Abstract
We apply the formalism of amplitude symmetries to the angular distribution of the decays B → D∗ℓν for ℓ = e, μ, τ . We show that the angular observables used to describe the distribution of this class of decays are not independent in absence of New Physics contributing to tensor operators. We derive sets of relations among the angular coefficients of the decay distribution for the massless and massive lepton cases which can be used to probe in a very general way the consistency among the angular observables and the underlying New Physics at work. We use these relations to access the longitudinal polarisation fraction of the D∗ using different angular coefficients from the ones used by Belle experiment. This in the near future can provide an alternative strategy to measure {F}_L^{Dast } in B → D∗τν and to understand the relatively high value measured by the Belle experiment. Using the same symmetries, we identify three observables which may exhibit a tension if the experimental value of {F}_L^{Dast } remains high. We discuss how these relations can be exploited for binned measurements. We also propose a new observable that could test for specific scenarios of New Physics generated by light right-handed neutrinos. Finally we study the prospects of testing these relations based on the projected experimental sensitivity of new experiments.
Highlights
Deviations appeared in other channels such as B → Kμμ and Bs → φμμ, and in a different type of observable, namely Lepton Flavour Universality Violating (LFUV) observables probing the universality of the lepton coupling in b → s comparing = e and = μ
Global fits within an Effective Field Theory (EFT) approach performed on the large set of observables available have shown the remarkable consistency of the deviations observed, which can be explained through various New Physics (NP) scenarios affecting only a limited number of operators by shifting the short-distance physics encoded in Wilson coefficients
If the latter agrees with the SM within large uncertainties, the precise Belle measurement of the integrated FLD∗ yields a relatively high value compared to the SM prediction, which appears difficult to accommodate with NP scenarios, as can be seen in refs. [22,23,24,25,26,27] which considered a wide set of NP benchmark points
Summary
The angular distribution for B → D∗ ν has been extensively studied in the literature [33–. Assuming that there are no light right-handed neutrinos, the distribution can be computed using the effective Hamiltonian:. + gT (cσμν b)( ̄Rσμν νL) + gT 5(cσμν γ5b)( ̄Rσμν νL) + h.c As it can be seen, we do not include right-handed neutrinos at this stage, which will be discussed later on. + I4 cos χ+I8 sin χ sin 2θ sin 2θD + I5 cos χ+I7 sin χ sin θ sin 2θD , where the angular coefficients Ii ≡ Ii(q2) are given in ref. Where i = 0, +, − and Hi correspond to vector and axial currents whereas HT,i correspond to tensor currents, and HP combines two amplitudes Ht and HP : HP =. The Hi amplitudes depend on form factors and on q2, but not on the lepton mass. The presence of 1/m in Hi+ means that the discussion of the limit m → 0 should be considered after expressing all the angular coefficients in terms of Hi
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