The $B_c\to \psi (2S)\pi$, ${\eta }_c(2S)\pi$ decays in the perturbative QCD approach

Abstract

Nonleptonic two body $B_c$ decays including radially excited $\psi (2S)$ or ${\eta }_c(2S)$ mesons in the final state are studied using the perturbative QCD approach based on $k_T$ factorization. The charmonium distribution amplitudes are extracted from the $n=2,l=0$ Schr$\ddot{o}$dinger states for the harmonic oscillator potential. Utilizing these distribution amplitudes, we calculate the numerical results of the $B_c\to \psi (2S),{\eta }_c(2S)$ transition form factors and branching fractions of $B_c\to \psi (2S)\pi ,{\eta }_c(2S)\pi$ decays. The ratio between two decay modes $B_c\to \psi (2S)\pi$ and $B_c\to J/\psi \pi$ is compatible with the experimental data within uncertainties, which indicate that the harmonic oscillator wave functions for $\psi (2S)$ and ${\eta }_c(2S)$ work well. It is found that the branching fraction of $B_c\to {\eta }_c(2S)\pi$, which is dominated by the twist-3 charmonium distribution amplitude, can reach the order of $10^{-3}$. We hope it can be measured soon in the LHCb experiment.

Comments: 9 pages, 3 figures,3 Tables