Kaon-Nucleon systems and their interactions in the Skyrme model

TL;DR

This paper investigates kaon-nucleon interactions using the Skyrme model, revealing a loosely bound state consistent with the observed $ar{K}N$ state and characterizing the interaction as attractive at medium range and repulsive at short range.

Contribution

It introduces a modified bound state approach within the Skyrme model to study weakly interacting kaon-nucleon systems, including the $ar{K}N$ bound state like $ ext{Lambda}(1405)$.

Findings

Found a $ar{K}N$ bound state with about 10 MeV binding energy.

Identified the $ar{K}N$ interaction as attractive in the middle range and repulsive at short range.

Abstract

We study kaon-nucleon systems in the Skyrme model in a method based on the bound state approach of Callan-Klebanov but with the kaon around the physical nucleon of the rotating hedgehog. This corresponds to the variation after projection, reversing the order of semiclassical quantization of $1/N_c$ expansion. The method, however, is considered to be suited to the study of weakly interacting kaon-nucleon systems including loosely $\bar{K}N$ bound states such as $\Lambda(1405)$. We have found a bound state with binding energy of order ten MeV, consistent with the observed state. We also discuss the $\bar{K}N$ interaction and find that it consists of an attraction in the middle range and a repulsion in the short range.