The X(4140) and X(4160) resonances in the e~+e~-→γJ/ψ? reaction

We investigate the J/Ψ? invariant mass distribution in the e~+e~-→γJ/Ψ? reaction at a center-of-mass energy of ■=4.6 GeV measured by the BESⅢ collaboration,which concluded that no significant signals were observed for e~+e~-→γX(4140) because of the low statistics.We show,however,that the J/Ψ? invariant mass distribution is compatible with the existence of the X(4140) state,appearing as a peak,and a strong cusp structure at the Ds~*■threshold,resulting from the molecular nature of the X(4160) state,which provides a substantial contribution to the reaction.This is consistent with our previous analysis of the B~+→J/Ψ?K~+decay measured by the LHCb collaboration.We strongly suggest further measurements of this process with more statistics to clarify the nature of the X(4140) and X(4160) resonances.