Unitarity constraints and the dispersive matrix

Abstract

We present updated estimates of $|V_{cb}|$ and $R(D^{(\ast )})$ based on all the available theoretical and experimental data on semileptonic $B\to D^{(\ast )}\ell \hat{I}{½}_{\ell }$ 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 $R^{\mathrm{th}}(D)=0.296\pm 0.008$ and $R^{\mathrm{th}}(D^{\ast })=0.262\pm 0.009$, which are consistent with the corresponding HFLAV averages at the $\simeq 2.0\ddot{I}ƒ$ and the $\simeq 1.5\ddot{I}ƒ$ level, respectively. Moreover, from a bin-per-bin study of the experimental data we obtain the values $|V_{cb}|=(41.0\pm 1.2)\cdot 10^{-3}$ from $B\to D$ decay and $|V_{cb}|=(39.92\pm 0.64)\cdot 10^{-3}$ from $B\to D^{\ast }$ one, whose differences with the latest inclusive determinations never exceed the $\simeq 2.5\ddot{I}ƒ$ level.

6 pages, 2 figures. Presented at the 12th Workshop on the CKM Unitarity Triangle, 18-22 September 2023, Santiago de Compostela