Looking for bound states and resonances in the $\eta^\prime K\bar K$ system

TL;DR

This study investigates the possibility of bound states or resonances in the $ ext{eta}^ ext{prime} K ar{K}$ system using Faddeev equations, but finds no evidence of such states.

Contribution

It applies Faddeev equations with Bethe-Salpeter input to analyze three-body interactions involving $ ext{eta}^ ext{prime}$ and kaons, exploring potential bound states.

Findings

No three-body bound states or resonances detected.

Uses coupled channel Bethe-Salpeter formalism for two-body interactions.

Provides theoretical constraints on $ ext{eta}^ ext{prime} K ar{K}$ system.

Abstract

Motivated by the continuous experimental investigations of $X(1835)$ in three-body decay channels like $\eta^\prime \pi^+ \pi^-$, we investigate the $\eta^\prime K \bar K$ system with the aim of searching for bound states and/or resonances when the dynamics involved in the $K\bar K$ subsystem can form the resonances: $f_0(980)$ in isospin 0 or $a_0(980)$ in isospin 1. For this, we solve the Faddeev equations for the three-body system. The input two-body $t$-matrices are obtained by solving Bethe-Salpeter equations in a coupled channel formalism. As a result, no signal of a three-body bound state or resonance is found.