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

TL;DR

This paper systematically investigates $B_c$ meson decays into charmonium and light or heavy mesons using perturbative QCD, predicting branching ratios, polarization fractions, and CP asymmetries, with results testable at LHCb.

Contribution

It provides the first comprehensive perturbative QCD predictions for various $B_c$ decay channels, including CP asymmetries and polarization fractions, aligning well with existing data.

Findings

Large branching ratios of $10^{-4}$ to $10^{-2}$ predicted.

Predicted transverse polarization fraction up to 48%.

Possible direct CP violation observed in certain decay modes.

Abstract

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