Determining the gluonic content of isoscalar mesons

We develop tools to determine the gluonic content of a resonance of known mass, width, and $J^{\mathrm{PC}}$ from its branching fraction in radiative quarkonium decays and production cross section in $\gamma \gamma$ collisions. We test the procedures by applying them to known $q\mathrm{q¯}$ mesons, then analyze four leading glueball candidates. We identify inconsistencies in data for $J/\psi \to \gamma f_0\mathrm{}\left(1500\right)\mathrm{}$ and $J/\psi \to \gamma f_J\mathrm{}\left(1710\right)\mathrm{}$ whose resolution can quantify their glueball status. When $\Gamma \left(f_0\mathrm{}\right(1500)\mathrm{}\to \gamma \gamma )$ and $\Gamma \left(f_J\mathrm{}\right(1710)\mathrm{}\to \gamma \gamma )$ are known, the $n\mathrm{n̄},s\overline{s},gg$ mixing angles can be determined. The enigmatic situation in the 1400–1500 MeV region of the isosinglet $0^{-+}$ sector is discussed.