New physics effects in purely leptonic B ∗ s decays
NNew physics effects in purely leptonic B ∗ s decays Suman Kumbhakar ∗ and Jyoti Saini † Indian Institute of Technology Bombay, Mumbai 400076, India Indian Institute of Technology Jodhpur, Jodhpur 342037, India (Dated: April 30, 2019)Recently several measurements in the neutral current sector b → sl + l − ( l = e or µ ) as well as inthe charged current sector b → cτ ¯ ν show significant deviations from their Standard Model predic-tions. It has been shown that two different new physics solutions can explain all the anomalies in b → sl + l − sector. Both these solutions are in the form of linear combinations of the two operators(¯ sγ α P L b )(¯ µγ α µ ) and (¯ sγ α P L b )(¯ µγ α γ µ ). We show that the longitudinal polarization asymmetryof the muons in B ∗ s → µ + µ − decay is a good discriminant between the two solutions if it can bemeasured to a precision of 10%, provided the new physics Wilson coefficients are real. If they arecomplex, the theoretical uncertainties in this asymmetry are too large to provide effective discrim-ination. We also investigate the potential impact of b → cτ ¯ ν anomalies on b → sτ + τ − transitions.We consider a model where the new phyics contributions to these two transitions are strongly cor-related. We find that the branching ratio of B ∗ s → τ + τ − can be enhanced by three orders ofmagnitude. I. INTRODUCTION
In the past few years, a number of anomalies have been observed in the decays of B mesons. They occur both in thecharged current (CC) transition b → cτ ¯ ν and in the flavor changing neutral current (FCNC) transitions b → sl + l − ( l = e or µ ). In the Standard Model (SM), the above CC transition occurs at tree level whereas the FCNC transitionsoccur only at loop level. The discrepancies, between the measured values and the SM predictions, vary for differentobservables.First, we discuss the anomalies in b → sl + l − transitions. They are1. In the decay B → K ∗ µ + µ − , some of the angular observables [1–3] are found to be in disagreement with theirrespective SM predictions [4]. The main discrepancy is in the angular observable P (cid:48) , which is at the level of 4 σ .2. The branching ratio of B s → φµ + µ − and the corresponding angular observables also differ from their SMpredictions [5, 6] at 3 . σ level.3. The SM predicts the ratio R K ≡ Γ( B + → K + µ + µ − ) / Γ( B + → K + e + e − ) (cid:39)
1. LHCb experiment measuredthis ratio in the q ( q = ( p B − p K ) ) range 1 . ≤ q ≤ . [7]. The measured value 0 . +0 . − . ( stat. ) ± . syst. ) deviates from the SM prediction by 2 . σ [8, 9].4. LHCb experiment also measured the ratio R K ∗ ≡ Γ( B → K ∗ µ + µ − ) / Γ( B → K ∗ e + e − ) in two different q ranges, (0 . ≤ q ≤ . ) (low q ) and (1 . ≤ q ≤ . ) (central q ). The SM predicts thisratio to be (cid:39) q [8, 9]. The measured values are 0 . +0 . − . ( stat. ) ± . syst. ) for low q and0 . +0 . − . ( stat. ) ± . syst. ) for central q [10]. These differ from the SM prediction by 2 . − . σ and2 . − . σ respectively.The anomalies in R K and R K ∗ , which are an indication of violation of lepton flavor universality (LFU) in theneutral current decays of b quark, can be explained by new physics (NP) in either b → se + e − or b → sµ + µ − or bothwhereas the first two anomalies require NP in b → sµ + µ − . Two kinds of NP amplitudes in b → se + e − transitionscan account for the R K and R K ∗ anomalies. These are • vector and/or axial-vector amplitudes which will have constructive interference with the SM amplitude. Themagnitude of such amplitude should be about 10% of the SM amplitude. • scalar, pseudoscalar or tensor amplitudes which do not interfere with the SM amplitude. A discussion of themost general NP contribution to b → se + e − is beyond the scope of this paper. ∗ Electronic address: [email protected] † Electronic address: [email protected] a r X i v : . [ h e p - ph ] A p r In this work, we will consider NP amplitudes only in b → sµ + µ − transition, because they can explain all fouranomalies in the FCNC decays of the B mesons. These amplitudes must have destructive interference with theSM amplitude so that the resulting values of R K and R K ∗ will be less than 1. That is, these NP amplitudes areconstrained to be vector and/or axial-vector amplitudes. Several groups [11–20] have performed global fits to identifythe Lorentz structure of the NP operators and to determine their Wilson coefficients (WCs) which can account forall the b → sµ + µ − anomalies. There are two distinct solutions, one with the operator of the form (¯ sγ α P L b )(¯ µγ α µ )and the other whose operator is a linear combination of (¯ sγ α P L b )(¯ µγ α µ ) and (¯ sγ α P L b )(¯ µγ α γ µ ) [18]. These resultssatisfy the requirement that only vector ( V ) and/or axial-vector ( A ) NP operators are allowed.It is interesting to look for new observables in the b → sµ + µ − sector in order to (a) find additional evidence forthe existence of NP and (b) to discriminate between the two NP solutions. These observables may be related to theobserved decay modes or may be associated with the decay modes yet to be observed such as B s → l + l − γ [21].The branching ratio of B ∗ s meson to di-muons is one such observable which is yet to be measured. In the SM, thisdecay mode is not subject to helicity suppression [22], unlike B s → µ + µ − [23]. Further, it is sensitive to NP operatorscontaining both V and A currents of leptons whereas B s → µ + µ − is sensitive only to the latter. A model independentanalysis of this decay was performed in ref. [24] to identify the NP operators which can lead to a large enhancementof its branching ratio. It was found that such an enhancement is not possible due to the constraints from the present b → sµ + µ − data. It would be desirable to construct a new observable related to this decay mode to see whether suchan observable has the potential to discriminate between the two existing NP solutions in b → sµ + µ − transition.In this work, we consider the longitudinal polarization asymmetry of muon in B ∗ s → µ + µ − decay, A LP ( µ ). Thisasymmetry is theoretically clean because it has a very mild dependence on the decay constants unlike the branchingratio. We first calculate the SM prediction of A LP ( µ ) and then study its sensitivity to the two NP solutions.As mentioned above, there are additional discrepancies in the CC decays of B mesons. Such decays are driven by b → cτ ¯ ν transition, which occurs at tree level in the SM. These discrepancies, which are listed below, are an indicationof LFU violation in the charged current decays of b quark.1. The current world averge of the ratio R D = B ( B → D τ ¯ ν ) / B ( B → D { e/µ } ¯ ν ), measured by BaBar and Belle,deviates 2 . σ from the SM prediction [25].2. There is a series of measurements of the ratio R D ∗ = B ( B → D ∗ τ ¯ ν ) / B ( B → D ∗ { e/µ } ¯ ν ) by BaBar, Belle andLHCb experiments. Recent world average of R D ∗ shows a discrepancy with respect to the SM prediction ata level of 3 . σ . Including the measurement correlation between R D and R D ∗ , the current experimental worldaverages of R D ( ∗ ) show a ∼ σ deviation from the SM predictions [25].3. The measured value of R J/ψ = B ( B → J/ψ τ ¯ ν ) / B ( B → J/ψµ ¯ ν ) by LHCb collaboration, is 1 . σ away from itsSM prediction [26].The NP operators which can account for R D ( ∗ ) anomaly are identified in ref [27]. In ref. [28] it was shown thatthere are only four independent NP solutions which can explain the present data in the b → cτ ¯ ν sector. Methods todiscriminate between these NP solutions were suggested in ref. [29]. The NP WCs of these solutions are about 10% ofthe SM values. Since this transition occurs at tree level in the SM, it is very likely that the NP operators also occur attree level. In the SM, the relation between the interaction eigenstates and mass eigenstates leads to the cancellationof FCNCs at tree level through GIM mechanism. However the relation between the interaction eigenstates of NP andthe mass eigenstates need not be the same as that in the SM. In such a situation, the NP will lead to tree level neutralcurrent b → sl + l − transitions. In ref. [30], a model is constructed where the tree level FCNC terms due to NP aresignificant for b → s τ + τ − but are suppressed for b → sl + l − where l = e or l = µ . The branching ratios for the decaymodes such as B → K ( ∗ ) τ + τ − , B s → τ + τ − and B s → φτ + τ − will have a large enhancement in this model [30]. Inthis work we study the effect of this NP on the branching ratio of B ∗ s → τ + τ − and the τ polarization asymmetry A LP ( τ ).This paper is organized as follows. In section II, we obtain the theoretical expressions for the longitudinal polar-ization asymmetry of the final state leptons in B ∗ s → l + l − decays, where l = e, µ or τ . This is done for the SM andfor the case of NP V and A operators. In section III, we obtain predictions of A LP ( µ ) in both the SM and the twoNP solutions which explain all b → sµ + µ − anomalies. In the same section we study the impact of tree level NP ofref. [30] on the branching ratio of B ∗ s → τ + τ − and A LP ( τ ). Finally in the section IV, we present our conclusions. II. CALCULATION OF LONGITUDINAL POLARIZATION ASYMMETRY FOR B ∗ s → l + l − DECAYA. Longitudinal Polarization Asymmetry in the SM
The pure leptonic decay B ∗ s → l + l − is induced by the quark level transition b → sl + l − . In the SM the correspondingeffective Hamiltonian is H SM = 4 G F √ π V ∗ ts V tb (cid:20) (cid:88) i =1 C i ( µ ) O i ( µ ) + C e π [ sσ µν ( m s P L + m b P R ) b ] F µν + C α em π ( sγ µ P L b )( lγ µ l ) + C α em π ( sγ µ P L b )( lγ µ γ l ) (cid:21) , (1)where G F is the Fermi constant, V ts and V tb are the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and P L,R = (1 ∓ γ ) / O i , i = 1 − , C ( µ ) → C eff ( µ, q ) and C ( µ ) → C eff ( µ, q ).The B ∗ s → l + l − amplitude can be parameterized in terms of the following form factors [22] (cid:104) | sγ µ b | B ∗ s ( p B ∗ s , (cid:15) ) (cid:105) = f B ∗ s m B ∗ s (cid:15) µ , (cid:104) | sσ µν b | B ∗ s ( p B ∗ s , (cid:15) ) (cid:105) = − if TB ∗ s ( p µB ∗ s (cid:15) ν − (cid:15) µ p νB ∗ s ) , (cid:104) | sγ µ γ b | B ∗ s ( p B ∗ s , (cid:15) ) (cid:105) = 0 , (2)where (cid:15) µ is the polarization vector of the B ∗ s meson and f B ∗ s and f TB ∗ s are the decay constants of B ∗ s meson. In theheavy quark limit they are related to f B s , the decay constant of B s meson, as f B ∗ s = f B s (cid:20) − α s π (cid:21) ,f TB ∗ s = f B s (cid:20) α s π (cid:18) log( m b µ ) − (cid:19)(cid:21) . (3)The decay constant f B s is defined through the relation (cid:104) | sγ µ γ b | B s ( p B s ) (cid:105) = − if B s p µB s . The SM amplitude for B ∗ s → l + l − decay is given by M SM = − α em G F √ π f B ∗ s V ∗ ts V tb m B ∗ s (cid:15) µ (cid:34)(cid:32) C eff + 2 m b f TB ∗ s m B ∗ s f B ∗ s C eff (cid:33) (cid:0) lγ µ l (cid:1) + C (cid:0) lγ µ γ l (cid:1)(cid:35) , (4)and the decay rate is found to beΓ SM = α em G F f B ∗ s m B ∗ s π | V ts V ∗ tb | (cid:113) − m l /m B ∗ s (cid:32) m l m B ∗ s (cid:33) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) C eff + 2 m b f TB ∗ s m B ∗ s f B ∗ s C eff (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) + (cid:32) − m l m B ∗ s (cid:33) | C | . (5)We define the longitudinal polarization asymmetry for the final state leptons in B ∗ s → l + l − decay. The unitlongitudinal polarization four-vector in the rest frame of the lepton ( l + or l − ) is defined as s αl ± = (cid:18) , ± −→ p l |−→ p l | (cid:19) . (6)In the dilepton rest frame (which is also the rest frame of B ∗ s meson), these unit polarization vectors become s αl ± = (cid:18) |−→ p l | m l , ± E l m l −→ p l |−→ p l | (cid:19) , (7)where E l , −→ p l and m l are the energy, momentum and mass of the lepton ( l + or l − ) respectively. We can define twolongitudinal polarization asymmetries, A + LP for l + and A − LP for l − , in the decay B ∗ s → l + l − as [31–33] A ± LP = [Γ( s l − , s l + ) + Γ( ∓ s l − , ± s l + )] − [Γ( ± s l − , ∓ s l + ) + Γ( − s l − , − s l + )][Γ( s l − , s l + ) + Γ( ∓ s l − , ± s l + )] + [Γ( ± s l − , ∓ s l + ) + Γ( − s l − , − s l + )] . (8)If the two spin projections, s l − and s l + are the same, the decay rate is given byΓ( ± s l − , ± s l + ) = N (cid:20) m l |C| + C C ∗ m l m B ∗ s (cid:110) i (cid:113) m B ∗ s − m l (cid:16) ε αβγν p αl − p βB ∗ s p γl + s νl − + ε αβγσ p αl − p βB ∗ s p γl + s σl + (cid:17) + im l m B ∗ s (cid:16) ε αβνσ p αl − p βB ∗ s s νl − s σl + − ε βγνσ p βB ∗ s p γl + s νl − s σl + (cid:17)(cid:111) + C ∗ C m l m B ∗ s (cid:110) − i (cid:113) m B ∗ s − m l (cid:16) ε αβγν p αl − p βB ∗ s p γl + s νl − + ε αβγσ p αl − p βB ∗ s p γl + s σl + (cid:17) − im l m B ∗ s (cid:16) ε αβνσ p αl − p βB ∗ s s νl − s σl + − ε βγνσ p βB ∗ s p γl + s νl − s σl + (cid:17)(cid:111)(cid:105) , (9)For opposite spin projections of s l − and s l + we haveΓ( ∓ s l − , ± s l + ) = N (cid:34) m B ∗ s |C| + C C ∗ m l m B ∗ s (cid:110) m l m B ∗ s (cid:16) − iε αβνσ p αl − p βB ∗ s s νl − s σl + + iε βγνσ p βB ∗ s p γl + s νl − s σl + ∓ m B ∗ s (cid:113) m B ∗ s − m l (cid:17) − i (cid:113) m B ∗ s − m l (cid:16) ε αβγν p αl − p βB ∗ s p γl + s νl − + ε αβγσ p αl − p βB ∗ s p γl + s σl + (cid:17)(cid:111) + C ∗ C m l m B ∗ s (cid:110) i (cid:113) m B ∗ s − m l (cid:16) ε αβγν p αl − p βB ∗ s p γl + s νl − + ε αβγσ p αl − p βB ∗ s s νl − s σl + (cid:17) + m l m B ∗ s (cid:16) ∓ m B ∗ s (cid:113) m B ∗ s − m l + iε αβνσ p αl − p βB ∗ s s νl − s σl + − iε βγνσ p βB ∗ s p γl + s νl − s σl + (cid:17)(cid:111) + 23 (cid:16) m B ∗ s − m l (cid:17) | C | (cid:21) . (10)In eqs. (9) and (10), we have used the abbreviations N = α em G F π | V tb V ∗ ts | f B ∗ s (cid:113) m B ∗ s − m l , C = (cid:18) C eff + m b f TB ∗ s m B ∗ s f B ∗ s C eff (cid:19) . Using eqs. (8),(9) and (10), we get the lepton polarization asymmetry to be A ± LP | SM = ∓ (cid:113) − m l /m B ∗ s Re (cid:20)(cid:18) C eff + m b f TB ∗ s m B ∗ s f B ∗ s C eff (cid:19) C ∗ (cid:21)(cid:16) m l /m B ∗ s (cid:17) (cid:12)(cid:12)(cid:12)(cid:12) C eff + m b f TB ∗ s m B ∗ s f B ∗ s C eff (cid:12)(cid:12)(cid:12)(cid:12) + (cid:16) − m l /m B ∗ s (cid:17) | C | . (11) B. Longitudinal polarization asymmetry in presence of NP
We now investigate the lepton polarization asymmetry in the presence of NP. As the NP solutions to the b → sl + l − anomalies are in the form of V and A operators, we consider the addition of these NP operators to the SM effectiveHamiltonian of b → sl + l − . Scalar and pseudo-scalar NP operators do not contribute to B ∗ s → l + l − decay because (cid:104) | ¯ sb | B ∗ s ( p B ∗ s , (cid:15) ) (cid:105) = (cid:104) | ¯ sγ b | B ∗ s ( p B ∗ s , (cid:15) ) (cid:105) = 0. The effective Hamiltonian now takes the form H eff ( b → sl + l − ) = H SM + H V A , (12)where H V A is H V A = α em G F √ π V ∗ ts V tb (cid:20) C NP ( sγ µ P L b )( lγ µ l ) + C NP ( sγ µ P L b )( lγ µ γ l ) (cid:21) . Here C NP are the NP Wilson coefficients. Within this NP framework, the branching ratio and A LP are obtained tobe B ( B ∗ s → l + l − ) = α em G F f B ∗ s m B ∗ s τ B ∗ s π | V ts V ∗ tb | (cid:113) − m l /m B ∗ s (cid:32) m l m B ∗ s (cid:33) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) C eff + 2 m b f TB ∗ s m B ∗ s f B ∗ s C eff + C NP (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) + (cid:32) − m l m B ∗ s (cid:33) | C + C NP | (cid:35) , (13) A ± LP | NP = ∓ (cid:113) − m l /m B ∗ s Re (cid:20)(cid:18) C eff + m b f TB ∗ s m B ∗ s f B ∗ s C eff + C NP (cid:19) (cid:0) C + C NP (cid:1) ∗ (cid:21)(cid:16) m l /m B ∗ s (cid:17) (cid:12)(cid:12)(cid:12)(cid:12) C eff + m b f TB ∗ s m B ∗ s f B ∗ s C eff + C NP (cid:12)(cid:12)(cid:12)(cid:12) + (cid:16) − m l /m B ∗ s (cid:17) (cid:12)(cid:12) C + C NP (cid:12)(cid:12) . (14) III. RESULTS AND DISCUSSIONA. A LP ( µ ) with NP solutions In this section we first calculate A LP ( µ ) for the B ∗ s → µ + µ − decay. The numerical inputs used for this calculationare listed in table I. The SM prediction is A + LP ( µ ) | SM = −A − LP ( µ ) | SM = 0 . ± . . (15)The uncertainty in this prediction (about 0 . Parameter Value m b . ± .
03 GeV [34] m B ∗ s . +1 . − . MeV [34] f B ∗ s /f B s . ± .
023 [35] f TB ∗ s /f B s .
95 [22]TABLE I: Numerical inputs used in our calculations.
Among the two NP solutions which can account for all the b → sµ + µ − anomalies [11, 18], only C NP ( µµ ) is non-zerofor the first solution whereas C NP ( µµ ) and C NP ( µµ ) are equal and opposite for the second solution. In table II wehave listed the NP WCs of these solutions along with the predictions of A ± LP ( µ ) for them. NP type NP WCs B ( B ∗ s → µ + µ − ) A + LP ( µ ) = −A − LP ( µ )SM 0 (1 . ± . × − . ± . C NP ( µµ ) − . ± .
19 (0 . ± . × − . ± . C NP ( µµ ) = − C NP ( µµ ) − . ± .
12 (0 . ± . × − . ± . A LP ( µ ) for B ∗ s → µ + µ − decay with real NP WCs.NP Type [Re(WC), Im(WC)] B ( B ∗ s → µ + µ − ) A + LP ( µ ) = −A − LP ( µ )(I) C NP ( µµ ) [( − . ± . , (0 . ± . . ± . × − . ± . C NP ( µµ ) = − C NP ( µµ ) (A) [( − . ± . , (1 . ± . . ± . × − . ± . − . ± . , ( − . ± . . ± . × − . ± . A LP ( µ ) for B ∗ s → µ + µ − decay with complex NP WCs. The NPWCs are taken from ref. [19] From this table it is obvious that the prediction of A LP ( µ ) for the first solution deviates from the SM at the level of3 . σ whereas, for the second solution, it is the same as that of the SM. Hence any large deviation in this asymmetrycan only be due to the first NP solution. We also provide the predictions for B ( B ∗ s → µ + µ − ) in table II. It is clearthat neither of the two solutions can be distinguished from each other or from the SM via the branching ratio.In the discussion above, the NP WCs are assumed to be real. If these WCs are complex, they can lead to variousCP asymmetries in B → ( K, K ∗ ) µ + µ − decays [36]. These asymmetries can distinguish between the two NP solutions.In ref. [19], it was assumed that C NP ( µµ ) and C NP ( µµ ) are complex and a fit to all the b → sµ + µ − data wasperformed. The resulting values of NP WCs from this fit are given in table III. The predictions for B ( B ∗ s → µ + µ − )and A LP ( µ ) are also given in this table. Because of the large uncertainties, neither of these two observables candistinguish between the two NP solutions. However, it is possible to make a distinction based on the CP asymmetriesmentioned above [19]. (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) R X (cid:144) R X SM B r (cid:72) B (cid:42) s (cid:174) ΤΤ (cid:76) (cid:45) (cid:45) R X (cid:144) R X SM A L P (cid:72) Τ (cid:76) FIG. 1: Left and right panels correspond to B ( B ∗ s → τ + τ − ) and A LP ( τ ) respectively. In both panels the yellow band represents1 σ range of these observables. The 1 σ and 2 σ ranges of R X /R SMX are indicated by blue and pink bands respectively. The greenhorizontal line corresponds to the SM value.
B. Effect of NP in B ∗ s → τ + τ − As mentioned in the introduction, anomalies are also observed in the b → cτ ¯ ν transitions. An NP model, which canaccount for these anomalies, is likely to contain NP amplitude for b → sτ + τ − transition also. Hence the branchingratio of B ∗ s → τ + τ − and τ longitudinal polarization asymmetry A LP ( τ ) will contain signatures of such NP. In theSM, the predictions for these quantities are B ( B ∗ s → τ + τ − ) = (6 . ± . × − , (16) A + LP ( τ ) | SM = −A − LP ( τ ) | SM = 0 . ± . . (17)The authors of ref. [30] constructed a model of NP which accounts for the anomalies in b → cτ ¯ ν . This model containstree level FCNC terms for b → s τ + τ − but not for b → sl + l − ( l = e, µ ). Therefore, the WCs C NP ( µµ ) and C NP ( µµ )have no relation to the WCs C NP ( τ τ ) and C NP ( τ τ ). The amplitude for b → sµ + µ − transition remains small enoughthat the constraints from R K and R K ∗ are satisfied. The WCs for the b → sτ + τ − transition have the form C ( τ τ ) = C SM − C NP ( τ τ ) ,C ( τ τ ) = C SM + C NP ( τ τ ) , (18)in this model, where C NP ( τ τ ) = 2 πα V cb V tb V ∗ ts (cid:32)(cid:115) R X R SMX − (cid:33) . (19)The ratio R X /R SMX is the weighted average of current experimental values of R D , R D ∗ and R J/ψ . From the currentmeasurements of these quantities, we estimate this ratio to be (cid:39) . ± .
06. This, in turn, leads to C NP ( τ τ ) ∼ O (100).Thus the NP contribution completely dominates the WCs and leads to greatly enhanced branching ratios for various B / B s meson decays involving b → s τ + τ − transition [30].We calculate B ( B ∗ s → τ + τ − ) and A LP ( τ ) as a function of R X /R SMX . The plot of B ( B ∗ s → τ + τ − ) vs. R X /R SMX is shown in left panel of fig. 1. We note, from this plot, that B ( B ∗ s → τ + τ − ) can be enhanced up to 10 − which isabout three orders of magnitude larger than the SM prediction. The plot of A LP ( τ ) vs. R X /R SMX is shown in theright panel of fig. 1. It can be seen that A LP ( τ ) is suppressed by about 5% in comparison to its SM value.The recent data on R D ( ∗ ) show less tension with the SM which leads to smaller values of R X /R SMX . As long as thisratio is greater than 1 .
05, the branching ratio of B ∗ s → τ + τ − is enhanced by an order of magnitude at least. When R X /R SMX ∼ . A LP ( τ ) exhibits some very interesting behaviour. In this case, the tree level FCNC NP contributionis similar in magnitude to the SM contribution (which occurs only at loop level). Due to the interference between thesetwo amplitudes, A LP ( τ ) changes sign and becomes almost ( − IV. CONCLUSIONS
There are several measurements in the decays induced by the quark level transition b → sl + l − which do not agreewith their SM predictions. All these discrepancies can be explained by considering NP only in b → sµ + µ − transition.These NP operators are required to have V and/or A form to account for the fact that R K and R K ∗ are less than1. A global analysis of all the measurements in b → sl + l − sector leads to only two NP solutions. The first solutionhas C NP ( µµ ) < C NP ( µµ ) = − C NP ( µµ ) <
0. In this work we consider the ability of themuon longitudinal polarization asymmetry in B ∗ s → µ + µ − decay to distinguish between these two solutions. Thisobservable is theoretically clean because it has only a very mild dependence on the decay constants. For the case ofreal NP WCs, we show that this asymmetry has the same value as the SM case for the second solution but is smallerby 11% for the first solution. Hence, a measurement of this asymmetry to 10% accuracy can distinguish betweenthese two solutions. But for the complex NP WCs, the discrimination power is lost because of the large theoreticaluncertainties.Further, we study the impact of the anomalies in b → cτ ¯ ν transitions on the branching ratio of B ∗ s → τ + τ − and A LP ( τ ). In ref. [30], a model was constructed where tree level NP leads to both b → sτ + τ − and b → cτ ¯ ν withmoderately large NP couplings. Within this NP model, we find that the present data in R D ( ∗ ) ,J/ψ sector implyabout three orders of magnitude enhancement in the branching ratio of B ∗ s → τ + τ − and a 5% suppression in A LP ( τ )compared to their SM predictions. We also show that A LP ( τ ) undergoes drastic changes when the NP amplitude issimilar in magnitude to the SM amplitude.To measure A LP ( µ ) or A LP ( τ ) in experiments, the final state leptons have to decay into secondary particles. Butfor muon, the measurement would be quite difficult as it does not decay within the detector. In the case of A LP ( τ ), itmay be possible for LHCb to reconstruct τ where the τ decays into multiple hadrons. This technique has been alreadyused to identify the τ leptons in B → D ∗ τ ¯ ν decay. Therefore a precise reconstruction from the decay products of the τ is necessary to measure the τ longitudinal polarization asymmetry in B ∗ s → τ + τ − . Acknowledgements
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