Wilson loops to 20th order numerical stochastic perturbation theory
Abstract
We calculate Wilson loops of various sizes up to 20 loops in SU(3) pure lattice gauge theory at different lattice sizes for Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate the perturbative series for various Wilson loops at high loop orders. We observe differences in the behavior of those series as function of the loop order. Up to we do not find evidence for the factorial growth of the expansion coefficients often assumed to characterize an asymptotic series. Based on the actually observed behavior we sum the series in a model parametrized by hypergeometric functions. Alternatively we estimate the total series in boosted perturbation theory using information from the first 14 loops. We introduce generalized ratios of Wilson loops of different sizes. Together with the corresponding Wilson loops from standard Monte Carlo measurements they enable us to assess their non-perturbative parts.
Keywords
Cite
@article{arxiv.1205.1659,
title = {Wilson loops to 20th order numerical stochastic perturbation theory},
author = {R. Horsley and G. Hotzel and E. -M. Ilgenfritz and R. Millo and Y. Nakamura and H. Perlt and P. E. L. Rakow and G. Schierholz and A. Schiller},
journal= {arXiv preprint arXiv:1205.1659},
year = {2013}
}
Comments
29 pages, 21 figures, version accepted for publication in Phys. Rev. D, some inconsistencies removed, more details added concerning the Langevin simulation, references added and updated