Lattice QCD, gauge fixing, and the transition to the perturbative regime

TL;DR

This paper discusses the challenges of gauge fixing in QCD, contrasting perturbative and nonperturbative regimes, and explores the relationship between Dyson-Schwinger calculations and lattice QCD results.

Contribution

It analyzes gauge fixing issues in QCD across regimes and examines the connection between Dyson-Schwinger methods and lattice calculations.

Findings

Gribov copies can be neglected in the perturbative regime.

Nonlocal gauges like Laplacian gauge avoid Gribov copies.

Dyson-Schwinger and lattice results show consistent infrared behavior.

Abstract

Perturbative QCD uses the Faddeev-Popov gauge-fixing procedure, which leads to ghosts and the local BRST invariance of the gauge-fixed perturbative QCD action. In the asymptotic regime, where perturbative QCD is relevant, Gribov copies can be neglected. In the nonperturbative regime, one must adopt either a nonlocal Gribov-copy free gauge (e.g., Laplacian gauge) or attempt to maintain local BRST invariance at the expense of admitting Gribov copies. These issues are explored and discussed. In addition, the relationship between recent Dyson-Schwinger based calculations of the infrared behavior of QCD Green's functions and the lattice calculation of these quantities is examined.