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Abstract

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

Topics & Concepts