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.

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Cited by in corpus (4)

• Study of the $DKK$ and $DK\bar{K}$ systems
• Possible bound states with hidden bottom from ${\bar{K}}^{(\ast )}{B}^{(\ast )}{\bar{B}}^{(\ast )}$ systems
• $J/\psi \to \gamma {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ and the structure observed around the $\bar{p}p$ threshold
• Different manifestations of S-matrix poles