Kaon-induced production of strange hidden-charm molecular pentaquarks $P^Λ_{ψs}$ from proton

In this work, we investigate the kaon-induced production of strange hidden-charm pentaquark $P^Λ_{ψs}$ states, including the $P^Λ_{ψs}(4459)$ and $P^Λ_{ψs}(4338)$ observed by the LHCb collaboration. Coupled-channel interactions involving the channels $\bar{K}N$, $Ξ_c^{(*)}\bar{D}^{(*)}$, $Ξ'_c\bar{D}^{(*)}$, $Λ_c\bar{D}_s^{(*)}$, and $ΛJ/ψ$ 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 $Ξ_c\bar{D}$ threshold is predicted in the $Λ_c\bar{D}_s$ channel, corresponding to $P^Λ_{ψs}(4338)$. Both molecular states near the $Ξ_c\bar{D}^*$ threshold with $J^P = 1/2^-$ and $J^P = 3/2^-$, associated with $P^Λ_{ψs}(4459)$, produce peaks in the $Ξ'_c\bar{D}$ channel, which vary significantly with the cutoff. Additionally, a molecular state with $J^P = 3/2^-$ near the $Ξ_c^*\bar{D}$ threshold gives rise to a peak in the $Ξ_c\bar{D}^*$ channel. In the higher energy region, from 4350 to 4550 MeV, although the cross sections in the $Λ_c\bar{D}_s^{(*)}$ 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.