Unitarity constraints and the dispersive matrix

We present updated estimates of $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ and $R(D^{(\ast )})$ based on all the available theoretical and experimental data on semileptonic $B\to D^{(\ast )}\mathrm{\ell }{\nu }_{\mathrm{\ell }}$ 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 $R^{\mathrm{t}\mathrm{h}}(D)=0.296\pm 0.008$ and $R^{\mathrm{t}\mathrm{h}}(D^{\ast })=0.262\pm 0.009$, 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 $\mathrm{\mid }{V}_{cb}\mathrm{\mid }=(41.0\pm 1.2)\cdot {10}^{-3}$ from $B\to D$ decay and $\mathrm{\mid }{V}_{cb}\mathrm{\mid }=(39.92\pm 0.64)\cdot {10}^{-3}$ from $B\to D^{\ast }$ one, whose differences with the latest inclusive determinations never exceed the $\simeq 2.5\sigma$ level.