Dispersive analysis of glueball masses

We develop an inverse matrix method to solve for resonance masses from a dispersion relation obeyed by correlation function. Given the operator product expansion (OPE) of function in deep Euclidean region, we obtain nonperturbative spectral density, which exhibits structures naturally. The value gluon condensate OPE is fixed producing $\rho$ meson mass formalism, and then input into relations scalar, pseudoscalar tensor glueballs. It shown that low-energy limit scalar glueball, derived discriminates lattice estimate triple-gluon single-instanton estimate. densities glueballs reveal double-peak structure: peak located at lower implies $f_0(500)$ $f_0(980)$ ($\eta$ ad $\eta'$) mesons contain small amount gluonium components, should be included (pseudoscalar) mixing frameworks. Another determines glueball around 1.50 (1.75) GeV with broad width about 200 MeV, suggesting $f_0(1370)$, $f_0(1500)$ $f_0(1710)$ ($\eta(1760)$) are glue-rich states. also predict topological susceptability $\chi_t^{1/4}=75$-78 deduced zero momentum. Our analysis gives no solution may attributed insufficient information currently available OPE.