Kaon-induced production of strange hidden-charm molecular pentaquarks \(P^\varLambda _{\psi s}\) from proton

Abstract

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