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

Based on the perturbative quantum chromodynamics (pQCD) approach and the quasi-two-body approximation, we have studied the three-body decays B s 0 → ψ (3686 , 3770) K π , which include the contributions of the intermediate resonances K ¯ 0 ∗ (1430) 0 , K ¯ ∗ (892) 0 , K ¯ ∗ (1410) 0 , K ¯ ∗ (1680) 0 , and 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 and π in the resonance region. First, the decays B s 0 → ψ (2 S , 1 D) K - π + were calculated, followed by the calculation of the branching ratios of the decays B s 0 → ψ (3686 , 3770) K - π + using the 2S–1D mixing scheme. In addition, the pQCD predictions for the decays B s 0 → ψ (2 S , 1 D) K π and B s 0 → ψ (3686 , 3770) K π were obtained using the narrow-width approximation relation given by the Clebsch–Gordan coefficients. Our work shows that the 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) K ¯ ∗ (892) 0 decay mode agree well with the currently available data within errors. Furthermore, the theoretical predictions of the ψ (2 S) and ψ (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 → ψ (3686 , 3770) K π are of the order of 10 - 5 and 10 - 6 , respectively, which can be verified using the ongoing LHCb and Belle II experiments. [ABSTRACT FROM AUTHOR]