$P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ productions in $e^{+}{e}^{-}$ collisions

In the present work, we propose to investigate the productions of $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ in the $e^{+}{e}^{-}\to p\bar{p}J\mathrm{/}\psi$ process. By using an effective Lagrangian approach, we estimate the cross section for the processes under consideration. For the $e^{+}{e}^{-}\to \bar{p}{P}_c(4312)$, $e^{+}{e}^{-}\to \bar{p}{P}_c(4440)$, and $e^{+}{e}^{-}\to \bar{p}{P}_c(4457)$ processes, the cross sections are evaluated to be ($46.6_{-34.5}^{+88.4}$) fb, ($57.4_{-42.5}^{+109}$) fb, and ($55.1_{-40.8}^{+105}$) fb at $\sqrt{s}=6$ GeV, respectively, where the central values are estimated with ${\mathrm{\Lambda }}_r=3.0$ GeV, and the uncertainties are resulted from the variations of ${\mathrm{\Lambda }}_r$ from 2.5 to 3.5 GeV. Considering that the $P_c$ states can decay into $J\mathrm{/}\psi p$, we estimate the cross sections for $e^{+}{e}^{-}\to p\bar{p}J\mathrm{/}\psi$ and the differential cross sections depending on the $J\mathrm{/}\psi p$ invariant mass. At $\sqrt{s}=6$ GeV, the cross sections for $e^{+}{e}^{-}\to p\bar{p}J\mathrm{/}\psi$ are estimated to be ($34.6_{-26.0}^{+68.0}$) fb. Moreover, our estimations indicate that the cross section resulted from the $P_c(4457)$ and ${\bar{P}}_c(4457)$ intermediate states is dominant. In the $J\mathrm{/}\psi p$ invariant mass spectrum, a splitting signal can be observed around 4.45 GeV, with the two peaks corresponding to $P_c(4440)$ and $P_c(4457)$.