Wilson loops to 20th order numerical stochastic perturbation theory

Horsley, R, Hotzel, G, Ilgenfritz, E-M, Millo, R, Nakamura, Y, Perlt, H, Rakow, PEL ORCID: 0000-0003-4486-2158, Schierholz, G and Schiller, A (2012) Wilson loops to 20th order numerical stochastic perturbation theory. Phys. Rev. D, 86 (5). 054502-.

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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 $n=20$ 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.

Item Type:	Article
Additional Information:	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
Uncontrolled Keywords:	hep-lat, hep-lat, hep-ph
Depositing User:	Symplectic Admin
Date Deposited:	07 Dec 2018 14:42
Last Modified:	19 Jan 2023 01:09
DOI:	10.1103/physrevd.86.054502
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3029718