Wilson loops in very high order lattice perturbation theory

TL;DR

This paper computes high-order Wilson loops in lattice QCD using Numerical Stochastic Perturbation Theory to analyze the perturbative series behavior and estimate the gluon condensate.

Contribution

It extends perturbative calculations of Wilson loops up to order 20 and compares different models to understand series behavior at high orders.

Findings

No factorial growth observed up to order 20.

Differences in series behavior between small and large Wilson loops.

Estimate of the gluon condensate from perturbative and Monte Carlo data.

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 $<\frac{\alpha}{\pi}GG>$.