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

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