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

Abstract

In the present work, we propose to investigate the productions of $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ in the $e^{+}{e}^{-}\to p\bar{p}J/\psi$ process by utilizing an effective Lagrangian approach, where $P_c(4312)$ is considered as ${\Sigma }_c\bar{D}$ molecular state with $J^P=1/2^{-}$, while $P_c(4440)$ and $P_c(4457)$ are considered as ${\Sigma }_c{\bar{D}}^{\ast }$ molecular states with $J^P=1/2^{-}$ and $J^P=3/2^{-}$, respectively. 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 ($27.8_{-17.9}^{+42.2}$) fb, ($38.7_{-25.1}^{+58.6}$) fb, and ($1.44_{-0.93}^{+2.18}$) fb at $\sqrt{s}=6$ GeV, respectively, where the central values are estimated with ${\Lambda }_r=2.5$ GeV, and the uncertainties are resulted from the variations of ${\Lambda }_r$ from 2.0 to 3.0 GeV. Considering that the $P_c$ states can decay into $J/\psi p$, we estimate the cross sections for $e^{+}{e}^{-}\to p\bar{p}J/\psi$ and the differential cross sections depending on the $J/\psi p$ invariant mass. At $\sqrt{s}=6$ GeV, the cross sections for $e^{+}{e}^{-}\to p\bar{p}J/\psi$ are estimated to be ($14.7_{-9.50}^{+22.2}$) fb. Moreover, our estimations indicate that the cross section resulted from the $P_c(4440)$ and ${\bar{P}}_c(4440)$ intermediate states is dominant. In the $J/\psi p$ invariant mass spectrum, our estimations reveal that the peak structure between 4.42 and 4.46 GeV primarily originates from $P_c(4440)$.