# Possibility to study the pentaquark states ${P}_{c}\left(4312\right)$, ${P}_{c}\left(4440\right)$, and ${P}_{c}\left(4457\right)$ in the reaction $\gamma p\to J/\psi p$

Wang, Xiao-Yun (Department of physics, Lanzhou University of Technology, Lanzhou 730050, China) ; Chen, Xu-Rong (Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China) ; He, Jun (Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu 210097, China)

11 June 2019

Abstract: Inspired by the observation of the pentaquark states ${P}_{c}\left(4312\right)$, ${P}_{c}\left(4440\right)$, and ${P}_{c}\left(4457\right)$ at LHCb, photoproduction of these three ${P}_{c}$ states via the interaction $\gamma p\to J/\psi p$ 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 $\mathrm{Br}\left[{P}_{c}\to J/\psi p\right]\simeq 3%$, is consistent with the existing experimental data of the $\gamma p\to J/\psi p$ 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 ${P}_{c}\left(4440\right)$ and ${P}_{c}\left(4457\right)$, higher precision, about $0.1\text{}\text{}\mathrm{nb}/10\text{}\text{}\mathrm{MeV}$, 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 $\gamma p\to J/\psi p$ 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 $\gamma p\to J/\psi p$ process in the near-threshold energy region around ${E}_{\gamma }\simeq 9.4–10.5\text{}\text{}\mathrm{GeV}$ is suggested and is accessible at CEBAF@JLab and COMPASS.

Published in: Physical Review D 99 (2019)
DOI: 10.1103/PhysRevD.99.114007