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

The decays $B_c^+ to B_{a} bar ell u_ell$ and $B_c^+ to B_{a}^{*}(to B_a gamma) bar ell u_ell$, 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.