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Instanton and Higher-Loop Perturbative Contributions to the QCD Sum-Rule Analysis of Pseudoscalar Gluonium

Instanton effects and three-loop perturbative contributions are incorporated into QCD sum-rule analyses of pseudoscalar ($J^{PC}=0^{-+}$) gluonium. Gaussian sum-rules are shown to be superior to Laplace sum-rules in optimized predictions for pseudoscalar gluonium states in the presence of instanton contributions. The Gaussian sum-rule analysis yields a pseudoscalar mass of $(2.65\pm 0.33) GeV$ and width bounded by $Γ<530 MeV$. The Laplace sum-rules provide corroborating evidence in support of the $\approx 2.7 GeV$ mass scale.