Particle configurations in the $NN\bar K$ system

TL;DR

This paper models the $NNar K$ kaonic cluster using three-body Faddeev equations, considering mass differences and charge independence breaking, to analyze particle configurations and spectra with phenomenological potentials.

Contribution

It introduces a detailed three-body model for the $NNar K$ system, accounting for isospin dependence and configuration variations, providing new insights into its mass and energy spectra.

Findings

Mass and energy spectra for different configurations are calculated.

Uncertainties in mass and energy are evaluated.

An analogy to $NNN$ models for nuclei is proposed.

Abstract

Three-body $AAB$ model for the $NN{\bar K}(s_{NN}=0)$ kaonic cluster is considered based on the configuration space Faddeev equations. Within a single-channel approach, the difference between masses of nucleons and kaons and the charge independence breaking of nucleon-nucleon interaction are taken into consideration. We definite the particle configurations in the system according to the particle masses and pair potentials. There are two sets of the particle configurations, $ ppK^-$, $np \bar{K^0}$ and $nn {\bar K}^0$, $npK^-$, charged and neutral. The three-body calculations are performed by applying $NN$ and $N\bar K$ phenomenological isospin-dependent potentials. The mass and energy spectra related to the particle configurations are presented. We evaluate the mass and energy uncertainties for the $NN\bar K$ model. An analogy to $NNN$ model for the $^3$H and $^3$He nuclei is proposed.