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We study the $\Xi(1620)$ resonance near the $\bar{K}\Lambda$ threshold in thelight of the recent experimental constraints. The Belle collaboration havefound a resonance peak of $\Xi(1620)$ slightly below the $\bar{K}^{0}\Lambda$threshold in the $\pi^{+}\Xi^{-}$ invariant mass spectrum, and the ALICEcollaboration have determined the $K^{-}\Lambda$ scattering length from themeasurement of the momentum correlation functions in the heavy ion collisions.Using the effective range expansion, we classify the nature of the pole of thenear-threshold eigenstate in terms of the scattering length, in the presence ofthe decay channel. It is shown that the quasibound state below the thresholdcan be described by only the scattering length, while the description of theresonance above the threshold requires the contribution from the effectiverange. Based on the chiral unitary approach, we construct a theoretical modelwhich generates the pole of $\Xi(1620)$ below the $\bar{K}\Lambda$ thresholdwith relatively narrow width, as reported by the Belle collaboration. It isquantitatively demonstrated that the spectrum of the $\Xi(1620)$ quasiboundstate is distorted by the effect of the nearby $\bar{K}\Lambda$ threshold. Wethen construct another model which reproduces the $K^{-}\Lambda$ scatteringlength by the ALICE collaboration. In this case, the eigenstate pole does notappear in the physically relevant Riemann sheets, and the spectrum shows a cuspstructure at the $\bar{K}\Lambda$ threshold. We finally examine thecompatibility of the value of the $\bar{K}\Lambda$ scattering length and thesubthreshold pole of $\Xi(1620)$ including the experimental uncertainties.

Analysis of $\Xi(1620)$ resonance and $\bar{K}\Lambda$ scattering length with chiral unitary approach