Virtual state and two-pole structure: $Ξ(1690)$ and $Ξ(1820)$ from BESIII data on $ψ(3686)\to K^-Λ\barΞ^+$

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 $\bar{K}\Lambda$, $\bar{K}\Sigma^{(*)}$, $\pi\Xi^{(*)}$, $\eta\Xi^{(*)}$, 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 $K\Sigma^*$ and $\pi\Xi^*$ 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.