Abstract
We propose improved lepton flavor universality (LFU) ratios in semileptonic Prightarrow V ell {bar{nu }} decays, when comparing mu and tau modes, that minimize the theoretical form-factor uncertainties. These optimized ratios are obtained with simple cuts or reweighting of the dilepton mass distributions, which imply a minimum loss of signal on the rare tauonic modes while maximizing the cancellation of theoretical uncertainties among the two modes. We illustrate the usefulness of these observables in B_crightarrow J/psi , B_crightarrow psi (2S), Brightarrow D^* and B_srightarrow D_s^* transitions, showing that in all cases we can reach {mathcal {O}}(1%) uncertainties on the SM predictions of the improved LFU ratios employing conservative form-factor uncertainties.
Highlights
The hints of lepton flavor universality (LFU) violation in charged-current semi-leptonic b → c ν decays [1,2,3,4,5,6,7], as well as in b → s transitions [8,9,10,11,12], represent one of the most fascinating challenges in particle physics
The purpose of this letter is to propose improved LFU ratios on Bc → J/ψ νand, more generally, any P → V νdecay suffering from large form-factor uncertainties, which would allow us to minimize the error on the corresponding Standard Model (SM) predictions. In these channels we can reduce the theory error on appropriate LFU ratios – at fixed form-factor uncertainty – taking into account that: (i) the only intrinsic theory error is the one induced by the scalar form factor; (ii) the scalar form factor generates a subleading contribution to the decay rate that vanishes at large dilepton invariant mass
The examples presented above provide a clear illustration of the virtues of the improved LFU ratios in obtaining SM predictions with a reduced theoretical error, both for cases where the error on the standard ratio is small, such as RD∗, as well as in cases where this error is very large, such as Rψ(2S)
Summary
The hints of lepton flavor universality (LFU) violation in charged-current semi-leptonic b → c ν decays [1,2,3,4,5,6,7], as well as in b → s transitions [8,9,10,11,12], represent one of the most fascinating challenges in particle physics. At present there is not a single measurement with a high statistical significance, but the global picture is very consistent These hints indicate a LFU violation of short-distance origin, encoded in the fourfermion semileptonic interaction. The source of the SM error on RJ/ψ and, partially, of the systematic error in the experimental result, is the poor knowledge of the Bc → J/ψ hadronic form factors. The knowledge of the latter is expected to improve soon thanks to lattice QCD calculations [21]. In these channels we can reduce the theory error on appropriate LFU ratios – at fixed form-factor uncertainty – taking into account that: (i) the only intrinsic theory error (i.e. the uncertainty associated to the non-universal part of the amplitude) is the one induced by the scalar form factor; (ii) the scalar form factor generates a subleading contribution to the decay rate that vanishes at large dilepton invariant mass
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