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

Abstract

Based on the perturbative quantum chromodynamics (pQCD) approach and the quasi-two-body approximation, we have studied the three-body decays B^{0}_{s}rightarrow psi (3686,3770)K pi , which include the contributions of the intermediate resonances overline{K }^{*}_{0}(1430)^{0}, overline{K }^{*}(892)^{0}, overline{K }^{*}(1410)^{0}, overline{K }^{*}(1680)^{0}, and 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 and pi in the resonance region. First, the decays B^{0}_{s}rightarrow psi (2S,1D)K ^{-}pi ^{+} were calculated, followed by the calculation of the branching ratios of the decays B^{0}_{s}rightarrow psi (3686,3770)K ^{-}pi ^{+} using the 2S–1D mixing scheme. In addition, the pQCD predictions for the decays B^{0}_{s}rightarrow psi (2S,1D)K pi and 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 overline{K }^{*}(892)^{0} resonance is the main contributor to the total decay, and the branching ratio and the longitudinal polarization fraction of the psi (2S)overline{K }^{*}(892)^{0} decay mode agree well with the currently available data within errors. Furthermore, the theoretical predictions of the psi (2S) and 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^{0}_{s}rightarrow psi (3686,3770)K pi are of the order of 10^{-5} and 10^{-6}, respectively, which can be verified using the ongoing LHCb and Belle II experiments.