Analysis of B0s → X(3872)[ψ(2S)]π+ π- (K plus K- ) decays

We have phenomenologically investigated the decays B0s -> X(3872)pi+pi -(K+K-) and B0s -> psi (2S)pi+pi-(K+K-). In our analysis, the scalar meson f0(980) is formed through the final state interactions of coupled channels pi pi and K <overline>K. Our findings indicate that the pi+pi- invariant mass distribution of the B0s -> psi (2S)pi+ pi - decay can be accurately reproduced. Furthermore, we have explored the pi+pi-(K+K-) invariant mass distribution of the B0s -> 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 cc<overline> state. Additionally, we have considered the contributions from f0(1500) to pi+pi- and the phi meson to K+K- in our analysis. Utilizing the model parameters, we have calculated the branching fraction of B0s -> X(3872)K+K-, and anticipate that the findings of our study can be experimentally tested in the future.