Very high order lattice perturbation theory for Wilson loops

TL;DR

This paper computes high-order perturbative Wilson loops in lattice gauge theories up to order 20, analyzing their behavior and estimating the gluon condensate by comparing with non-perturbative results.

Contribution

It extends perturbative calculations of Wilson loops to unprecedented high orders and investigates their series behavior, challenging assumptions of factorial growth.

Findings

No evidence of factorial growth in perturbative coefficients up to order 20

Series can be summed using hypergeometric functions or boosted perturbation theory

Estimate of the gluon condensate from perturbative and non-perturbative data

Abstract

We calculate perturbative Wilson loops of various sizes up to loop order $n=20$ at different lattice sizes for pure plaquette and tree-level improved Symanzik gauge theories using the technique of Numerical Stochastic Perturbation Theory. This allows us to investigate the behavior of the perturbative series at high orders. We observe differences in the behavior of perturbative coefficients as a function of the loop order. Up to $n=20$ we do not see evidence for the often assumed factorial growth of the coefficients. Based on the observed behavior we sum this series in a model with hypergeometric functions. Alternatively we estimate the series in boosted perturbation theory. Subtracting the estimated perturbative series for the average plaquette from the non-perturbative Monte Carlo result we estimate the gluon condensate.