We investigate the possibility of studying the strange hidden-charm pentaquark state $P_{ cs}(4459)$ by photon-induced reactions on a proton target in an effective Lagrangian approach. The production process is described by the $t$-channel $K^{ -}$ exchange, the $u$-channel $\Lambda$ exchange, the contract term, and the $s$- channel nucleon pole. Our theoretical approach is based on the assumption that $P_{ cs}(4459)$ with $J^{ P}=1/2^{ -}$ or $J^{ P}=3/2^{ -}$ can be interpreted as a molecule composed of $\bar{ D}^{ *}\Xi_c$. Using the coupling constants of the $P^{ J^P}_{ cs}$ to $\gamma{ }\Lambda$ and $K^{ -}p$ channels obtained from molecule picture of the $P^{ J^{ P}}_{ cs}(4459)$, the total cross-sections of the process $\gamma{ }p\to{ }P^{ J^P}_{ cs}K^{ +}$ is evaluated. Our calculation indicates that the cross-section for $\gamma{ }p\to{ }P^{ 1/2^{ -}}_{ cs}K^{ +}$ and $\gamma{ }p\to{ }P^{ 3/2^{ -}}_{ cs}K^{ +}$ are of the order of 10.0 pb and 5.0 pb, respectively. In addition, we compute the cross-section by assuming $P_{ cs}(4459)$ as a compact pentaquark and find it is quite different from the results of $\bar{ D}^{ *}\Xi_c$ molecule. Those results can be measured in future experiments, such as the Electron-Ion Collider in China and the United States. And can be used to test the nature of the $P_{ cs}$.
Categories: hep-ph nucl-th
