Other
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006slft.confe.215m&link_type=abstract
Proceedings of the XXIVth International Symposium on Lattice Field Theory. July 23-28, 2006, Tucson, Arizona., p.215.1
Other
Scientific paper
The notion of a non-perturbative effect is ambiguous if it requires the subtraction of a perturbative part defined by a diverging series. A common procedure consists in dropping the order of mini- mal contribution and the higher orders. This allows us to isolate very accurately the one-instanton effect for the double-well potential. For the one plaquette gauge theory, an exact analytical expres- sion can be written for the non-perturbative part. We report recent attempts to extend this approach to the average plaquette of quenched QCD. Our goal is to express the non-perturbative effects in terms of expressions of the form (β )B e-Aβ calculable semi-classically. The situation is compli- cated by zeroes of the partition function in the complex β plane (presumably near 5.75 ± i0.2). We discuss two methods to describe the intermediate and large order behavior of the perturbative series. One is inspired by mean field theory (logarithmic specific heat) and reproduces accurately the known perturbative series with only two free parameters. A diagrammatic interpretation of this fact is still lacking. The other is based on infra-red renormalons with a factorial growth show- ing up at order larger than 20 and a possible effective theory interpretation. These extrapolations are compatible with the non-perturbative part of the plaquette being proportional to a4 . We pro- pose an exponential parametrization to the corrections to the universal part of the beta function and find results compatible with the suggestion of a2 corrections made by C. Allton. To the memory of Thomas Branson and James Van Allen
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