Unitarity constraints and the dispersive matrix

Abstract

We present updated estimates of $\vert V_{cb} \vert$ and $R(D^{(*)})$ based on all the available theoretical and experimental data on semileptonic $B \to D^{(*)} \ell \nu_\ell$ decays. These values have been obtained by using the Dispersive Matrix method to describe the hadronic form factors. By analysing all the lattice data we get the theoretical values $R^{\rm th}(D) = 0.296 \pm 0.008$ and $R^{\rm th}(D^*) = 0.262 \pm 0.009$, which are consistent with the corresponding HFLAV averages at the $\simeq 2.0\,\sigma$ and the $\simeq 1.5\,\sigma$ level, respectively. Moreover, from a bin-per-bin study of the experimental data we obtain the values $\vert V_{cb} \vert = (41.0 \pm 1.2) \cdot10^{-3}$ from $B \to D$ decay and $\vert V_{cb} \vert = (39.92 \pm 0.64) \cdot10^{-3}$ from $B \to D^*$ one, whose differences with the latest inclusive determinations never exceed the $\simeq 2.5\,\sigma$ level.