The role of $X(4140)$ and $X(4160)$ in the reactions of $B^+ \to J/\psi \phi K^+$

Abstract

We have studied the $J/\psi\phi$ mass distribution of the process $B^+\to J/\psi\phi K^+$ from the threshold to about 4250 MeV, by considering the contribution of the $X(4140)$ with a narrow width, together with the $X(4160)$ state. Our results show that the cusp structure at the $D^*_s\bar{D}^*_s$ threshold is tied to the molecular nature of the $X(4160)$ state.