written as M(V ! `+` ) = v(p2; s2) (p); where Aq`; BVq`; CVq`; DVq` are dimensionless parameters which depend on the Wilson coef V cients of the operators controlling the V ! `+` decays at the perturbative level, and on width and RV=` are given by [V ! ``] = 1 4x`2 jAqV`j2 1+2x`2 +jBVq`j2 1 4x`2 + 1 4x`2 + 2Re hAqV`CVq`i x` 1 RV=` ' q 2 1 + 2x2 + jBV j 4x2 + 2Re A Within the SM, A`;SM Qq and B`;SM; C`;SM; D`;SM V V V ' 0. For the SM calculations q + CSq`LeReLqRqL + CSq`ReReLqLqR + h:c:i : CVq`LL + CVq`RR + CVq`LR + CVq`RL L`q = CVq`RReR We nd: AqV` = BVq` = parametrization: q jV (p)i = fV mV q jV (p)i = ifVT [ (p)p (p)p ] ; the heavy quark limit fV = f T . This is an excellent approximation for the V 5q jV (p)i = 0. The meson. For The e ective eld theory and Lorentz invariant operators: LLQQ; eLuQ; eLQd; LLuu; LLdd; eeuu; eedd; eeQQ; new (scalar or vector) boson. Following ref. [27], we specify the NP eld content which in the quark interaction basis): L) (uL uL)+( L L) dL dL +(eL eL) (uL uL)+(eL eL) dL dL ; (eL eL)(uL uL)+(eL eL) dL dL OV1L = ( L OV2L = OV3L = ( L OV4L = ( L OSL = OT = (eR ( L eL) dL uL + (eL eR) (uL eR) (uR L) (uR uR) + (eL eL) (uR uR) ; uL) + (eR eR) dL dL ; (eReL) (uRuL) + (eR L) (uRdL) ; eL) (uR OD = HL lL;R lL;R and the dipole operators modify the Z ! Field content Fierz identities (eL) (uQ) (uL) (eQ) Lc Q (euc) Qd (eL) Lu (uL) e) Q e Qe (eQ) (euc) (uce) (edc) dce 2 OVL + 2OV2L 136 OV1L + 14 OV2L OVL 8 OT OT OVL (3; 1)+2=3 (3; 3)+2=3 (3; 1) 1=3 (3; 3) 1=3 (1; 2)+1=2 (3; 2)+7=6 (3; 1) 1=3 (1; 2)+1=2 (3; 1)+2=3 (3; 2) 5=6 (3; 2)+1=6 (3; 2)+7=6 (3; 2) 5=6 (3; 2)+1=6 (3; 2) 5=6 (3; 2)+7=6 (3; 2)+5=3 (3; 1) 1=3 (3; 1)+2=3 (3; 1) 4=3 arising from this operator is given by RV=` ' RV=;S`M of Z-pole observables [68] constrain this e ect to be smaller than 10 5 . For more details by the mixing with four fermion operators, in which case ne-tuning cancelation may be needed to ensure that the Z-pole constraints are not violated. our analysis. Numerical results have the right quantum numbers to modify the b ! c transition. For each case, we and (2S) states. Some of the simpli ed models we 2 = 9 (corresponding to 3 with one degree of freedom) are included. Note that in some cases only one of the decay modes, i.e. , is modi ed, due to the speci c (1; 2)+1=2 UV eld content S (3; 1) 1=3 (3; 1)+2=3 (3; 2) 5=6 Current measurement Achievable uncertainty (with current data) R =(`1S) 1:005 0:025 0:39 0:05 R =(`2S) 0.389-0.390 { Predicted modi cation to R =(`1S) Decrease by 0:2%{0:4% Decrease by 0:3%{4:0% Decrease by 0:5%{1:6% V = for more details. and NC e ective operators by O ( level splitting is typically of order nal results As concerns the avor structure of the fundamental couplings, we impose a global transitions in the rst and second generation.1 To determine uniquely the avor strucQ3 = operators (generated by the S and D elds) one could choose alignment to the up-mass basis. In this case neither cLcR ! Nevertheless, other NC operators which result in bLbL ! transitions are generated. and cRcR ! once up-alignment is taken. We assume no signi cant mixing between the NP and SM elds (this is crucial for at the TeV scale. We stress again that, once an anomaly is found in LFU of decays, these be necessary in some cases [71]. elds is absent due real and denote Xij XiXj . evident from the accurate SM predictions. (See also gures 1{2 in ref. [50].) As for the it to the SM point. The latter gives 2 As concerns kinematical observables, the q2 distribution of ] is hardly as analysed in ref. [49] are expected to be small. (1; 3)0 interaction Lagrangian: We introduce a vector-boson, color-singlet, SU(2)L-triplet W 0 (1; 3)0 with the following Integrating out W 0 , we obtain the following EFT Lagrangian: EFT = L3 = The relevant CC interactions are given by The best- t-point (BFP) and 95% C.L. intervals are given by LCC = bL) + h:c:: g1B2FP = 7:7 g12 = [4:4; 10:9] 2 = 0:5; @ 95% C:L:: where g12 has the same Lorentz structure as in the SM. The relevant NC interactions are given by LNC = nd the following non-universalities R =(`1S) = 0:989 R =(`2S) = 0:990 R =(`3S) = 0:990 R =(`2S) = 0:390: (3; 1)+2=3 ing interaction Lagrangian: We introduce a vector-boson, color-triplet, SU(2)L-singlet U (3; 1)+2=3 with the followLU = g1Q3U= L3 + g2d3U= e3 + h:c:: d3) + h:c: 2Vcbg1g2 ( R L) (cLbR) + h:c:: Integrating out U , we obtain the following EFT Lagrangian: . Given the 95% C.L. intervals quoted above, we nd the following 2Mg1Ug22 ( R L) bLbR + h:c: : EFT = LCC = LNC = They induce only non-universalities R =(`1S) = 0:952 R =(`2S) = 0:949 R =(`3S) = 0:946 { 10 { The relevant CC interactions are given by The BFP which explains R(D( )) is given by g1g2 < 0 and = (3:3; 0:4) 2 = 0: The 95% C.L. intervals are presented in gure 1. The q2 distribution of [B ! D modi ed compared to the SM one. Yet, as is evident from gure 3b, this change is not very signi cant given the current uncertainties. The relevant NC interactions are given by of R =(`1S). (3; 3)+2=3 We introduce a vector-boson, color-triplet, SU(2)L-triplet X (3; 3)+2=3 with the following interaction Lagrangian: LX = gQ3 aX= L3 + h:c:: Integrating out X , we obtain the following EFT Lagrangian: LX EFT = Q3 = The relevant CC interactions are given by The BFP and 95% C.L. interval are given by LCC = bL) + h:c:: g 2 BFP = 0 jgj2 = [0; 1:5] 2 = 20:4; @ 95% C:L:: Lorentz structure as in the SM. The relevant NC interactions are given by LNC = nd the following non-universalities R =(`1S) = 0:992; R =(`2S) = 0:993 R =(`3S) = 0:994 R =(`2S) = 0:390: (3; 1) 1=3 interaction Lagrangian: We introduce a scalar-boson, color-triplet, SU(2)L-singlet S (3; 1) 1=3 with the following LNC = 2jM1jS2 Vc2b ( L 2MS2 Vcb ( R L) (cRcL) + cL) + h:c: : They induce only non-universalities . Given the 95% C.L. intervals quoted above, we nd the following We impose a global 3B L symmetry, which prevent an additional Yukawa couplings of 1 2 Lc3 Q3 (e3uc2) + h:c: = j 1j The relevant CC interactions are given by R =(`2S) = 0:389 LCC = The BFP which explains R(D( )) is given by 1 2 < 0 and ( R L)(cRbL) bL) + h:c:: 2 BFP; j 2j = (0:3; 0:9) 2 = 0: signi cant given the current uncertainties. The relevant NC interactions are given by (3; 3) 1=3 interaction Lagrangian: We introduce a scalar-boson, color-triplet, SU(2)L-triplet S (3; 3) 1=3 with the following LT = We impose global 3B L symmetry to forbid T QQ terms. Integrating out T , we obtain the following EFT Lagrangian: EFT = 2 L3 a 3 aL3 = The relevant CC interactions are given by The BFP and 95% C.L. interval are given by 2 BFP = 0 j j2 = [0; 3:0] 2 = 20:4; @ 95% C:L:: Lorentz structure as in the SM. The relevant NC interactions are given by nd the following non-universalities R =(`1S) = 0:992 R =(`2S) = 0:994 R =(`3S) = 0:995 R =(`2S) = 0:390: (1; 2)+1=2 A scalar-boson, color-singlet, SU(2)L-doublet generates only scalar couplings. (3; 2)+7=6 ing interaction Lagrangian: We introduce a scalar-boson, color-triplet, SU(2)L-doublet D (3; 2)+7=6 with the followIntegrating out D, we obtain the following EFT Lagrangian: The relevant CC interactions are given by The BFP and 95% C.L. interval are given by EFT = jM1D2j jQ3e3j2 + h:c: : LCC = 2M D2 ( R L) (cRbL) + bL) + h:c:: MD 2 = 17; 12 = [0; 0:6] @ 95% C:L:: The q2 distribution of [B ! D ] is modi ed compared to the SM one. Yet, as is evident The relevant NC interactions are given by LNC = 2M D2 Vcb ( R L) (cRcL) + cL) + h:c: : nd the following non-universalities R =(`1S) = 0:889{0:992; R =(`2S) = 0:879{0:994; R =(`3S) = 0:873{0:995; R =(`2S) = 0:386{0:390: (3; 2) 5=6 ing interaction Lagrangian: We introduce a vector-boson, color-triplet, SU(2)L-doublet V (3; 2) 5=6 with the follow LV = g1Q3V= ec3 + g2L3V= dc3 + h:c:: Integrating out V , we obtain the following EFT Lagrangian: The relevant CC interactions are given by The BFP and 95% C.L. interval are given by 2Vcbg1g2 ( R L) (cLbR) + h:c:: g12 = [1:9; 5:9] @ 95% C:L:: MV 2 = 8:2; LCC = g1B2FP = 4:0 L3 + h:c: EFT = LNC = They induce only non-universalities 2Mg1Vg22 ( R L) bLbR + h:c: : . Given the 95% C.L. intervals quoted above, we nd the following The q2 distribution of [B ! D ] is modi ed compared to the SM one. Yet, as is evident The relevant NC interactions are given by R =(`1S) = 0:976 R =(`2S) = 0:976 R =(`3S) = 0:976 from ref. [2]. Discussion and future prospects ]. Data points and error bars are taken { 16 { Non-universality in leptonic decays was tested by CLEO [60] for the 1S; 2S and 3S states, and by BaBar [61] for the 1S state. These measurements read R =(1S); BaBar = 1:005 R =(1S); CLEO = 1:02 R =(2S); CLEO = 1:04 R =(3S); CLEO = 1:05 0:013stat 0:022syst; 0:02stat 0:04stat 0:08stat 0:05syst; 0:05syst; 0:05syst: states, respectively. The (2S) on-resonance sample collected by BaBar (Belle) is about 10 (16) times larger than CLEO's sample. The (3S) on-resonance sample collected by BaBar (Belle) is about 20 (2) times larger than CLEO's sample. Analyzing these existing 2 percent. Additional improvement can be achieved by using the cascade chains, which will render this error negligible. on the di erent total e ciencies and event shapes. The larger statistics can to study the (3S) into one test of universality. Eq. (1.6) as a function of m (nS), R =`(m (nS)) = 1 + 2x2;1S 2#1=2 where x ;1S the di erent this part of the error with a combined analysis. { 17 { BESII [73] measurement reads BR( (2S) ! 10 3 using 14M the statistical error by a factor of 3. (KEDR also measures this tauonic branching ratio [74] but it is not used by the PDG t.) The relative systematic uncertainty on ) (as measured by BaBar) is 10% [75], while the relative systematic BR( (2S) ! be achieved in Bess III to start probing the relevant parameter space. Summary and conclusions There is a 3:9 evidence that the ratio R(D( )) )= (B ! D( )` ), where ` = new bosons which mediate the B decay at tree level. There are seven such or two SU(2)L-doublet quark elds. Consequently, a variety of processes, in addition to , are a ected. Some of these, such as t ! c + decay, Bc ! decay [24, 41], decay [51, 59], and bb =cc ! scattering [47], have been previously of observables: lepton non-universality in leptonic decays of the vector-mesons, parameterized by the ratio RV=` )= (V ! ``). hand, for could be explained by operators which do not a ect V ! accuracy of about 1.5%. If Belle II operates below the (4S) resonance, it can contribute { 18 { Acknowledgments The leptonic width in the SM 0 [V ! ``] = 4 4x`2)1=2 1 + 2x`2 : 0 [V ! ``] 1 + Ztree + QCD + EM : The tree-level Z mediated correction is 4Qqc2W s2W 8Qqc2W s2W 1+2x`2 exchange. The corrections to namely evaluating ( ) at a ect RV=`. = m2V =m2Z and gVq = T 2Qqs2W . This is an O(10 4) correction, well below the be absorbed in the de nition of the vector meson form factor, fV . absent: the Landau-Yang theorem [78, 79] implies M(V ) = 0 for massive vector are taken into account by using the running couplings, { 19 { we quote here the inclusive [V ! `+` depend on the experimental setup. It reads [80] + ] at one-loop order in QED, which does not EM = 4x`2] 1 + log[x`2] 16x`2(2 + 3x`2) + 16x`2 1 + 2x`2 log 4 + 3 + 16x`2 (2 log 4) ' 0:002 + 0:006x`2: We further estimate the two-loop non-universality e ect to be 2 loop = O We therefore consider, for all practical purposes, [V ! ``] = 4 Qq2(1 4xl2)1=2 1 + 2xl2 log 4) ; RV=` = (1 4x2)1=2 1 + 2x2 log[4]) : Other EFT operators Z mediated operators Here we consider the following set of dimension six operators LHl = iCH1` Hy D! + iCHe Hy D! decays are given by AqV` = BVq` = CH1` +CH3`=4+CHe CH1` + CH3`=4 2Qqs2W , and for the Z vertex corrections we . 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Daniel Aloni, Aielet Efrati, Yuval Grossman, Yosef Nir. Y and ψ leptonic decays as probes of solutions to the R(D (*)) puzzle, Journal of High Energy Physics, 2017, 1-27, DOI: 10.1007/JHEP06(2017)019