Production of $P^\Lambda_{\psi s}(4338)$ from $\Xi_b$ decay

In the present work, we investigate the production of the newly observed $P^\Lambda_{\psi s}(4338)$ state in $\Xi_b^-$ decay, where the $P^\Lambda_{\psi s}(4338)$ is assigned as a $\Xi_c \bar{D}$ molecular state. By using an effective Lagrangian approach, we evaluate the branching fractions of $\Xi_b^-\rightarrow P^\Lambda_{\psi s}(4338)K^-$ via the triangle loop mechanism. The branching fractions of $\Xi_b^-\rightarrow P^\Lambda_{\psi s}(4338)K^-$ are in the order of $10^{-4}$; the result is compared with our previous work of $\Xi_b^-\rightarrow P^\Lambda_{\psi s}(4459)K^-$. We also predict the ratio of $P^\Lambda_{\psi s}(4459)$ and $P^\Lambda_{\psi s}(4338)$ productions in the decay $\Xi_b^- \to P^\Lambda_{\psi s} K^- \to J/\psi \Lambda K^-$. The predicted branching fractions and their ratios could be tested experimentally, which may be helpful for understanding the molecular picture of $P^\Lambda_{\psi s}(4338)$ as well as other hidden-charm pentaquark states with strangeness. Moreover, the experimental potential of observing $P^\Lambda_{\psi s}(4338)$ in the $\Xi^-_b\to K^- J/\psi \Lambda$ is discussed.