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

TL;DR

This paper analyzes the $J/9\u03c6$ invariant mass distribution in $e^+e^- o \u03b3 J/9\u03c6$ at 4.6 GeV, suggesting the possible existence of the $X(4140)$ and $X(4160)$ resonances based on limited data and theoretical models.

Contribution

The study proposes that the observed structures in the invariant mass distribution are compatible with the $X(4140)$ and $X(4160)$ states, highlighting the molecular nature of the latter and calling for more data.

Findings

Possible signals for $X(4140)$ and $X(4160)$ resonances.

Compatibility of data with molecular interpretation of $X(4160)$.

Need for higher statistics measurements.

Abstract

We investigate the $J/\psi \phi$ invariant mass distribution of the $e^+e^-\to \gamma J/\psi\phi$ 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 $J/\psi \phi$ 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 $D^*_s\bar{D}^*_s$ 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 $B^+\to J/\psi\phi K^+$ 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.