CP Violation in Two-Body Hadronic Decays of $B_c$ Meson

Using the next-to-leading order low energy effective Hamiltonian, the CP asymmetries for the $B_{c}$ meson decays into meson pair are calculated in the spectator approximation. We do not compute the hadronic matrix elements directly, instead, we use the amplitude ratios to estimate the CP asymmetries. This is quite,different from the previous works in the literature. The values of the momentum squared carried by the virtual particles in timelike penguin dirgrams are also carefully discussed. From our calculated results, the best decay modes to observe CP violation in $B_{c}$ decays would be $B_{c}^-\to{\bar D}^{*0}K^{*-}$, ${\bar D}^{0}K^{*-}$, ${\bar D}^{*0} K^{-}$, ${\bar D}^{0}K^{-}$ and $B_{c}^-\to{\eta}_{c}D^{-}$, which need about $10^8$ of $B_{c}^{\pm}$ events in experiment.