Study of the quasi-two-body decays with perturbative QCD approach

Ze-Rui Liang; Feng-Bo Duan; Xian-Qiao Yu

doi:10.1140/epjc/s10052-019-6877-2

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2019) 79: 370
https://doi.org/10.1140/epjc/s10052-019-6877-2

Regular Article - Theoretical Physics

Study of the quasi-two-body decays $B^{0}_{s} \rightarrow \psi (3770) (\psi (3686))\pi ^+\pi ^-$ with perturbative QCD approach

Ze-Rui Liang, Feng-Bo Duan and Xian-Qiao Yu^*

School of Physical Science and Technology, Southwest University, Chongqing, 400715, China

^* e-mail: yuxq@swu.edu.cn

Received: 27 November 2018
Accepted: 13 April 2019
Published online: 29 April 2019

Abstract

In this note, we study the contributions from the S-wave resonances, $f_{0}(980)$ and $f_{0}(1500)$ , to the $B^{0}_{s}\rightarrow \psi (3770)\pi ^ {+}\pi ^{-}$ decay by introducing the S-wave $\pi \pi$ distribution amplitudes within the framework of perturbative QCD approach. Both the resonant and the non-resonant contributions are contained in the scalar form factor in the S-wave distribution amplitude $\Phi ^S_{\pi \pi }$ . Since the vector charmonium meson $\psi (3770)$ is a S–D wave mixed state, we calculate the branching ratios of S-wave and D-wave, respectively, and the results indicate that $f_{0}(980)$ is the main contribution of the considered decay, and the branching ratio of the $\psi (2S)$ mode is in good agreement with the experimental data. We also take the S–D mixed effect into the $B^{0}_{s}\rightarrow \psi (3686)\pi ^ {+}\pi ^{-}$ decay. Our calculations show that the branching ratio of $B^{0}_{s}\rightarrow \psi (3770)(\psi (3686))\pi ^ {+}\pi ^{-}$ can be at the order of $10^{-5}$ , which can be tested by the running LHCb experiments.