The , decays in the perturbative QCD approach

Zhou Rui; Wen-Fei Wang; Guang-xin Wang; Li-hua Song; Cai-Dian Lü

doi:10.1140/epjc/s10052-015-3528-0

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2015) 75: 293
https://doi.org/10.1140/epjc/s10052-015-3528-0

Regular Article - Theoretical Physics

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

Zhou Rui¹^*, Wen-Fei Wang²^,3, Guang-xin Wang¹, Li-hua Song¹ and Cai-Dian Lü³

¹ College of Sciences, North China University of Science and Technology, Tangshan, 063009, China
² Department of Physics and Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, Shanxi, China
³ Center for Future High Energy Physics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China

^* e-mail: jindui1127@126.com
^** e-mail: zhourui@ncst.edu.cn

Received: 17 May 2015
Accepted: 17 June 2015
Published online: 27 June 2015

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 $$n = 2, l = 0$$ Schrödinger 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 indicates 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.