$\vert V_{cb} \vert$ and $R(D^{(*)})$ using lattice QCD and unitarity

TL;DR

This paper introduces a novel unitarity-based, non-perturbative method using lattice QCD to accurately determine the CKM matrix element |V_{cb}| and the ratios R(D^{(*)}), addressing previous uncertainties and discrepancies in experimental and theoretical results.

Contribution

It develops a new unitarity-based approach to extract |V_{cb}| and R(D^{(*)}) using lattice QCD data without assuming specific FF shapes or relying heavily on experimental constraints.

Findings

|V_{cb}| from B→D is (41.0 ± 1.2)×10^{-3}, consistent with inclusive determinations.

|V_{cb}| from B→D* is (40.4 ± 1.8)×10^{-3}, with larger uncertainty due to preliminary data.

R(D) and R(D*) are estimated as 0.296(8) and 0.261(20), respectively, differing from experimental values by ~1.4σ.

Abstract

The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cb}|$ is extracted from exclusive semileptonic $B \to D^{(*)}$ decays adopting a novel unitarity-based approach which allows to determine in a full non-perturbative way the relevant hadronic form factors (FFs) in the whole kinematical range. By using existing lattice computations of the $B \to D^{(*)}$ FFs at small recoil from FNAL/MILC and JLQCD Collaborations, we show that it is possible to extrapolate their behavior also at large recoil without assuming any specific momentum dependence and without constraining their shape using experimental data. Thus, we address the extraction of $|V_{cb}|$ from the experimental data on the semileptonic $B \to D^{(*)} \ell \nu_\ell$ decays, obtaining $\vert V_{cb}\vert = (41.0 \pm 1.2 ) \cdot 10^{-3}$ from $B \to D$ using as input the final FNAL/MILC lattice data for the FFs and $|V_{cb}| = (40.4 \pm 1.8 ) \cdot 10^{-3}$ from $B \to D^*$ using the preliminary JLQCD lattice data. Our result from $B \to D$ is consistent within $\sim 1$ standard deviation with the most recent inclusive determination $|V_{cb}|_{incl} = (42.00 \pm 0.65) \cdot 10^{-3}$. The resulting uncertainty is comparable with those obtained in literature using experimental data to constrain the shape of the FFs. Our result from $B \to D^*$, though consistent with $|V_{cb}|_{incl} $, is still based on preliminary lattice data for the FFs and its uncertainty is greater than the ones obtained in literature using experimental data to constrain the shape of the FFs. We investigate also the issue of Lepton Flavor Universality thanks to new theoretical estimates of the ratios $R(D^{(*)})$, namely $R(D) = 0.296(8)$ using final FNAL/MILC lattice results, and $R(D^{*}) = 0.261(20)$ using preliminary JLQCD and FNAL/MILC lattice data. Our findings differ by $\sim 1.4\sigma$ from the latest experimental determinations.