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.

arXiv comment5 pages, 5 figures

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• Canonical interpretation of the $X(4140)$ state within the ${}^3{P}_0$ model
• The resonances $X(4140)$, $X(4160)$, and $P_{cs}(4459)$ in the decay of ${\Lambda }_b\to J/\psi \Lambda \varphi$
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• The role of electromagnetic interaction in the $X(3872)$ and its analogs
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• Strong decays of $a_0$, $f_0$, $f_2$, and $K_2^{\ast }$ resonances as dynamically generated states of two vector mesons