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.

9 pages, 3 figures,3 Tables

References in corpus (7)

• Big-Bang Nucleosynthesis
• Beauty mesons in lattice QCD with exact chiral symmetry
• Estimation of Semileptonic Decays of $B_c$ Meson to S-wave Charmonia with NRQCD
• S-wave ground state charmonium decays of $B_c$ mesons in the perturbative QCD approach
• Study of Bc --> J/psi pi, etac pi decays with perturbative QCD approach
• Weak productions of new charmonium in semi-leptonic decays of B_c
• Phenomenological study of the $B_c$ $\to$ $BP$, $BV$ decays with perturbative QCD approach

Cited by in corpus (7)

• The S-wave resonance contributions in the $B_s^0$ decays into $\psi (2S,3S)$ plus pion pair
• Relativistic corrections to light-cone distribution amplitudes of S-wave $B_c$ mesons and heavy quarkonia
• Quasi-two-body decays $B\to {\eta }_c(1S,2S)[\rho (770),\rho (1450),\rho (1700)\to ]\pi \pi$ in the perturbative QCD approach
• Quasi-two-body decays $B\to D{K}^{\ast }(892)\to DK\pi$ in the perturbative QCD approach
• Exclusive nonleptonic Bc-meson decays to S-wave charmonium states
• Branching ratios, $CP$ asymmetries and polarizations of $B\to \psi (2S)V$ decays
• Charmless $B_c\to VV$ decays in the QCD factorization approach