Understanding $P_{cs}(4459)$ as a hadronic molecule in the ${\mathrm{\Xi }}_b^{-}\to J\mathrm{/}\psi \mathrm{\Lambda }{K}^{-}$ decay

Recently, the LHCb Collaboration reported on the evidence for a hidden charm pentaquark state with strangeness, i.e., $P_{cs}(4459)$, in the $J\mathrm{/}\psi \mathrm{\Lambda }$ invariant mass distribution of the ${\mathrm{\Xi }}_b^{-}\to J\mathrm{/}\psi \mathrm{\Lambda }{K}^{-}$ decay. In this work, assuming that $P_{cs}(4459)$ is a ${\bar{D}}^{\ast }{\mathrm{\Xi }}_c$ molecular state, we study this decay via triangle diagrams $\Xi_b\rightarrow \bar{D}s^{()}\Xi_c\to (\bar{D}^{()}\bar{K})\Xi_c\to P{cs} \bar{K}\to (J/\psi\Lambda) \bar{K}$. Our study shows that the production yield of a spin 3/2 ${\bar{D}}^{\ast }{\mathrm{\Xi }}_c$ state is approximately one order of magnitude larger than that of a spin $1\mathrm{/}2$ state due to the interference of ${\bar{D}}_s{\mathrm{\Xi }}_c$ and ${\bar{D}}_s^{\ast }{\mathrm{\Xi }}_c$ intermediate states. We obtain a model independent constraint on the product of couplings $g_{P_{cs}{\bar{D}}^{\ast }{\mathrm{\Xi }}_c}$ and $g_{P_{cs}J\mathrm{/}\psi \mathrm{\Lambda }}$. With the predictions of two particular molecular models as inputs, we calculate the branching ratio of $\Xi_b^-\to (P_{cs}\to)J/\psi\Lambda K^- $ and compare it with the experimental measurement. We further predict the lineshape of this decay which could be useful to future experimental studies.