Deeply quasi-bound state in single- and double-$\bar{K}$ nuclear clusters

TL;DR

This paper presents new calculations of the quasi-bound state energies in kaonic nuclear clusters using four-body Faddeev equations, exploring different interaction models and their effects on binding energies and widths.

Contribution

It introduces a novel application of non-relativistic four-body Faddeev-type equations with Hilbert-Schmidt expansion to study kaonic clusters, analyzing model dependencies.

Findings

Binding energy of the $K^{-}K^{-}pp$ state is approximately 80-94 MeV.

Width varies from 5-8 MeV for two-pole models to 24-31 MeV for one-pole models.

Model choice significantly affects the predicted properties of the quasi-bound state.

Abstract

New calculations of the quasi-bound state positions in $K^{-}K^{-}pp$ kaonic nuclear cluster are performed using non-relativistic four-body Faddeev-type equations in AGS form. The corresponding separable approximation for the integral kernels in the three- and four-body kaonic clusters is obtained by using the Hilbert-Schmidt expansion procedure. Different phenomenological models of $\bar{K}N-\pi\Sigma$ potentials with one- and two-pole structure of $\Lambda$(1405) resonance and separable potential models for $\bar{K}$-$\bar{K}$ and nucleon-nucleon interactions, are used. The dependence of the resulting four-body binding energy on models of $\bar{K}N-\pi\Sigma$ interaction is investigated. We obtained the binding energy of the $K^{-}K^{-}pp$ quasi-bound state $\sim$ 80-94 MeV with the phenomenological $\bar{K}N$ potentials. The width is about $\sim$ 5-8 MeV for the two-pole models of the interaction, while the one-pole potentials give $\sim$ 24-31 MeV width.