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

TL;DR

This paper calculates decay rates and CP asymmetries of $B_c$ meson non-leptonic two-body decays using the Salpeter method, identifying promising channels for observing CP violation.

Contribution

It introduces a relativistic approach to compute hadron transition matrix elements for $B_c$ decays, focusing on specific final state particles and CP violation observables.

Findings

Identifies key decay channels for observing CP violation in $B_c$ decays.

Predicts the number of $B_c$ events needed to detect CP violation.

Highlights promising decay modes involving $ ext{eta}_c$, $D$, $D^*$, and $J/ ext{Psi}$.

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 $B_c^-\rightarrow \eta_c +D^-(D^{*-}_0)$, which need about $\sim10^7$ $B_c$ events in experiment. Decays to $ \eta_c +D^{*-}(D_s^-), h_c+D^-(D^{*-})(D^{*-}_0), J/\Psi+D^{*-}$ are also hopeful channels.