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

High Energy Physics - Phenomenology