Gaussian Sum-Rules, Scalar Gluonium, and Instantons

Abstract

Gaussian sum-rules relate a QCD prediction to a two-parameter Gaussian-weighted integral of a hadronic spectral function, providing a clear conceptual connection to quark-hadron duality. In contrast to Laplace sum-rules, the Gaussian sum-rules exhibit enhanced sensitivity to excited states of the hadronic spectral function. The formulation of Gaussian sum-rules and associated analysis techniques for extracting hadronic properties from the sum-rules are reviewed and applied to scalar gluonium. With the inclusion of instanton effects, the Gaussian sum-rule analysis results in a consistent scenario where the gluonic resonance strength is spread over a broad energy range below 1.6 GeV, and indicates the presence of gluonium content in more than one hadronic state.