$\bar{K}NN$ Absorption within the Framework of the Fixed Center Approximation to Faddeev equations

TL;DR

This paper develops a nonperturbative method using the Fixed Center Approximation to Faddeev equations to evaluate the $ar{K}$ absorption width in the $ar{K}NN$ system, revealing a significant increase in the width due to absorption channels.

Contribution

It introduces a full nonperturbative calculation of $ar{K}$ absorption in the $ar{K}NN$ system using the Fixed Center Approximation, improving upon previous qualitative and perturbative approaches.

Findings

Absorption width increases by about 30 MeV due to channels.

Total width of the states reaches approximately 80 MeV.

Rescattering effects significantly impact the resonance properties.

Abstract

We present a method to evaluate the $\bar{K}$ absorption width in the bound $\bar{K}NN$ system. Most calculations of this system ignore this channel and only consider the $\bar{K}N \rightarrow \pi \Sigma$ conversion. Other works make a qualitative calculation using perturbative methods. Since the $ \Lambda(1405) $ resonance is playing a role in the process, the same resonance is changed by the presence of the absorption channels and we find that a full nonperturbative calculation is called for, which we present here. We employ the Fixed Center Approximation to Faddeev equations to account for $\bar{K}$ rescattering on the $ (NN) $ cluster and we find that the width of the states found previously for $ S=0 $ and $ S=1 $ increases by about 30 MeV due to the $\bar{K}NN$ absorption, to a total width of about 80 MeV.