Production of $J/\psi p \bar p$ in electron-positron collisions

The discoveries of the hidden-charm $P_c$ pentaquarks by the LHCb Collaboration have been not confirmed by other experiments yet. It is desirable to investigate the feasibility of observing them in other experiments. We present an order-of-magnitude estimate of the cross section of the $e^+e^-\to J/\psi p \bar p$ process, where the hidden-charm pentaquarks may be searched for, and find it to be of $\mathcal{O}(4~\text{fb})$ when the $e^+e^-$ c.m. energy is around 6 GeV. The cross section for $e^+e^-\to P_c \bar p$ is then estimated to be $\lesssim \mathcal{O}(0.1~\text{pb})$. Thus, it is promising to search for $P_c$ at the future high-luminosity super tau-charm facilities with annual integrated luminosity about $1~ab^{-1}$. We also predict the branching fraction of $\Upsilon\to J/\psi p\bar p$ to be of $\mathcal{O}(2\times 10^{-6})$, which can be tested at $B$ factories.