Remarks on non-perturbative three--body dynamics and its application to the $KK\bar K$ system

TL;DR

This paper presents a formalism for relativistic three-body problems that maintains correct analytic structure and applies it to the $KKar K$ system, illustrating the formation of hadronic molecules like $a_0(980)$ and $f_0(980)$.

Contribution

It introduces a new formalism that balances covariance and analyticity in relativistic three-body dynamics, applied specifically to the $KKar K$ system.

Findings

Demonstrates the emergence of $a_0(980)$ and $f_0(980)$ as hadronic molecules.

Provides a framework for treating relativistic three-body problems with correct analytic structure.

Abstract

A formalism is discussed that allows for a straightforward treatment of the relativistic three-body problem while keeping the correct analytic structure. In particular it is demonstrated that sacrificing covariance for analyticity can be justified by the hierarchy of different contributions in the spirit of an effective field theory. For definiteness the formalism is applied to the $KK\bar K$ system allowing for the emergence of the $a_0(980)$ and the $f_0(980)$ as hadronic molecules. For simplicity all inelastic channels are switched off.