Optimized Lepton Universality Tests in $B\to V\ell \bar{\nu }$ decays

Abstract

We propose improved Lepton Flavor Universality (LFU) ratios in semileptonic $P\to V\ell \bar{\nu }$ 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 $B_c\to J/\psi$, $B_c\to \psi (2S)$, $B\to D^{\ast }$ and $B_s\to D_s^{\ast }$ transitions, showing that in all cases we can reach $\mathcal{O}(1\%)$ uncertainties on the SM predictions of the improved LFU ratios employing conservatives form-factor uncertainties.

Comments: 6 pages, 2 figures. Version to appear in EPJC