The X(4140) and X(4160) resonances in the e⁺e^- γj/ψφ reaction

We investigate the J/ψφ invariant mass distribution in the e⁺e^- → γ ψφJψφ reaction at a center-of-mass energy of √s = 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/ψφ invariant mass distribution is compatible with the existence of the X(4140) state, appearing as a peak, and a strong cusp structure at the D_s∗D_s∗ 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/ψφ 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.