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

TL;DR

This paper introduces optimized LFU ratios in semileptonic B and Bc decays that reduce theoretical uncertainties, enabling more precise tests of lepton flavor universality with minimal signal loss.

Contribution

It presents a method to improve LFU ratio measurements by minimizing form-factor uncertainties through simple cuts or reweighting, applicable across multiple decay channels.

Findings

Achieved approximately 1% theoretical uncertainty in SM predictions.

Demonstrated the method's effectiveness in various B and Bc decay modes.

Enhanced the precision of lepton universality tests.

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.