Role of $B_c^+ \to B_{s,d}^{(*)} \, \bar \ell \, \nu_\ell$ in the Standard Model and in the search for BSM signals

The decays $B_c^+ \to B_{a} \bar \ell \nu_\ell$ and $B_c^+ \to B_{a}^{*}(\to B_a \gamma) \bar \ell \nu_\ell$, with $a=s,d$ and $\ell=e,\mu$, are studied in the Standard Model (SM) and in the extension based on the low-energy Hamiltonian comprising the full set of dimension-$6$ semileptonic $c \to s,d$ operators with left-handed neutrinos. Tests of $\mu/e$ universality are investigated using such modes. The heavy quark spin symmetry is applied to relate the relevant hadronic matrix elements and to exploit lattice QCD results on $B_c$ form factors. Optimized observables are selected, and the pattern of their correlations is studied to identify the effects of the various operators in the extended low-energy Hamiltonian.