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S-wave ground state charmonium decays of $B_c$ mesons in the perturbative QCD approach

We make a systematic investigation on the two-body nonleptonic decays $B_c\rightarrow J/Ψ(η_c),M$ by employing the perturbative QCD approach based on $k_T$ factorization, where $M$ is a light pseudoscalar or vector or a heavy charmed meson. We predict the branching ratios and direct CP asymmetries of these $B_c$ decays and also the transverse polarization fractions of $B_c\rightarrow J/ΨV,J/ψD^{*}_{(s)}$ decays. It is found that these decays have a large branching ratios of the order of $10^{-4} - 10^{-2}$ and could be measured by the future LHC-b experiment. Our predictions for the ratios of branching fractions $\frac{\mathcal {BR}(B_c^+\rightarrow J/ΨD_s^+)} {\mathcal {BR}(B_c^+\rightarrow J/Ψπ^+)}$ ,$\frac{\mathcal {BR}(B_c^+\rightarrow J/ΨD_s^{*+})} {\mathcal {BR}(B_c^+\rightarrow J/ΨD_s^+)}$ and $\frac{\mathcal {BR}(B_c^+\rightarrow J/ΨK^+)} {\mathcal {BR}(B_c^+\rightarrow J/Ψπ^+)}$ are in good agreement with the data. A large transverse polarization fraction which can reach $48\%$ is predicted in $B_c^+\rightarrow J/ΨD_s^{*+}$ decay, which is consistent with the data. We find a possible direct CP violation in $B_c\rightarrow J/ψD^{*}$ decays, which are helpful to test the CP violating effects in $B_c$ decays.