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

Abstract

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

Comments: 8 pages, 5 figures, 3 tables; (v2) statistical errors of pole values corrected; (v3) efficiency-corrected and background-subtracted data are analyzed; a figure of Dalitz plot distribution added; (v4) published version