The $X(4140)$ and $X(4160)$ resonances in the $e^{+}{e}^{-}\to \gamma J/\psi \varphi$ reaction

Abstract

We investigate the $J/\psi \varphi$ invariant mass distribution of the $e^{+}{e}^{-}\to \gamma J/\psi \varphi$ reaction at a center of mass energy of $\sqrt{s}=4.6$~GeV measured by the BESIII collaboration, who concludes that no significant signals are observed for $e^{+}{e}^{-}\to \gamma X(4140)$ because of the low statistics. We show, however, that the three bump structures in the $J/\psi \varphi$ invariant mass distribution, though given only by three data points, are compatible with the existence of the $X(4140)$ state, appearing as a peak, and a strong cusp structure at the $D_s^{\ast }{\bar{D}}_s^{\ast }$ threshold, resulting from the molecular nature of the $X(4160)$ state, which also provides a substantial contribution to the reaction. This is consistent with our previous analysis on the $B^{+}\to J/\psi \varphi K^{+}$ decay measured by the LHCb collaboration. We strongly call for the measurement of this process with more statistics to further pin down the nature of the $X(4140)$ and $X(4160)$ resonances.

Comments: 5 pages, 5 figures