Glueball-quarkonia content and decay of scalar-isoscalar mesons

Abstract

We investigate the hadronic two-body decay modes of the scalar-isoscalar ${f}_{0}(1370),$ ${f}_{0}(1500)$ and ${f}_{0}(1710)$ 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 ${f}_{0}(1500)$ and give predictions for the partial decay widths of ${f}_{0}(1370)$ and ${f}_{0}(1710),$ providing thus a sensitive test of the proposed mixing scheme.