One- versus two-pole $\bar{K}N - \pi \Sigma$ potential: $K^- d$ scattering length

TL;DR

This study examines how different models of the $ar{K}N$ interaction, with one or two poles for the $ ext{Lambda}(1405)$ resonance, influence the $K^- d$ scattering length using coupled-channel Faddeev equations.

Contribution

The paper introduces new $ar{K}N - \pi \Sigma$ potentials that fit experimental data and explores their impact on the $K^- d$ scattering length within a coupled-channel framework.

Findings

Two-pole models significantly affect the scattering length values.

New potentials successfully reproduce experimental data.

Comparison with approximations highlights their limitations.

Abstract

We investigated the dependence of the $K^- d$ scattering length on models of $\bar{K}N$ interaction with one or two poles for $\Lambda(1405)$ resonance. The $\bar{K}NN - \pi \Sigma N$ system is described by coupled-channel Faddeev equations in AGS form. Our new two-body $\bar{K}N - \pi \Sigma$ potentials reproduce all existing experimental data on $K^- p$ scattering and kaonic hydrogen atom characteristics. New models of $\Sigma N - \Lambda N$ interaction were also constructed. Comparison with several approximations, usually used for scattering length calculations, was performed.