The S-wave resonance contributions in the decays into plus pion pair

Zhou Rui; Ya Li; Wen-Fei Wang

doi:10.1140/epjc/s10052-017-4772-2

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2017) 77: 199
https://doi.org/10.1140/epjc/s10052-017-4772-2

Regular Article - Theoretical Physics

The S-wave resonance contributions in the $B^{0}_{s}$ decays into $\psi (2S,3S)$ plus pion pair

Zhou Rui¹^*, Ya Li² and Wen-Fei Wang³

¹ College of Sciences, North China University of Science and Technology, Tangshan, 063009, China
² Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, 210023, Jiangsu, China
³ Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, Shanxi, China

^* e-mail: jindui1127@126.com

Received: 16 January 2017
Accepted: 19 March 2017
Published online: 29 March 2017

Abstract

The three-body decays $B^0_s \rightarrow \psi (2S,3S) \pi ^+ \pi ^-$ are studied based on the perturbative QCD approach. With the help of the nonperturbative two-pion distribution amplitudes, the analysis is simplified into the quasi-two-body processes. Besides the traditional factorizable and nonfactorizable diagrams at the leading order, the next-to-leading order vertex corrections are also included to cancel the scale dependence. The $$f_0(980)$$ , $$f_0(1500)$$ resonance contributions as well as the nonresonant contributions are taken into account using the presently known $\pi \pi$ time-like scalar form factor for the $s\bar{s}$ component. It is found that the predicted $B^0_s \rightarrow \psi (2S) \pi ^+ \pi ^-$ decay spectra in the pion pair invariant mass shows a similar behavior as the experiment. The calculated S-wave contributions to the branching ratio of $B^0_s \rightarrow \psi (2S) \pi ^+ \pi ^-$ is $6.0\times 10^{-5}$ , which is in agreement with the LHCb data $\mathcal {B}(B^0_s \rightarrow \psi (2S) \pi ^+ \pi ^-)=(7.2\pm 1.2)\times 10^{-5}$ within errors. The estimate of $\mathcal {B}(B^0_s \rightarrow \psi (3S) \pi ^+ \pi ^-)$ can reach the order of $10^{-5}$ , pending the corresponding measurements.