Production potential of hidden-strange molecular pentaquarks through the ${\pi }^{-}p\to K^{\ast }\Sigma$ process

Abstract

In this study, applying the effective Lagrangian approach, we investigate the reaction ${\pi }^{-}p\to K^{\ast }\Sigma$ to explore the production of the hidden-strange molecular pentaquarks $P_{s\bar{s}}$. Specifically, we analyze two scenarios, where the $J^P$ quantum numbers of $P_{s\bar{s}}$ are $3/2^{-}$ and $1/2^{-}$. Our results show that the contribution from $s$-channel $P_{s\bar{s}}$ exchange dominates the total cross section, surpassing those from $t$-channel $K^{(\ast )}$ exchange and $u$-channel $\Sigma$ exchange. Additionally, we present predictions for the differential cross section of the ${\pi }^{-}p\to K^{\ast }\Sigma$ process. Finally, we extend the 2-to-2 scattering process to the 2-to-3 Dalitz process and provide theoretical predictions for this scenario. Our findings suggest that the cross section for the ${\pi }^{-}p\to K^{\ast }\Sigma \to K^{+}{\pi }^{-}{\Sigma }^0$ process can reach several tens of $\mu b$ near the threshold, making it highly favorable for experimental measurement. However, the current scarcity of experimental data for the ${\pi }^{-}p\to K^{\ast }\Sigma$ reaction at threshold energy limits our ability to determine the properties of the hidden-strange molecular pentaquarks $P_{s\bar{s}}$ and related physical quantities. Therefore, additional experimental measurements of the ${\pi }^{-}p\to K^{\ast }\Sigma$ reaction at threshold are strongly encouraged, and correlation studies could be pursued at facilities such as J-PARC, AMBER, and upcoming HIKE and HIAF meson beam experiments.

Comments: 12 Pages, 17 Figures, 6 Tables