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

Abstract

We present an updated determination of the values of $|V_{cb}|$, $R(D^{\ast })$ and $|V_{ub}|/|V_{cb}|$ based on the new data on semileptonic $B\to D^{\ast }\ell \hat{I}{½}_{\ell }$ decays by the Belle and Belle-II Collaborations and on the recent theoretical progress in the calculation of the form factors relevant for semileptonic $B\to D^{\ast }\ell \hat{I}{½}_{\ell }$ and $B_s\to K\ell \hat{I}{½}_{\ell }$ decays. In particular we present results derived by applying either the Dispersive Matrix (DM) method of Refs. [1-6] or the more standard Boyd-Grinstein-Lebed (BGL) [7] approach to the most recent values of the form factors determined in lattice QCD. Using all the available lattice results for the form factors from the DM method we get the theoretical value $R^{\mathrm{th}}(D^{\ast })=0.262\pm 0.009$ and we extract from a bin-per-bin analysis of the experimental data the value $|V_{cb}|=(39.92\pm 0.64)\cdot 10^{-3}$. Our result for $R(D^{\ast })$ is consistent with the latest experimental world average $R^{\exp }(D^{\ast })=0.284\pm 0.012$ [8]} at the $\simeq 1.5\ddot{I}ƒ$ level. Our value for $|V_{cb}|$ is compatible with the latest inclusive determinations $|V_{cb}{|}^{\mathrm{incl}}=(41.97\pm 0.48)\cdot 10^{-3}$ [9] and $|V_{cb}{|}^{\mathrm{incl}}=(41.69\pm 0.63)\cdot 10^{-3}$ [10] within $\simeq 2.6$ and $\simeq 2.0$ standard deviations, respectively. From a reappraisal of the calculations of $|V_{ub}|/|V_{cb}|$, we also obtain $|V_{ub}|/|V_{cb}|=0.087\pm 0.009$ in good agreement with the result $|V_{ub}|/|V_{cb}|=0.0844\pm 0.0056$ from the latest FLAG review [11].

28 pages, 9 figures, 6 tables. Recent update of the HPQCD results for the semileptonic $B\to D^{\ast }$ form factors included in the lattice inputs for the bin-per-bin analyses. Figs. 1-2,4,6-8 and Tables 1-4 updated. Main conclusions unchanged. Covariance matrices for various theoretical observables added as appendix for applications to phenomenological studies