Non-perturbative bounds for $B \to D^{(*)}\ell\nu_{\ell}$ decays and phenomenological applications

TL;DR

This paper introduces a non-perturbative dispersive matrix method to accurately determine hadronic form factors and CKM matrix elements from $B o D^{(*)}\,\ell\nu_{\ell}$ decays, with applications to lepton flavor universality tests.

Contribution

It presents a novel dispersive matrix approach for non-perturbative extraction of form factors across the full kinematic range without assumptions on their dependence.

Findings

Estimated |V_{cb}| values consistent with inclusive determinations.

Calculated R(D) and R(D*) ratios aligning with experimental averages.

Applied method to recent lattice QCD data for form factors.

Abstract

We show how to extract the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $\vert V_{cb} \vert$ from exclusive semileptonic $B \to D^{(*)}$ decays by using the Dispersive Matrix (DM) method. It is a new approach which allows to determine in a full non-perturbative way the hadronic form factors (FFs) in the whole kinematical range, without making any assumption on their dependence on the momentum transfer. We investigate also the issue of Lepton Flavor Universality (LFU) by computing a pure theoretical estimate of the ratio $R(D^{(*)})$. Our approach is applied to the preliminary LQCD computations of the FFs, published by the FNAL/MILC [1] and the JLQCD [2] Collaborations, for the $B \to D^*$ decays and to the final ones, computed by FNAL/MILC [3], for the $B \to D$ transitions . Since the FNAL/MILC Collaborations have recently published the final results of their LQCD computations of the FFs [4] for the $B \to D^*$ case, we present also the results of our procedure after its application on these data. We find $ \vert V_{cb} \vert = (41.0 \pm 1.2) \cdot 10^{-3}$ and $\vert V_{cb} \vert = (41.3 \pm 1.7) \cdot 10^{-3}$ from $B \to D$ and $B \to D^*$ decays, respectively. These estimates are consistent within $1\sigma$ with the most recent inclusive determination $\vert V_{cb}\vert_{incl} = (42.16 \pm 0.50) \cdot 10^{-3}$ [5]. Furthermore, we obtain $R(D) = 0.289(8)$ and $R(D^*) = 0.269(8)$, which are both compatible with the latest experimental averages [6] at the $\sim$1.6$\sigma$ level.