# Possibility to study pentaquark states $P_{c}(4312), P_{c}(4440)$, and $P_{c}(4457)$ in $\gamma p\rightarrow J/\psi p$ reaction

## TL;DR

This study investigates the photoproduction of pentaquark states $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ via $ ext{ }\gamma p
ightarrow J/ ext{ extbackslash}psi p$ reactions, predicting observable peaks and providing guidance for experimental detection.

## Contribution

It introduces a theoretical approach to study pentaquark photoproduction, predicting observable signals and analyzing the roles of different exchange processes in the reaction.

## Key findings

- Cross sections consistent with experimental data assuming 3% branching ratio.
- Two peaks from $P_c(4440)$ and $P_c(4457)$ are observable with high experimental precision.
- Pomeron exchange dominates at forward angles, $s$-channel $P_c$ exchanges are significant near threshold.

## Abstract

Inspired by the observation of the pentaquark states $P_{c}(4312),P_{c}(4440)$ and $P_{c}(4457)$ at LHCb, photoproduction of these three $P_{c}$ states via the interaction $\gamma p\rightarrow J/\psi p$ is investigated in an effective Lagrangian approach. The $t$-channel Pomeron exchange diffractive process is considered as the main background for the $J/\psi $ photoproduction. The numerical results show that the theoretical cross section, which is calculated by assuming a branching ratio $Br[P_{c}\rightarrow J/\psi p]\simeq 3\%$, is consistent with the existing experimental data of the $ \gamma p\rightarrow J/\psi p$ process. With such a branching ratio, if experimental precision reaches 0.1 nb within a bin of 100 MeV for photon energy, two peaks are expected to be obviously observed in the $J/\psi $ photoproduction. To observe the two-peak structure from $P_{c}(4440)$ and $ P_{c}(4457)$, higher precision, about 0.1nb/10 MeV, is required to distinguish two close pentaquarks. If the physical branching ratio is larger, the requirement of experimental precision will be reduced. The differential cross sections for reaction $\gamma p\rightarrow J/\psi p$ are also present. It is found that the $t$-channel Pomeron exchange provides a sharp increase at extreme forward angles and gives a sizable contribution at most energy points, while the contributions from the $s$-channel $P_{c}$ exchanges play important roles at threshold energies. The experimental measurement of the $\gamma p\rightarrow J/\psi p$ process in the near-threshold energy region around $E_{\gamma }\simeq 9.4-10.5$ GeV is suggested, and is accessible at CEBAF@JLab and COMPASS.