Searching for strange hidden-charm pentaquark state $P_{cs}(4459)$ in ${\hat{I}}^{3}p\to K^{+}{P}_{cs}(4459)$ reaction

Abstract

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 $\hat{I}›$ 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 ${\bar{D}}^{\ast }\hat{I}{ž}_c$. Using the coupling constants of the $P_{cs}^{J^P}$ to ${\hat{I}}^3\hat{I}›$ and $K^{-}p$ channels obtained from molecule picture of the $P_{cs}^{J^P}(4459)$, the total cross-sections of the process ${\hat{I}}^{3}p\to P_{cs}^{J^P}{K}^{+}$ is evaluated. Our calculation indicates that the cross-section for ${\hat{I}}^{3}p\to P_{cs}^{1/2^{-}}{K}^{+}$ and ${\hat{I}}^{3}p\to P_{cs}^{3/2^{-}}{K}^{+}$ 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 ${\bar{D}}^{\ast }\hat{I}{ž}_c$ 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 $P_{cs}$.

arXiv admin note: text overlap with arXiv:2107.03773