$P_{c}(4312)$, $P_{c}(4440)$, 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 $e^{+} e^{-} \rightarrow p \bar{p} J/\psi$ 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 $e^{+} e^{-} \rightarrow \bar{p} P_{c}(4312)$, $e^{+} e^{-} \rightarrow \bar{p} P_{c}(4440)$, and $e^{+} e^{-} \rightarrow \bar{p} P_{c}(4457)$ processes, the cross sections are evaluated to be ($27.8^{+42.2}_{-17.9}$) fb, ($38.7^{+58.6}_{-25.1}$) fb, and ($1.44^{+2.18}_{-0.93}$) 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 $e^{+} e^{-} \rightarrow p \bar{p} J/\psi$ and the differential cross sections depending on the $J/\psi p$ invariant mass. At $\sqrt{s}=6$ GeV, the cross sections for $e^{+} e^{-} \rightarrow p \bar{p} J/\psi$ are estimated to be ($14.7^{+22.2}_{-9.50}$) 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 $P_{c}(4440)$.