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

Abstract

We have phenomenologically investigated the decays $B_s^0 \to X(3872) π^+π^- (K^+ K^-)$ and $B_s^0 \to ψ(2S) π^+ π^- (K^+K^-)$. In our analysis, the scalar meson $f_0(980)$ is formed through the final state interactions of coupled channels $ππ$ and $K\bar{K}$. Our findings indicate that the $π^+π^-$ invariant mass distribution of the $B_s^0 \to ψ(2S)π^+π^-$ decay can be accurately reproduced. Furthermore, we have explored the $π^+π^- (K^+ K^-)$ invariant mass distribution of the $B_s^0 \to X(3872) π^+π^- (K^+ K^-)$ 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 $c\bar{c}$ 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 $B_s^0 \to X(3872) K^+ K^-$, and anticipate that the findings of our study can be experimentally tested in the future.