Exclusive determinations of vert V_{cb} vert and R(D^{*}) through unitarity

Abstract

In this work we apply the Dispersive Matrix (DM) method of Di Carlo et al. (Phys Rev D 104:054502, 2021) and Martinelli et al. (Phys Rev D 105:034503, 2022) to the lattice computations of the Form Factors (FFs) entering the semileptonic B rightarrow D^* ell nu _ell decays, recently produced by the FNAL/MILC Collaborations (Fermilab Lattice, MILC collaboration, Semileptonic form factors for B rightarrow D^*ell nu at nonzero recoil from 2 + 1-flavor lattice QCD. arXiv:2105.14019) 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 vert V_{cb} vert from the experimental data and compute the theoretical value of R(D^*). Our final result for vert V_{cb} vert reads vert V_{cb} vert = (41.3 pm 1.7) cdot 10^{-3}, compatible with the most recent inclusive estimate at the 0.5sigma level. Moreover, we obtain the pure theoretical value R(D^*) = 0.275 pm 0.008, which is compatible with the experimental world average at the sim 1.3 sigma level.