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

TL;DR

This paper investigates the nature of the $ ext{Xi}(1620)$ resonance near the $ar{K} ext{Lambda}$ threshold using a chiral unitary approach, reconciling experimental data from Belle and ALICE collaborations through theoretical modeling.

Contribution

It introduces a chiral unitary model that explains the $ ext{Xi}(1620)$ as a quasibound state and analyzes the impact of the $ar{K} ext{Lambda}$ threshold on its spectral features.

Findings

The $ ext{Xi}(1620)$ can be described as a quasibound state below threshold.

The spectrum is significantly affected by the nearby $ar{K} ext{Lambda}$ threshold.

The model reproduces experimental scattering lengths and pole structures.

Abstract

We study the $\Xi(1620)$ resonance near the $\bar{K}\Lambda$ threshold in the light of the recent experimental constraints. The Belle collaboration have found a resonance peak of $\Xi(1620)$ slightly below the $\bar{K}^{0}\Lambda$ threshold in the $\pi^{+}\Xi^{-}$ invariant mass spectrum, and the ALICE collaboration have determined the $K^{-}\Lambda$ scattering length from the measurement of the momentum correlation functions in the heavy ion collisions. Using the effective range expansion, we classify the nature of the pole of the near-threshold eigenstate in terms of the scattering length, in the presence of the decay channel. It is shown that the quasibound state below the threshold can be described by only the scattering length, while the description of the resonance above the threshold requires the contribution from the effective range. Based on the chiral unitary approach, we construct a theoretical model which generates the pole of $\Xi(1620)$ below the $\bar{K}\Lambda$ threshold with relatively narrow width, as reported by the Belle collaboration. It is quantitatively demonstrated that the spectrum of the $\Xi(1620)$ quasibound state is distorted by the effect of the nearby $\bar{K}\Lambda$ threshold. We then construct another model which reproduces the $K^{-}\Lambda$ scattering length by the ALICE collaboration. In this case, the eigenstate pole does not appear in the physically relevant Riemann sheets, and the spectrum shows a cusp structure at the $\bar{K}\Lambda$ threshold. We finally examine the compatibility of the value of the $\bar{K}\Lambda$ scattering length and the subthreshold pole of $\Xi(1620)$ including the experimental uncertainties.