Scalar glueballs: Constraints from the decays into $\eta$ or ${\eta }^{\prime }$

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 ${\eta }^{\prime }$. In this framework, we analyse existing data and look forward to new data into $\eta$ and ${\eta }^{\prime }$ channels. For now, the $f_0(1710)$ has the largest glueball component and a sizable branching ratio into $\eta {\eta }^{\prime }$, testable at BESIII.

Comments: 7 pages, 1 figure. Included error bars from fit and added references. Matches PRD version