LAUSR

We investigate the \begin{document}$ J/\psi \phi $\end{document} invariant mass distribution in the \begin{document}$ e^+e^-\to \gamma J/\psi\phi $\end{document} reaction at a center-of-mass energy of \begin{document}$ \sqrt{s} = 4.6 $\end{document} GeV measured by the BESIII collaboration, which concluded that no significant signals were observed for \begin{document}$ e^+e^- \to \gamma X(4140) $\end{document} because of the low statistics. We show, however, that the \begin{document}$ J/\psi \phi $\end{document} invariant mass distribution is compatible with the existence of the \begin{document}$ X(4140) $\end{document} state, appearing as a peak, and a strong cusp structure at the \begin{document}$ D^*_s\bar{D}^*_s $\end{document} threshold, resulting from the molecular nature of the \begin{document}$ X(4160) $\end{document} state, which provides a substantial contribution to the reaction. This is consistent with our previous analysis of the \begin{document}$ B^+\to J/\psi\phi K^+ $\end{document} decay measured by the LHCb collaboration. We strongly suggest further measurements of this process with more statistics to clarify the nature of the \begin{document}$ X(4140) $\end{document} and \begin{document}$ X(4160) $\end{document} resonances.