Analysis of B_s^0 → X(3872) [ψ(2S)] π^+π^- (K^+ K^-) decays

We have phenomenologically investigated the decays B_s^0 → X(3872) π^+π^- (K^+ K^-) and B_s^0 →ψ(2S) π^+ π^- (K^+K^-). In our analysis, the scalar meson f_0(980) is formed through the final state interactions of coupled channels ππ and KK̅. Our findings indicate that the π^+π^- invariant mass distribution of the B_s^0 →ψ(2S)π^+π^- decay can be accurately reproduced. Furthermore, we have explored the π^+π^- (K^+ K^-) invariant mass distribution of the B_s^0 → X(3872) π^+π^- (K^+ K^-) decay, accounting for the different production mechanisms between X(3872) and ψ(2S), up to a global factor. It is found that the production rates for X(3872) and ψ(2S) are much different, which indicates that the structure of X(3872) is more complicated than the ψ(2S), which is a conventional cc̅ state. Additionally, we have considered the contributions from f_0(1500) to π^+π^- and the ϕ meson to K^+ K^- in our analysis. Utilizing the model parameters, we have calculated the branching fraction of B_s^0 → X(3872) K^+ K^-, and anticipate that the findings of our study can be experimentally tested in the future.