Exclusive determinations of $|V_{cb}|$ and $R(D^{\ast })$ through unitarity

Abstract

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 $B\to D^{\ast }\ell \hat{I}{½}_{\ell }$ 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 $|V_{cb}|$ from the experimental data and compute the theoretical value of $R(D^{\ast })$. Our final result for $|V_{cb}|$ reads $|V_{cb}|=(41.3\pm 1.7)\cdot 10^{-3}$, compatible with the most recent inclusive estimate at the $0.5\ddot{I}ƒ$ level. Moreover, we obtain the pure theoretical value $R(D^{\ast })=0.275\pm 0.008$, which is compatible with the experimental world average at the $\sim 1.3\ddot{I}ƒ$ level.

20 pages, 5 figures, 2 tables. Revised version including appendices describing the DM method, the application of the unitarity filters and the implementation of the kinematical constraints. Results and conclusions unchanged. Matches published version in EPJC