A Gaussian Sum-Rules Analysis of Scalar Glueballs

Although marginally more complicated than the traditional Laplace sum-rules, Gaussian sum-rules have the advantage of being able to probe excited and ground states with similar sensitivity. Gaussian sum-rule analysis techniques are applied to the problematic scalar glueball channel to determine masses, widths and relative resonance strengths of low-lying scalar glueball states contributing to the hadronic spectral function. A key feature of our analysis is the inclusion of instanton contributions to the scalar gluonic correlation function. Compared with the next-to-leading Gaussian sum-rule, the analysis of the lowest-weighted sum-rule (which contains a large scale-independent contribution from the low energy theorem) is shown to be unreliable because of instability under QCD uncertainties. The analysis of the next-to-leading sum-rule demonstrates that a single narrow resonance does not provide an adequate description of the hadronic spectral function. However, phenomenological models which distribute resonance strength over a broad region, such as a very wide resonance or well-separated narrow resonances, lead to excellent agreement between the theoretical prediction and phenomenological models. Our results indicate that the resonance contributions to the hadronic spectral function are spread over the region 1–1.6 GeV, either in the form of two narrow resonances at the ends of this range, or a wide resonance centered in this range.