Eur. Phys. J. C (2025) 85: 492
https://doi.org/10.1140/epjc/s10052-025-14220-y

Regular Article - Theoretical Physics

Kaon-induced production of strange hidden-charm molecular pentaquarks $P_{\psi s}^{\Lambda }$ from proton

¹ School of Physics and Technology, Nanjing Normal University, 210097, Nanjing, China
² School of Microelectronics and Control Engineering, Changzhou University, 213164, Changzhou, China

^a junhe@njnu.edu.cn

Received: 7 March 2025
Accepted: 21 April 2025
Published online: 5 May 2025

Abstract

In this work, we investigate the kaon-induced production of strange hidden-charm pentaquark $P_{\psi s}^{\Lambda }$ states, including the $P_{\psi s}^{\Lambda }(4459)$ and $P_{\psi s}^{\Lambda }(4338)$ observed by the LHCb collaboration. Coupled-channel interactions involving the channels $\overline{K}N$, $\Xi _c^{(\ast )}{\overline{D}}^{(\ast )}$, ${\Xi }_c^{\prime }{\overline{D}}^{(\ast )}$, ${\Lambda }_c\overline{D}_s^{(\ast )}$, and $\Lambda J/\psi$ are studied using effective Lagrangians to describe these interactions. The potential kernels are constructed within the one-boson-exchange model and implemented into the quasipotential Bethe–Salpeter equation to calculate the scattering amplitudes. From these amplitudes, the partial-wave cross sections for kaon-induced production are predicted alongside the poles corresponding to strange hidden-charm molecular pentaquarks. The analysis reveals complex structures in the cross sections due to molecular states. A structure near the ${\Xi }_c\overline{D}$ threshold is predicted in the ${\Lambda }_c{\overline{D}}_s$ channel, corresponding to $P_{\psi s}^{\Lambda }(4338)$. Both molecular states near the ${\Xi }_c{\overline{D}}^{\ast }$ threshold with $J^P=1/2^{-}$ and $J^P=3/2^{-}$, associated with $P_{\psi s}^{\Lambda }(4459)$, produce peaks in the ${\Xi }_c^{\prime }\overline{D}$ channel, which vary significantly with the cutoff. Additionally, a molecular state with $J^P=3/2^{-}$ near the ${\Xi }_c^{\ast }\overline{D}$ threshold gives rise to a peak in the ${\Xi }_c{\overline{D}}^{\ast }$ channel. In the higher energy region, from 4350 to 4550 MeV, although the cross sections in the ${\Lambda }_c\overline{D}_s^{(\ast )}$ channels are substantial, no distinct structures corresponding to strange hidden-charm pentaquarks are identified, apart from some threshold-related cusps. These results provide valuable theoretical insights and serve as a foundation for future experimental studies of strange hidden-charm pentaquarks using kaon beams at J-PARC and JLab.