Asymptotic behavior of the ghost propagator in SU3 lattice gauge theory

TL;DR

This paper investigates the asymptotic behavior of the ghost propagator in SU(3) lattice gauge theory, demonstrating that lattice data aligns with high-order perturbative predictions and analyzing the dependence on perturbation order and scheme.

Contribution

It introduces an efficient algorithm for computing the Faddeev-Popov operator and provides continuum-extrapolated lattice data consistent with four-loop perturbation theory.

Findings

Lattice data matches four-loop perturbation theory from 2.0 to 6.0 GeV

Effective Lambda_MS depends on perturbation order and scheme

Truncation of series explains dependency magnitude

Abstract

We study the asymptotic behavior of the ghost propagator in the quenched SU(3) lattice gauge theory with Wilson action. The study is performed on lattices with a physical volume fixed around 1.6 fm and different lattice spacings: 0.100 fm, 0.070 fm and 0.055 fm. We implement an efficient algorithm for computing the Faddeev-Popov operator on the lattice. We are able to extrapolate the lattice data for the ghost propagator towards the continuum and to show that the extrapolated data on each lattice can be described up to four-loop perturbation theory from 2.0 GeV to 6.0 GeV. The three-loop values are consistent with those extracted from previous perturbative studies of the gluon propagator. However the effective $\Lambda_{\ms}$ scale which reproduces the data does depend strongly upon the order of perturbation theory and on the renormalization scheme used in the parametrization. We show how the truncation of the perturbative series can account for the magnitude of the dependency in this energy range. The contribution of non-perturbative corrections will be discussed elsewhere.