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

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 $\bar{K}N$, ${\Xi }_c^{(\ast )}{\bar{D}}^{(\ast )}$, ${\Xi }_c^{\prime }{\bar{D}}^{(\ast )}$, ${\Lambda }_c{\bar{D}}_s^{(\ast )}$, 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 ${\Xi }_c\bar{D}$ threshold is predicted in the ${\Lambda }_c{\bar{D}}_s$ channel, corresponding to $P_{\psi s}^{\Lambda }(4338)$. Both molecular states near the ${\Xi }_c{\bar{D}}^{\ast }$ threshold with $J^P=1/2^{-}$ and $J^P=3/2^{-}$, associated with $P_{\psi s}^{\Lambda }(4459)$, produce peaks in the ${\Xi }_c^{\prime }\bar{D}$ channel, which vary significantly with the cutoff. Additionally, a molecular state with $J^P=3/2^{-}$ near the ${\Xi }_c^{\ast }\bar{D}$ threshold gives rise to a peak in the ${\Xi }_c{\bar{D}}^{\ast }$ channel. In the higher energy region, from 4350 to 4550 MeV, although the cross sections in the ${\Lambda }_c{\bar{D}}_s^{(\ast )}$ 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.

9 pages, 4 figures

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