Pole determination of $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ and possible $P_{\psi s}^{\mathrm{\Lambda }}(4255)$ in $B^{-}\to J\mathrm{/}\psi \mathrm{\Lambda }\bar{p}$

First hidden-charm pentaquark candidate with strangeness, $P_{\psi s}^{\mathrm{\Lambda }}(4338)$, was recently discovered in $B^{-}\to J\mathrm{/}\psi \mathrm{\Lambda }\bar{p}$ by the LHCb Collaboration. $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ shows up as a bump at the ${\mathrm{\Xi }}_c\bar{D}$ threshold in the $J\mathrm{/}\psi \mathrm{\Lambda }$ invariant mass ($M_{J\mathrm{/}\psi \mathrm{\Lambda }}$) distribution. The $M_{J\mathrm{/}\psi \mathrm{\Lambda }}$ distribution also shows a large fluctuation at the ${\mathrm{\Lambda }}_c{\bar{D}}_s$ threshold, hinting the existence of a possible $P_{\psi s}^{\mathrm{\Lambda }}(4255)$. In this work, we determine the $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ and $P_{\psi s}^{\mathrm{\Lambda }}(4255)$ pole positions for the first time. For this purpose, we fit a $B^{-}\to J\mathrm{/}\psi \mathrm{\Lambda }\bar{p}$ model to the $M_{J\mathrm{/}\psi \mathrm{\Lambda }}$, $M_{J\mathrm{/}\psi \bar{p}}$, $M_{\mathrm{\Lambda }\bar{p}}$, and $\cos {\theta }_{K^{\ast }}$ distributions from the LHCb simultaneously; ${\chi }^2\mathrm{/}\mathrm{n}\mathrm{d}\mathrm{f}\sim 1.21$. Then we extract $P_{\psi s}^{\mathrm{\Lambda }}$ poles from a unitary ${\mathrm{\Xi }}_c\bar{D}$-${\mathrm{\Lambda }}_c{\bar{D}}_s$ coupled-channel scattering amplitude built in the model. In our default fit, the $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ pole is found at $(4338.2\pm 1.4)-(1.9\pm 0.5)i$ MeV while the $P_{\psi s}^{\mathrm{\Lambda }}(4255)$ pole at $4254.7\pm 0.4$ MeV. The $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ and $P_{\psi s}^{\mathrm{\Lambda }}(4255)$ are mostly ${\mathrm{\Xi }}_c\bar{D}$ bound and ${\mathrm{\Lambda }}_c{\bar{D}}_s$ virtual states, respectively. Through our analysis, the data disfavors a hypothesis of $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ as merely a kinematical effect. This pole determination, which is important in its own right, sets a primary basis to study the nature of the $P_{\psi s}^{\mathrm{\Lambda }}$ states.