Semileptonic $B\to D^{\ast }$ decays from light to $\tau$ leptons: the extraction of the form factor $F_2$ from data

We extend the Standard Model (SM) analysis of Ref. [1], which was limited to light leptons in the final state, to the semileptonic $B\to D^{\ast }\tau {\nu }_{\tau }$ decay. By using quantities that can be analised without the knowledge of $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$, we derive important information about the helicity amplitudes and the hadronic form factors that can be compared with the predictions of lattice QCD calculations. In particular, there is a difficulty in reproducing simultaneously the experimental values of $R(D^{\ast })$ and of other quantities relevant for the semitauonic decays within the SM. As a byproduct of our analysis, we also present a determination of $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ from the total decay rate.