  Topological charge screening in the QCD vacuum is found to provide crucial
nonperturbative contributions to the short-distance expansion of the
pseudoscalar (0^{-+}) glueball correlator. The screening contributions enter
the Wilson coefficients and are an indispensable complement to the direct
instanton contributions. They restore consistency with the anomalous axial Ward
identity and remedy several flaws in the 0^{-+} glueball sum rules caused by
direct instantons in the absence of screening (lack of resonance signals,
violation of the positivity bound and of the underlying low-energy theorem).
The impact of realistic instanton size distributions and the (gauge-invariant)
renormalization of the instanton contributions are also discussed. Predictions
for the 0^{-+} glueball mass and decay constant are presented.
