Investigate the strong coupling of $g_{X J/\psi\phi}$ in $X(4500) \to J/\psi \phi$ by using the three-point sum rules and the light-cone sum rules

We assign $X(4500)$ as a D-wave tetraquark state and study the decay of $X(4500)$ $\to$ $J/\psi \phi$. The mass and the decay constant of $X(4500)$ are calculated by using the SVZ sum rules. For the decay width of $X(4500)$ $\to$ $J/\psi \phi$, we present the calculation within the framework of both the three-point sum rules and the light-cone sum rules. The strong coupling $g_{X J/\psi \phi}$ is obtained by considering the soft-meson approximation when we use the light-cone sum rules calculation. Both calculations show that the decay of $X(4500)$ $\to$ $J/\psi\phi$ close to the total width of $X(4500)$ if we assign $X$(4500) as a D-wave tetraquark. In this paper, only the hidden-charm decay channel is considered. With these results and those from the open-charm decay channel, we are able to give a more rational conclusion when comparing with the total width of $X(4500)$. In the future, experiments will be more helpful in determining whether or not this structure of $X(4500)$ is appropriate.