Abstract
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.
Highlights
The Bc meson, first observed by the CDF Collaboration [1], is interesting since it has the structure of the heavy quarkonium but it decays weakly
The semileptonic Bc decays induced by the c → s transition are expected to constitute the largest fraction of semileptonic modes [7,40,41,42,43,44,45,46,47,48,49,50]
The semileptonic Bc decays induced by the c → s; d transitions play an interesting role in Standard Model (SM) and in the search of beyond the Standard Model (BSM) effects analogous to the ones emerging in B decays
Summary
The Bc meson, first observed by the CDF Collaboration [1], is interesting since it has the structure of the heavy quarkonium but it decays weakly. The measurement of BðBc → J=ψτντÞ is important in this regard [11] Such effects can be analyzed in an effective theory framework extending the low-energy SM Hamiltonian that governs the c → ðs; dÞlνl transitions with the inclusion of the full set of semileptonic dimension operators with lepton flavour dependent Wilson coefficients. The hadronic matrix elements of the new operators can be given in terms of the same independent functions entering in the SM ones, invoking the heavy quark spin symmetry. The appendixes contain the relations among the hadronic form factors obtained by the heavy quark spin symmetry (Appendix A), and the coefficient functions of the full angular distribution of the four-body radiative modes Bc → BÃs;dð→ Bs;dγÞlνl (Appendix B). With such expressions the various observables can be computed by suitable integrations of the distribution in Eq (3)
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