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Based on the perturbative quantum chromodynamics (pQCD) approach and thequasi-two-body approximation, we have studied the three-body decaysB^{0}_{s}\rightarrow \psi(3686,3770)\emph{K}\pi, which include thecontributions of the intermediate resonances \bar{\emph{K}}^{*}_{0}(1430)^{0},\bar{\emph{K}}^{*}(892)^{0}, \bar{\emph{K}}^{*}(1410)^{0},\bar{\emph{K}}^{*}(1680)^{0}, and \bar{\emph{K}}^{*}_{2}(1430)^{0}. Thetime-like form factors corresponding to the distribution amplitudes of the S,P, and D-wave of the kaon-pion pair have been adopted in the parameterizedform, which describe the interactions between \emph{K} and \pi in the resonanceregion. First, the decays B^{0}_{s}\rightarrow \psi(2S,1D)\emph{K}^{-}\pi^{+}have been calculated followed by the calculation of the branching ratios of thedecays B^{0}_{s}\rightarrow \psi(3686,3770)\emph{K}^{-}\pi^{+} using the 2S-1Dmixing scheme. In addition, the pQCD predictions for the decaysB^{0}_{s}\rightarrow \psi(2S,1D)\emph{K}\pi and B^{0}_{s}\rightarrow\psi(3686,3770)\emph{K}\pi have been obtained using the narrow-widthapproximation relation given by the Clebsch-Gorden coefficients. Our work showsthat the \bar{\emph{K}}^{*}(892)^{0} resonance is the main contributor to thetotal decay, and the branching ratio and the longitudinal polarization fractionof the \psi(2S)\bar{\emph{K}}^{*}(892)^{0} decay mode agree well with thecurrently available data within errors. Furthermore, the theoreticalpredictions 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 pQCDpredictions for branching ratios of decays B^{0}_{s}\rightarrow\psi(3686,3770)\emph{K}\pi are of the order of 10^{-5} and 10^{-6},respectively, which can be verified using the ongoing LHCb and Belle IIexperiments.

european physical journal. c, particles and fields

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