The $B_c\rightarrow \psi(2S)\pi$, $\eta_c(2S)\pi$ decays in the perturbative QCD approach

TL;DR

This paper calculates the decay rates of specific $B_c$ meson decays into radially excited charmonium states using perturbative QCD, providing predictions compatible with experimental data and suggesting measurable branching fractions.

Contribution

It introduces a method to compute $B_c$ decay form factors and branching ratios involving $ ext{2S}$ charmonium states using harmonic oscillator wave functions within the perturbative QCD framework.

Findings

The ratio of $B_c ightarrow ext{2S} ext{ states}$ to $J/\psi$ decays agrees with experimental data.

Branching fraction of $B_c ightarrow ext{2S} ext{ states}$ can reach $10^{-3}$.

Harmonic oscillator wave functions effectively describe radially excited charmonium states.

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 $B_c\rightarrow \psi(2S),\eta_c(2S)$ transition form factors and branching fractions of $B_c\rightarrow \psi(2S)\pi, \eta_c(2S)\pi$ decays. The ratio between two decay modes $B_c\rightarrow \psi(2S)\pi$ and $B_c\rightarrow J/\psi\pi$ 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 $B_c\rightarrow \eta_c(2S)\pi$, 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.