Three-body antikaon-nucleon systems

TL;DR

This review summarizes precise three-body calculations of antikaon-nucleon systems, exploring bound states, scattering processes, and the dependence on two-body interactions using Faddeev equations.

Contribution

It provides a comprehensive overview of exact three-body results in antikaon-nucleon physics, highlighting the role of different potentials and the accuracy of approximate methods.

Findings

Identification of quasi-bound states in $K^- pp$ and $K^- K^- p$ systems

Analysis of near-threshold $K^- d$ scattering and scattering lengths

Assessment of the accuracy of approximate calculation methods

Abstract

The paper contains a review of the exact or accurate results achieved in the field of the three-body antikaon-nucleon physics. Different states and processes in $\bar{K}NN$ and $\bar{K}\bar{K}N$ systems are considered. In particular, quasi-bound states in $K^- pp$ and $K^- K^- p$ systems were investigated together with antikaonic deuterium atom. Near-threshold scattering of antikaons on deuteron, including the $K^- d$ scattering length, and applications of the scattering amplitudes are also discussed. All exact three-body results were calculated using some form of Faddeev equations. Different versions of $\bar{K}N$, $\Sigma N$, $\bar{K}\bar{K}$, and $NN$ potentials, specially constructed for the calculations, allowed investigation of the dependence of the three-body results on the two-body input. Special attention is paid to the antikaon-nucleon interaction, being the most important for the three-body systems. Approximate calculations, performed additionally to the exact ones, demonstrate accuracy of the commonly used approaches.