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Definition and parametrization of non-perturbative effects in quenched QCD

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 minimal 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 expression 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 beta^B exp(-A beta) calculable semi-classically. The situation is complicated by zeroes of the partition function in the complex $β$ plane (presumably near 5.75 pm i 0.2). 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 showing 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 a^4. We propose an exponential parametrization to the corrections to the universal part of the beta function and find results compatible with the suggestion of a^2 corrections made by C. Allton.