Scalar glueballs: Constraints from the decays into $\eta$ or $\eta'$

Abstract

We study the mixing of the scalar glueball into the isosinglet mesons $f_0 (1370)$, $f_0(1500)$, and $f_0(1710)$ to describe the two-body decays to pseudoscalars. We use an effective Hamiltonian and employ the two-angle mixing scheme for $\eta$ and $\eta'$. In this framework, we analyse existing data and look forward to new data into $\eta$ and $\eta'$ channels. For now, the $f_0 (1710)$ has the largest glueball component and a sizable branching ratio into $\eta\eta'$, testable at BESIII.