Glueball-quarkonia content and decay of scalar-isoscalar mesons

We investigate the hadronic two-body decay modes of the scalar-isoscalar $f_0\mathrm{}\left(1370\right),$ $f_0\mathrm{}\left(1500\right)\mathrm{}$ and $f_0\mathrm{}\left(1710\right)\mathrm{}$ states as resulting from the mixture of the lowest lying scalar glueball with the isoscalar states of the ground state ${}^3{P}_0$ $Q\overline{Q}$ nonet. In the decay analysis we take into account the direct coupling of the quarkonia and glueball components of the $f_0$ states to the quarkonia components of the two-meson final state with the decay dynamics inspired by the strong coupling limit of QCD. We calculate partial decay widths for the $f_0$ states in the proposed three-state mixing schemes and discuss their compatibility with the observed decay features. Finally, we determine the glueball-quarkonia content of the $f_0$ states from a detailed fit to experimental decay data of $f_0\mathrm{}\left(1500\right)\mathrm{}$ and give predictions for the partial decay widths of $f_0\mathrm{}\left(1370\right)\mathrm{}$ and $f_0\mathrm{}\left(1710\right),$ providing thus a sensitive test of the proposed mixing scheme.