Fully coupled-channel study of $K^-pp$ resonance in a chiral SU(3)-based $\bar{K}N$ potential

TL;DR

This study investigates the $K^-pp$ resonance as a coupled-channel three-body system using a chiral SU(3)-based potential and a complex scaling method, revealing a shallow bound state with specific energy and width.

Contribution

It introduces a self-consistent approach with an averaged threshold prescription to accurately analyze the $K^-pp$ resonance using a fully coupled-channel complex scaling method.

Findings

$K^-pp$ is a shallow bound state with 14-50 MeV binding energy.

Resonance width is estimated at 8-19 MeV.

Method successfully finds self-consistent solutions for the resonance.

Abstract

We have investigated the most essential kaonic nucleus "$K^-pp$" as a resonant state of the $\bar{K}NN$-$\pi\Sigma N$-$\pi\Lambda N$ coupled channel system using a chiral SU(3)-based $\bar{K}N$ potential. We treat the "$K^-pp$" resonance adequately with a fully coupled-channel complex scaling method (full ccCSM). Self-consistency needs to be considered for the energy dependence of the chiral SU(3)-based potential. In the present study, we propose a simple prescription for the treatment of self-consistency, considering the {\it averaged threshold} and {\it averaged binding energy of mesons}. With this prescription, we have successfully found the self-consistent solutions of the "$K^-pp$" three-body resonance. The results indicate that the "$K^-pp$" system is bound rather shallowly. In particular, when the potential parameters are constrained with the latest $\bar{K}N$ scattering length, the binding energy and half of the mesonic decay width are obtained as $14-50$ MeV and $8-19$ MeV, respectively.