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We present an updated determination of the values of $\vert V_{cb} \vert$,$R(D^*)$ and $\vert V_{ub} \vert/\vert V_{cb} \vert$ based on the new data onsemileptonic $B \to D^* \ell \nu_\ell$ decays by the Belle and Belle-IICollaborations and on the recent theoretical progress in the calculation of theform factors relevant for semileptonic $B \to D^* \ell \nu_\ell$ and $B_s \to K\ell \nu_\ell$ decays. In particular we present results derived by applyingeither the Dispersive Matrix (DM) method of Refs. [1-6] or the more standardBoyd-Grinstein-Lebed (BGL) [7] approach to the most recent values of the formfactors determined in lattice QCD. Using all the available lattice results forthe form factors from the DM method we get the theoretical value $R^{\rmth}(D^*) = 0.266 \pm 0.009$ and we extract from a bin-per-bin analysis of theexperimental data the value $\vert V_{cb} \vert = (40.16 \pm 0.53)\cdot10^{-3}$. Our result for $R(D^*)$ is compatible with the latestexperimental world average $R^{\rm exp}(D^*) = 0.284 \pm 0.012$ [8] at the$\simeq 1.2\,\sigma$ level. Our value for $\vert V_{cb} \vert$ is consistentwith the latest inclusive determinations $\vert V_{cb} \vert^{\rm incl} =(41.97 \pm 0.48) \cdot 10^{-3}$ [9] and $\vert V_{cb} \vert^{\rm incl} =(41.69\pm 0.63) \cdot 10^{-3}$ [10] within $\simeq 2.5$ and $\simeq 1.9$standard deviations, respectively. From a reappraisal of the calculations of$\vert V_{ub} \vert / \vert V_{cb} \vert$, we also obtain $\vert V_{ub} \vert /\vert V_{cb} \vert = 0.087\pm 0.009$ in good agreement with the result $\vertV_{ub} \vert / \vert V_{cb} \vert = 0.0844\pm 0.0056$ from the latest FLAGreview [11].

Updates on the determination of $\vert V_{cb} \vert$, $R(D^{*})$ and $\vert V_{ub} \vert/\vert V_{cb} \vert$