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

Abstract

We make a systematic investigation on the two-body nonleptonic decays $B_c\to J/\Psi ({\eta }_c),M$ 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 $B_c\to J/\Psi V,J/\psi D_{(s)}^{\ast }$ 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 $\frac{\mathcal{B}\mathcal{R}(B_c^{+}\to J/\Psi D_s^{+})}{\mathcal{B}\mathcal{R}(B_c^{+}\to J/\Psi {\pi }^{+})}$ ,$\frac{\mathcal{B}\mathcal{R}(B_c^{+}\to J/\Psi D_s^{\ast +})}{\mathcal{B}\mathcal{R}(B_c^{+}\to J/\Psi D_s^{+})}$ and $\frac{\mathcal{B}\mathcal{R}(B_c^{+}\to J/\Psi K^{+})}{\mathcal{B}\mathcal{R}(B_c^{+}\to J/\Psi {\pi }^{+})}$ are in good agreement with the data. A large transverse polarization fraction which can reach $48\%$ is predicted in $B_c^{+}\to J/\Psi D_s^{\ast +}$ decay, which is consistent with the data. We find a possible direct CP violation in $B_c\to J/\psi D^{\ast }$ decays, which are helpful to test the CP violating effects in $B_c$ decays.

Comments: 38 pages, 4 figures, 6 tables