$|V_{cb}|$, LFU and $SU(3)_F$ symmetry breaking in $B_{(s)} \to D_{(s)}^{(*)} \ell \nu_\ell$ decays using Lattice QCD and Unitarity

TL;DR

This paper employs a unitarity-based dispersion matrix approach with lattice QCD data to non-perturbatively determine form factors and extract |V_{cb}| from exclusive B decays, also exploring LFU and SU(3)_F symmetry breaking effects.

Contribution

It introduces a model-independent, non-perturbative method to determine semileptonic form factors across the entire kinematic range using lattice results and unitarity bounds.

Findings

Extracted |V_{cb}| = (41.2 ± 0.8) × 10^{-3}, compatible with inclusive results.

Computed LFU ratios R(D) and R(D^*) consistent with experimental data within 1.3σ.

Observed potential SU(3)_F symmetry breaking effects in lattice form factors at large recoil.

Abstract

We present an application of the unitarity-based dispersion matrix (DM) approach to the extraction of the CKM matrix element $|V_{cb}|$ from the experimental data on the exclusive semileptonic $B_{(s)} \to D_{(s)}^{(*)} \ell \nu_\ell$ decays. The DM method allows to achieve a non-perturbative, model-independent determination of the momentum dependence of the semileptonic form factors. Starting from lattice results available at large values of the 4-momentum transfer and implementing non-perturbative unitarity bound, the behaviour of the form factors in their whole kinematical range is obtained without introducing any explicit parameterization of their momentum dependence. We consider the four exclusive semileptonic $B_{(s)} \to D_{(s)}^{(*)} \ell \nu_\ell$ decays and extract $|V_{cb}|$ from the experimental data for each transition. The average over the four channels is $|V_{cb}| = (41.2 \pm 0.8) \cdot 10^{-3} $, which is compatible with the latest inclusive determination at $1\sigma$ level. We address also the issue of Lepton Flavour Universality by computing pure theoretical estimates of the $\tau/\ell$ ratios of the branching fractions for each channel, where $\ell$ is a light lepton. In the case of a light spectator quark we obtain $R(D^*) = 0.275(8)$ and $R(D) = 0.296(8)$, which are compatible with the corresponding experimental values within $1.3\sigma$. In the case of a strange spectator quark we obtain $\textit{R}(D_s^*) =0.2497(60)$ and $\textit{R}(D_s) = 0.298(5)$. The different values for $R(D_s^*)$ and $R(D^*)$ may reflect $SU(3)_F$ symmetry breaking effects, which seem to be present in some of the lattice form factors, especially at large values of the recoil.