Production of 1−+ exotic charmonium-like states in electron-positron collisions

The absence of observed charmonium-like states with the exotic quantum numbers J P C = 1 − + has prompted us to investigate the production rates of the 1 − + D D ‾ 1 ( 2420 ) and D ⁎ D ‾ 1 ( 2420 ) hadronic molecules, which we refer to as η c 1 and η c 1 ′ , 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 ) → γ η c 1 and ψ ( 4415 ) → γ η c 1 ′ . Using these decay widths, we estimate the cross sections for producing η c 1 and η c 1 ′ 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 ⁎ D ‾ 1 ( 2420 ) and D ⁎ D ‾ 2 ⁎ ( 2460 ) thresholds, respectively.