Semileptonic B decays matrix elements

TL;DR

This paper introduces a non-perturbative, model-independent dispersion matrix approach to extract CKM matrix elements from semileptonic B decays, providing precise form factor behavior and consistent CKM values with experimental data.

Contribution

The paper presents a novel unitarity-based dispersion matrix method for determining semileptonic form factors without explicit parameterization, improving the extraction of |V_{cb}| from experimental data.

Findings

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

Computed theoretical ratios R(D) and R(D*) consistent with experimental measurements.

Demonstrated the effectiveness of the method on B→π decay as a benchmark.

Abstract

We present some applications 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 $B_{(s)} \to D_{(s)}^{(*)} \ell \nu_\ell$ 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 bounds, the behaviour of the form factors in their whole kinematical range is obtained without introducing any explicit parameterization of their momentum dependence. We firstly illustrate the effectiveness of the method by considering the case of the semileptonic $B \rightarrow \pi$ decay, which is a good benchmark since the kinematic range is large. Then, we focus on the four exclusive semileptonic $B_{(s)} \to D_{(s)}^{(*)} \ell \nu_\ell$ decays and we 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} $. We find, for the first time, an exclusive value 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. 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 $\textit{R}(D_s) = 0.298(5)$.