  Nonperturbative Wilson coefficients of the operator product expansion (OPE)
for the spin-0 glueball correlators are derived and analyzed. A systematic
treatment of the direct instanton contributions is given, based on realistic
instanton size distributions and renormalization at the operator scale. In the
pseudoscalar channel, topological charge screening is identified as an
additional source of (semi-) hard nonperturbative physics. The screening
contributions are shown to be vital for consistency with the anomalous axial
Ward identity, and previously encountered pathologies (positivity violations
and the disappearance of the 0^{-+} glueball signal) are traced to their
neglect. On the basis of the extended OPE, a comprehensive quantitative
analysis of eight Borel-moment sum rules in both spin-0 glueball channels is
then performed. The nonperturbative OPE coefficients turn out to be
indispensable for consistent sum rules and for their reconciliation with the
underlying low-energy theorems. The topological short-distance physics strongly
affects the sum rule results and reveals a rather diverse pattern of glueball
properties. New predictions for the spin-0 glueball masses and decay constants
and an estimate of the scalar glueball width are given, and several
implications for glueball structure and experimental glueball searches are
discussed.
