Analysis of $B_s^0\to X(3872)[\psi (2S)]{\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ decays

Abstract

We have phenomenologically investigated the decays $B_s^0\to X(3872){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ and $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$. In our analysis, the scalar meson $f_0(980)$ is formed through the final state interactions of coupled channels $\pi \pi$ and $K\bar{K}$. Our findings indicate that the ${\pi }^{+}{\pi }^{-}$ invariant mass distribution of the $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}$ decay can be accurately reproduced. Furthermore, we have explored the ${\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ invariant mass distribution of the $B_s^0\to X(3872){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ decay, accounting for the different production mechanisms between $X(3872)$ and $\psi (2S)$, up to a global factor. It is found that the production rates for $X(3872)$ and $\psi (2S)$ are much different, which indicates that the structure of $X(3872)$ is more complicated than the $\psi (2S)$, which is a conventional $c\bar{c}$ state. Additionally, we have considered the contributions from $f_0(1500)$ to ${\pi }^{+}{\pi }^{-}$ and the $\varphi$ 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.

Comments: 7 pages, 6 figures. Typos are corrected, and couplings are renormalized to be dimentionless