Exclusive determinations of $$\vert V_{cb} \vert $$ | V cb | and $$R(D^{*})$$ R ( D ∗ ) through unitarity

Abstract

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 $$B \rightarrow D^* \ell \nu _\ell $$ B → D ∗ ℓ ν ℓ decays, recently produced by the FNAL/MILC Collaborations (Fermilab Lattice, MILC collaboration, Semileptonic form factors for $$B \rightarrow D^*\ell \nu $$ B → D ∗ ℓ ν at nonzero recoil from 2 + 1-flavor lattice QCD. arXiv:2105.14019 ) at small, but non-vanishing values of the recoil variable ( $$w-1$$ 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 $$\vert V_{cb} \vert $$ | V cb | from the experimental data and compute the theoretical value of $$R(D^*)$$ R ( D ∗ ) . Our final result for $$\vert V_{cb} \vert $$ | V cb | reads $$\vert V_{cb} \vert = (41.3 \pm 1.7) \cdot 10^{-3}$$ | V cb | = ( 41.3 ± 1.7 ) · 10 - 3 , compatible with the most recent inclusive estimate at the $$0.5\sigma $$ 0.5 σ level. Moreover, we obtain the pure theoretical value $$R(D^*) = 0.275 \pm 0.008$$ R ( D ∗ ) = 0.275 ± 0.008 , which is compatible with the experimental world average at the $$\sim 1.3 \sigma $$ ∼ 1.3 σ level.