Probing Non-leptonic Two-body Decays of $B_c$ meson

Abstract

Rates and CP asymmetries of the non-leptonic two-body decay of $B_c$ are calculated based on the low energy effective Hamiltonian. We concentrate on such $b$ quark decays of the processes with $0^{-}$ and $1^{-}$ S-wave particles and/or $0^{+}$ and $1^{+}$ P-wave particles in the final states. The Salpeter method, which is the relativistic instantaneous approximation of the original Bethe-Salpeter equation, is used to derive hadron transition matrix elements. Based on the calculation, it is found that the best decay channels to observe CP violation are $B_c^{-}\to {\eta }_c+D^{-}(D_0^{\ast -})$, which need about $\sim 10^7$ $B_c$ events in experiment. Decays to ${\eta }_c+D^{\ast -}(D_s^{-}),h_c+D^{-}(D^{\ast -})(D_0^{\ast -}),J/\Psi +D^{\ast -}$ are also hopeful channels.

Comments: 17 pages, 2 figures, 7 tables