On the pole content of coupled channels chiral approaches used for the $\bar{K}N$ system

TL;DR

This paper compares various chiral SU(3) models for antikaon-nucleon interactions, analyzing their pole structures and revealing differences in how they predict subthreshold amplitudes and the nature of the $ ext{Lambda}(1405)$ resonance.

Contribution

It provides a detailed comparison of chiral models, analyzing their pole contents and the origins of these poles through the zero coupling limit, offering new insights into the $ ext{Lambda}(1405)$ resonance formation.

Findings

Models predict significantly different subthreshold $K^{-}p$ and $K^{-}n$ amplitudes.

Pole structures vary notably among models, especially regarding the $ ext{Lambda}(1405)$.

Zero coupling limit analysis clarifies the origin of poles in different approaches.

Abstract

Several theoretical groups describe the antikaon-nucleon interaction at low energies within approaches based on the chiral SU(3) dynamics and including next-to-leading order contributions. We present a comparative analysis of the pertinent models and discuss in detail their pole contents. It is demonstrated that the approaches lead to very different predictions for the $K^{-}p$ amplitude extrapolated to subthreshold energies as well as for the $K^{-}n$ amplitude. The origin of the poles generated by the models is traced to the so-called zero coupling limit, in which the inter-channel couplings are switched off. This provides new insights into the pole contents of the various approaches. In particular, different concepts of forming the $\Lambda(1405)$ resonance are revealed and constraints related to the appearance of such poles in a given approach are discussed.