Studies of the resonance components in the B${}_s$ decays into charmonia plus kaon pair

In this work, the decays of Bs meson to a charmonium state and a K${}^{+}$K${}^{-}$ pair are carefully investigated in the perturbative QCD approach. Following the latest fit from the LHCb experiment, we restrict ourselves to the case where the produced K${}^{+}$K${}^{-}$ pair interact in isospin zero S, P, and D wave resonances in the kinematically allowed mass window. Besides the dominant contributions of the ϕ(1020) resonance in the P-wave and f${}_2^{\prime }$(1525) in the D-wave, other resonant structures in the high mass region as well as the S-wave components are also included. The invariant mass spectra for most of the resonances in the B${}_s$→J/ψK${}^{+}$K${}^{-}$ decay are well reproduced. The obtained three-body decay branching ratios can reach the order of 10${}^{-4}$, which seem to be accessible in the near future experiments. The associated polarization fractions of those vector-vector and vector-tensor modes are also predicted, which are compared with the existing data from the LHCb Collaboration.