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 105:034503, 2022) to lattice computations Form Factors (FFs) entering semileptonic $$B \rightarrow D^* \ell \nu _\ell $$ B → D ∗ ℓ ν decays, recently produced by FNAL/MILC Collaborations (Fermilab Lattice, MILC collaboration, Semileptonic form factors for D^*\ell at nonzero recoil from 2 + 1-flavor QCD. arXiv:2105.14019 ) small, but non-vanishing values variable ( $$w-1$$ w - 1 ). Thanks DM obtain FFs in whole kinematical range accessible decay a completely model-independent non-perturbative way, implementing exactly both unitarity constraints. Using our theoretical bands extract $$\vert V_{cb} \vert | V cb experimental data compute value $$R(D^*)$$ R ( ) . Our final result reads = (41.3 \pm 1.7) \cdot 10^{-3}$$ = 41.3 ± 1.7 · 10 3 , compatible with most recent inclusive estimate $$0.5\sigma 0.5 σ level. Moreover, pure $$R(D^*) 0.275 0.008$$ 0.275 0.008 which is world average $$\sim 1.3 \sigma ∼ 1.3