Besides being important to determine Standard Model parameters such as the CKM matrix elements $|V_{cb}|$ and $|V_{ub}|$, semileptonic $B$ decays seem also promising to reveal new physics (NP) phenomena, in particular in connection with the possibility of uncovering lepton flavour universality (LFU) violating effects. In this view, it could be natural to connect the tensions in the inclusive versus exclusive determinations of $|V_{cb}|$ to the anomalies in the ratios $R(D^{(*)})$ of decay rates into $tau$ vs $mu, e$. However, the question has been raised about the role of the parametrization of the hadronic $B to D^{(*)}$ form factors in exclusive $B$ decay modes. We focus on the fully differential angular distributions of $bar B to D^* ell^-{bar u}_ell$ with $D^* to D pi$ or $D^* to D gamma$, the latter mode being important in the case of $B_s to D_s^*$ decays. We show that the angular coefficients in the distributions can be used to scrutinize the role of the form factor parametrization and to pin down deviations from SM. As an example of a NP scenario, we include a tensor operator in the $b to c$ semileptonic effective Hamiltonian, and discuss how the angular coefficients allow to construct observables sensitive to this structure, also defining ratios useful to test LFU.
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