Production of $1^{-+}$ exotic charmonium-like states in electron-positron collisions

Abstract

The absence of observed charmonium-like states with the exotic quantum numbers $J^{PC}=1^{-+}$ has prompted us to investigate the production rates of the $1^{-+}$ $D\bar D_1(2420)$ and $D^*\bar D_1(2420)$ hadronic molecules, which we refer to as $η_{c1}$ and $η_{c1}^{\prime}$, respectively, in electron-positron collisions. Assuming a hadronic molecular nature for the vector charmonium-like states $ψ(4360)$ and $ψ(4415)$, we evaluate the radiative decay widths of $ψ(4360)\toγη_{c1}$ and $ψ(4415)\toγη_{c1}^{\prime}$. Using these decay widths, we estimate the cross sections for producing $η_{c1}$ and $η_{c1}^{\prime}$ in electron-positron annihilations, as well as the event numbers at the planned Super $τ$-Charm Facility. Our results suggest that the ideal energy region for observing these states is around $4.44$ and $4.50$ GeV, just above the $D^* \bar D_1(2420)$ and $D^*\bar D_2^*(2460)$ thresholds, respectively.