Contributions of S-, P-, and D-wave resonances to the quasi-two-body decays in the perturbative QCD approach

Wen Liu; Xian-Qiao Yu

doi:10.1140/epjc/s10052-022-10352-7

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 441
https://doi.org/10.1140/epjc/s10052-022-10352-7

Regular Article - Theoretical Physics

Contributions of S-, P-, and D-wave resonances to the quasi-two-body decays $B_{s}^{0} \to ψ (3686, 3770) K π$ $B^{0}_{s} \rightarrow \psi (3686,3770)K \pi$ in the perturbative QCD approach

Wen Liu and Xian-Qiao Yu^b

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

^b yuxq@swu.edu.cn

Received: 17 September 2021
Accepted: 20 April 2022
Published online: 13 May 2022

Abstract

Based on the perturbative quantum chromodynamics (pQCD) approach and the quasi-two-body approximation, we have studied the three-body decays $B_{s}^{0} \to ψ (3686, 3770) K π$ $B^{0}_{s}\rightarrow \psi (3686,3770)K \pi$ , which include the contributions of the intermediate resonances ${\bar{K}}_{0}^{*} {(1430)}^{0}$ $\overline{K }^{*}_{0}(1430)^{0}$ , ${\bar{K}}^{*} {(892)}^{0}$ $\overline{K }^{*}(892)^{0}$ , ${\bar{K}}^{*} {(1410)}^{0}$ $\overline{K }^{*}(1410)^{0}$ , ${\bar{K}}^{*} {(1680)}^{0}$ $\overline{K }^{*}(1680)^{0}$ , and ${\bar{K}}_{2}^{*} {(1430)}^{0}$ $\overline{K }^{*}_{2}(1430)^{0}$ . The time-like form factors corresponding to the distribution amplitudes of the S-, P-, and D-wave of the kaon–pion pair were adopted in parameterized form, and describe the interactions between $K$ $$K $$ and $π$ $\pi$ in the resonance region. First, the decays $B_{s}^{0} \to ψ (2 S, 1 D) K^{-} π^{+}$ $B^{0}_{s}\rightarrow \psi (2S,1D)K ^{-}\pi ^{+}$ were calculated, followed by the calculation of the branching ratios of the decays $B_{s}^{0} \to ψ (3686, 3770) K^{-} π^{+}$ $B^{0}_{s}\rightarrow \psi (3686,3770)K ^{-}\pi ^{+}$ using the 2S–1D mixing scheme. In addition, the pQCD predictions for the decays $B_{s}^{0} \to ψ (2 S, 1 D) K π$ $B^{0}_{s}\rightarrow \psi (2S,1D)K \pi$ and $B_{s}^{0} \to ψ (3686, 3770) K π$ $B^{0}_{s}\rightarrow \psi (3686,3770)K \pi$ were obtained using the narrow-width approximation relation given by the Clebsch–Gordan coefficients. Our work shows that the ${\bar{K}}^{*} {(892)}^{0}$ $\overline{K }^{*}(892)^{0}$ resonance is the main contributor to the total decay, and the branching ratio and the longitudinal polarization fraction of the $ψ (2 S) {\bar{K}}^{*} {(892)}^{0}$ $\psi (2S)\overline{K }^{*}(892)^{0}$ decay mode agree well with the currently available data within errors. Furthermore, the theoretical predictions of the $ψ (2 S)$ $\psi (2S)$ and $ψ (3686)$ $\psi (3686)$ decay modes are very close, indicating that they can be regarded as the same meson state. Finally, the pQCD predictions for branching ratios of decays $B_{s}^{0} \to ψ (3686, 3770) K π$ $B^{0}_{s}\rightarrow \psi (3686,3770)K \pi$ are of the order of $10^{- 5}$ $10^{-5}$ and $10^{- 6}$ $10^{-6}$ , respectively, which can be verified using the ongoing LHCb and Belle II experiments.

© The Author(s) 2022

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Funded by SCOAP³

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Contributions of S-, P-, and D-wave resonances to the quasi-two-body decays Bs0→ψ(3686,3770)Kπ in the perturbative QCD approach

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Contributions of S-, P-, and D-wave resonances to the quasi-two-body decays $B_{s}^{0} \to ψ (3686, 3770) K π$ $B^{0}_{s} \rightarrow \psi (3686,3770)K \pi$ in the perturbative QCD approach