Exclusive determinations of $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ and $R(D^{\ast })$ through unitarity

In this work we apply the Dispersive Matrix (DM) method of Refs. [1,2] to the lattice computations of the Form Factors (FFs) entering the semileptonic $B \to D^* \ell \nu_\ell$ decays, recently produced by the FNAL/MILC Collaborations [3] at small, but non-vanishing values of the recoil variable ($w-1$). Thanks to the DM method we obtain the FFs in the whole kinematical range accessible to the decay in a completely model-independent and non-perturbative way, implementing exactly both unitarity and kinematical constraints. Using our theoretical bands of the FFs we extract $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ from the experimental data and compute the theoretical value of $R(D^{\ast })$. Our final result for $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ reads $\vert V_{cb} \vert = (41.3 \pm 1.7) \cdot 10^{-3}$,compatiblewiththemostrecentinclusiveestimateatthe$0.5\sigma$level\mathrm{.}Moreover,weobtainthepuretheoreticalvalue$R(D^*) = 0.275 \pm 0.008$, which is compatible with the experimental world average at the $\sim 1.3\sigma$ level.