Wilson loops in very high order lattice perturbation theory

Abstract

We calculate Wilson loops of various sizes up to loop order $n=20$ for lattice sizes of $L^4 (L=4, 6, 8, 12)$ using the technique of Numerical Stochastic Perturbation Theory in quenched QCD. This allows to investigate the behaviour of the perturbative series at high orders. We discuss three models to estimate the perturbative series: a renormalon inspired fit, a heuristic fit based on an assumed power-law singularity and boosted perturbation theory. We have found differences in the behavior of the perturbative series for smaller and larger Wilson loops at moderate $n$. A factorial growth of the coefficients could not be confirmed up to $n=20$. From Monte Carlo measured plaquette data and our perturbative result we estimate a value of the gluon condensate $<\frac{\alpha}{\pi}GG>$.