Looking for bound states and resonances in the ${\eta }^{\prime }K\bar{K}$ 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.