Investigating the color-suppressed decays $\Lambda_b\rightarrow \Lambda \psi$ in the perturbative QCD approach

Abstract

The nonleptonic two-body $\Lambda_b\rightarrow \Lambda\psi $ decays with $\psi=J/\psi$ or $\psi(2S)$ are investigated based on the perturbative QCD approach. These are color-suppressed processes in which the nonfactorizable contributions are confirmed to be dominant. Angular momentum conservation allows us to describe the concerned decays by four independent complex helicity amplitudes. It is observed that the negative-helicity states for the $\Lambda$ baryon are preferred as expected in the left-handed nature of the charged-current interaction. The obtained results for the helicity amplitudes are used to compute the branching ratios and various observable parameters, which are then compared to the existing theoretical predictions and experimental data. In particular, we predict the ratio $\mathcal{R}=\frac{\mathcal{B}(\Lambda_b\rightarrow\Lambda \psi(2S))}{\mathcal{B}(\Lambda_b\rightarrow\Lambda J/\psi)}=0.47^{+0.02}_{-0.00}$ in comparison with $0.508\pm 0.023$ from the Particle Data Group at the level of 1 standard deviation. We also briefly explore the long-distance contributions to the semileptonic $\Lambda_b \rightarrow \Lambda l^+l^-$ decays in the kinematic regions where the dilepton invariant masses are around the $J/\psi$ and $\psi(2S)$ resonances.