Quasi-bound state in the $\bar{K}NNN$ system

TL;DR

This study investigates the quasi-bound state of the $ar{K}NNN$ system using four-body Faddeev equations, revealing binding energies and widths that depend on the interaction models, and providing insights into exotic antikaon-nucleon systems.

Contribution

The paper presents the first exact four-body calculations of the $ar{K}NNN$ system, analyzing the dependence of quasi-bound state properties on different two-body interaction models.

Findings

Binding energies range from 30.5 to 34.5 MeV with chiral potentials.

Binding energies range from 46.4 to 52.0 MeV with phenomenological potentials.

Four-body widths are approximately 38.2 to 50.9 MeV.

Abstract

The paper is devoted to the $\bar{K}NNN$ system, which is an exotic system consisting of an antikaon and three nucleons. Dynamically exact four-body Faddeev-type equations were solved and characteristics of the quasi-bound state in the system were evaluated. Three antikaon-nucleon and three nucleon-nucleon potentials were used, so the dependence of the four-body pole positions on the two-body interaction models was studied. The resulting binding energies $B^{\rm Chiral}_{K^-ppn} \sim 30.5 - 34.5$ MeV obtained with chirally motivated and $B^{\rm SIDD}_{K^-ppn} \sim 46.4 - 52.0$ MeV obtained with phenomenological antikaon-nucleon potentials are close to those obtained for the $K^- pp$ system with the same $\bar{K}N$ and $NN$ potentials, while the four-body widths $\Gamma_{K^- ppn} \sim 38.2 - 50.9$ MeV are smaller.