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 (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 Bs → 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.PACS numbers: 13.25. Hw, 12.38.Bx, 14.40.Nd
I. INTRODUCTIONThe three-body mode B s → J/ψK + K − is of particular interest in searches for intermediate states in the B s decay chain. Since the LHCb Collaboration [1] found no obvious structures in the J/ψK + invariant mass distribution, the B s → J/ψK + K − decay proceeds predominantly via B s → J/ψR with the quasi-two-body intermediate state R subsequently decaying into K + K − . For the concerned B s decay, the K + K − system arise from pure ss source, and thus these resonances are isoscalar. Taking into account the conservation of P -parity and C-parity, the produced resonances are limited to quantum numbers J P C = 0 ++ , 1 −− , 2 ++ , ... with isospin I = 0. Among them, the largest component comes from the φ(1020) in a P -wave configuration [2]. Several Collaborations [1,3,4] have presented a measurement of the B s → J/ψφ(1020) mode with φ(1020) decays to K + K − . The current world averages of the absolute branching ratio B(B s → J/ψφ(1020)) can reach the order of 10 −3 . Another P -wave resonance φ(1680), whose contribution has more than 2 statistical standard deviation (σ) significance, is also included by the LHCb Collaboration [1] in its best fit model. Two well known scalar resonances, the f 0 (980) and f 0 (1370), are observed in the K + K − mass spectrum by LHCb [1], which is the only data set available so far for the S-wave resonant structures.Contributions from D-wave resonances are known to be non-negligible in this decay. The first observation of the decay sequence B s → J/ψf ′ 2 (1525), f ′ 2 (1525) → K + K − , was recently reported by the LHCb Collaboration [5], and later confirmed by the D0 Collaboration [6]. Subsequently, the LHCb Collaboration [1] have determined the final state composition of the decay channel using a modified Dalitz plot analysis where the decay angular distributions are included. The best fit model includes a nonresonant component and eight resonance states, whose absolute branching ratios are measured relative to that of the normalization decay mode B + → J/ψK...