Scalar glueball mixing and decay

We provide the first explanation of the counter-intuitive scalar glueball couplings to pseudoscalar mesons found in lattice QCD and predict hitherto uncalculated decay modes. Significant $a_1\pi$ and $\left(\pi \pi {)}_S\right(\pi \pi {)}_S$ couplings are found. We demonstrate the equivalence of linear and quadratic mass matrices for glueball-quarkonium mixing. The equivalence of formalisms which deal with a glueball-quarkonium basis and only a quarkonium basis is demonstrated. We show that the $f_0\mathrm{}\left(1500\right)\mathrm{}$ is not the heaviest state arising from glueball-quarkonium mixing for a glueball mass consistent with lattice QCD. The masses and couplings of scalar mesons, as well as their valence content, are calculated.