Improved Fixed Center Approximation of the Faddeev equations for the $\bar{K}NN$ system with S=0

TL;DR

This paper refines the Fixed Center Approximation for the $ar{K} NN$ system with S=0 by including charge exchange and intermediate state effects, resulting in a slightly less bound state with a width of about 50 MeV.

Contribution

It introduces an improved FCA method for the $ar{K} NN$ system that accounts for charge exchange and intermediate states, providing more accurate binding energy estimates.

Findings

System is bound by about 35 MeV.

Inclusion of charge exchange reduces binding by 6 MeV.

Explicit $\pi N \Sigma$ contribution decreases binding by 3 MeV.

Abstract

We extend the Fixed Center Approximation (FCA) to the Faddeev Equations for the $\bar{K} NN$ system with S=0, including the charge exchange mechanisms in the $\bar{K}$ rescattering which have been ignored in former works within the FCA. We obtain similar results to those found before, but the binding is reduced by 6 MeV. At the same time we also evaluate the explicit contribution the $\pi N \Sigma$ intermediate state in the three body system and find that it produces and additional small decrease in the binding of about 3 MeV. The system appears bound by about 35 MeV and the width omitting two body absorption, is about 50 MeV.