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 techniqu
es are applied to the problematic scalar glueball channel to determine mass
es, widths and relative resonance strengths of low-lying scalar glueball st
ates contributing to the hadronic spectral function. A feature of our analy
sis is the inclusion of instanton contributions to the scalar gluonic corre
lation function. Compared with the next-to-leading gaussian sum-rule, the a
nalysis of the lowest-weighted sum-rule (which contains a large scale-indep
endent contribution from the low energy theorem) is shown to be unreliable
because of instability under QCD uncertainties. However, the presence of in
stanton effects leads to approximately consistent mass scales in the lowest
weighted and next-lowest weighted sum-rules. The analysis of the next-to-l
eading sum-rule demonstrates that a single narrow resonance model does not
provide an adequate description of the hadronic spectral function. Conseque
ntly, we consider a wide variety of phenomenological models which distribut
e resonance strength over a broad region - some of which lead to excellent
agreement between the theoretical prediction and phenomenological models. I
ncluding QCD uncertainties, our results indicate that the hadronic contribu
tions to the spectral function stem from a pair of resonances with masses i
n the range 0.8-1.6 GeV, with the lighter of the two potentially having a l
arge width. (C) 2001 Elsevier Science B.V. All rights reserved.