Virtual state and two-pole structure: $\Xi (1690)$ and $\Xi (1820)$ from BESIII data on $\psi (3686)\to K^{-}\Lambda {\bar{\Xi }}^{+}$

Abstract

We investigate the nature of the $\Xi (1690)$ and $\Xi (1820)$ resonances by analyzing the recent BESIII data on $\psi (3686)\to K^{-}\Lambda {\bar{\Xi }}^{+}$ within a coupled-channel rescattering framework. The calculation includes the channels $\bar{K}\Lambda$, $\bar{K}{\Sigma }^{(\ast )}$, $\pi {\Xi }^{(\ast )}$, $\eta {\Xi }^{(\ast )}$, and $K\Omega$. A direct fit to the data reveals that the $\Xi (1690)$ is best described as a virtual state located right below the $\bar{K}\Sigma$ threshold, a feature that naturally explains its very sharp peak observed in the $K^{-}\Lambda$ invariant mass spectrum. In contrast, the $\Xi (1820)$ exhibits a two-pole structure originating mainly from the coupled contributions of the $K{\Sigma }^{\ast }$ and $\pi {\Xi }^{\ast }$ channels, showing a two-pole pattern similar to that of the well-known $\Lambda (1405)$ and accounting for the unexpectedly broad width measured by BESIII. These findings provide new insights into the dynamical generation of hyperon resonances and highlight the importance of high-precision data from charmonium decays.

Comments: 13 pages, 6 figures