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

TL;DR

This paper investigates the roles of the $X(4140)$ and $X(4160)$ states in the decay process $B^+ o J/ ext{ extphi} ext{K}^+$, analyzing their contributions to the $J/ extphi$ mass distribution and exploring the molecular nature of $X(4160)$.

Contribution

The study provides a detailed analysis of the $J/ extphi$ mass spectrum in $B^+$ decays, highlighting the significance of the $X(4140)$ and $X(4160)$ states and linking the cusp structure to the molecular nature of $X(4160)$.

Findings

The $X(4140)$ contributes as a narrow resonance.

The $X(4160)$ is associated with a cusp at the $D_s^* ar{D}_s^*$ threshold.

The cusp structure indicates a molecular nature of $X(4160)$.

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.