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

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 $B \to D^{(*)} \ell ν_\ell$ 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 $\sim 1.4σ$ from the latest experimental determinations.