Abstract
In this work, the decays of B_s 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 phi (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 B_srightarrow J/psi K^+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.
Highlights
IntroductionThe 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/ψ K +
S-wave resonant structures.Contributions from D-wave resonances are known to be non-negligible in this decay
Since the light spectator quark momentum k moves with the kaon pair in the plus direction, the minus component of its parton momentum should be very small, it can be neglected in the hard kernel, and integrated out in the definition of the two-kaon distribution amplitudes
Summary
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/ψ K +. The LHCb Collaboration [7] improved their measurements, in which the fit fractions of six resonances including φ(1020), φ(1680), f2(1270), f2(1525), f2(1750), f2(1950) together with a S-wave structure in Bs → J/ψ K + K − are determined. The PQCD approach so far, has been successfully applied to the studies of the resonance contributions to the three-body B/Bs decays in several recent papers [24,25,26,27,28,29,30,31,32,33,34]. The factorization formulas for the decay amplitudes are collected in the Appendix
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