$J/\psi \Lambda $ femtoscopy and the nature of $P_{\psi s}^{\Lambda}(4338)$

Over the past two decades, numerous exotic hadron states have been discovered, yet their underlying nature remains unclear. It is widely acknowledged that understanding hadron-hadron interactions is essential to unraveling their properties. Hadron spectroscopy is a powerful tool for this endeavor, providing rich experimental data that can shed light on exotic systems. Recently, the LHCb experiment analyzed the process $B^{-} \rightarrow J/\psi \Lambda \bar{p}$ and observed a narrow peak in the $J/\psi \Lambda$ invariant mass spectrum, regarding it as a candidate for a pentaquark. In this work, we extract the coupled-channel $J / \psi \Lambda-\bar{D} \Xi_c-\bar{D}_s \Lambda_c$ potential based on the $J/\psi \Lambda$ invariant mass spectrum. Our results indicate the existence of a bound state below the $\bar{D} \Xi_c$ mass threshold, corresponding to the experimentally measured state $P_{cs}(4338)$. Furthermore, we predict the scattering lengths and momentum correlation functions for the $J/\psi \Lambda$ and $\bar{D}\Xi_c$ channels, which serve as theoretical references for future femtoscopy experiments.