Analysis of the Ξ(1620) resonance and (K)over-barΛ scattering length with a chiral unitary approach

We study the Xi(1620) resonance near the (K) over bar Lambda threshold in the light of recent experimental constraints. The Belle Collaboration have found a resonance peak of Xi(1620) slightly below the (K) over bar (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 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 (K) over bar 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 (K) over bar 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 sheet, and the spectrum shows a cusp structure at the (K) over bar Lambda threshold. We finally examine the compatibility of the value of the (K) over bar Lambda scattering length and the subthreshold pole of Xi(1620) including the experimental uncertainties.