[Paper Review] The Landau gauge gluon propagator in 4D SU(2) lattice gauge theory revisited: Gribov copies and scaling properties

I. L. Bogolubskya, E.-M. Ilgenfritz+2 more|arXiv (Cornell University)|Dec 11, 2009

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This study revisits the Landau gauge gluon propagator in 4D SU(2) lattice gauge theory using simulated annealing for gauge fixing to minimize Gribov copy effects. It finds that the gluon propagator exhibits decoupling-type infrared behavior with a finite infrared limit, and confirms multiplicative renormalizability and scaling across large lattices, supporting the decoupling solution over the scaling solution.

ABSTRACT

Lattice results for the gluon propagator in SU(2) pure gauge theory obtained on large lattices are presented. Simulated annealing is used throughout to fix the Landau gauge. We concentrate on checks for Gribov copy effects and for scaling properties. Our findings are similar to the ones in the SU(3) case, supporting the decoupling-type infrared behaviour of the gluon propagator.

Motivation & Objective

• To investigate Gribov copy effects on the gluon propagator in 4D SU(2) lattice gauge theory using improved gauge fixing.
• To test scaling and multiplicative renormalizability of the gluon propagator on large lattices with fixed physical volume.
• To compare simulated annealing and overrelaxation gauge fixing methods in the context of infrared behavior and finite-size effects.
• To assess whether the observed decoupling-type behavior persists under improved gauge fixing and larger volumes.

Proposed method

• Simulated annealing (SA) is used as the primary gauge fixing algorithm to minimize Gribov copy effects, with cooling from T_max = 1.1 to T_min = 0.01.
• The Landau gauge is fixed by maximizing the gauge functional F_U[g] = (1/N_c) ∑_{x,μ} Re Tr gUg†, ensuring local maxima are sought.
• Lattice ensembles are generated at fixed physical volume (~10 fm) using (L, β) pairs: (40, 2.2), (56, 2.3), (80, 2.4), (112, 2.5).
• The gluon propagator is computed and multiplicative renormalization is applied via the momentum-subtraction (MOM) scheme at μ² = 5.8 GeV² to ensure Z_ren(μ²) = 1.
• Finite-size effects are assessed by comparing renormalized dressing functions Z_ren(q²) across different lattice sizes.
• The analysis excludes Z(2) flips to isolate the impact of gauge fixing method and volume scaling.

Experimental results

Research questions

• RQ1 Does the choice of gauge fixing method—simulated annealing versus overrelaxation—affect the infrared behavior of the gluon propagator in SU(2) lattice gauge theory?
• RQ2 To what extent do Gribov copy effects influence the gluon propagator at low momenta, and do they diminish with increasing lattice volume?
• RQ3 Is the gluon propagator multiplicative renormalizable across different lattice cutoffs when physical volume is held constant?
• RQ4 Do scaling properties of the gluon propagator hold on large lattices, and are finite-size effects negligible in the infrared region?

Key findings

• The gluon propagator exhibits a finite infrared limit at q² < 0.2 GeV² when using simulated annealing, indicating decoupling-type behavior, in contrast to overrelaxation which shows stronger Gribov effects.
• A noticeable difference in the gluon propagator between simulated annealing and overrelaxation is observed in the deep infrared, confirming significant Gribov copy effects in the latter.
• The renormalized gluon dressing function Z_ren(q²) for L = 56, 80, and 112 lattices collapses onto a single curve, confirming multiplicative renormalizability and scaling.
• Scaling violations are observed at β = 2.2 (L = 40), attributed to lattice artifacts, while larger lattices show consistent results within statistical uncertainties.
• Finite renormalization factors Z(μ², β)/Z(μ², β=2.5) are 0.815 (β=2.2), 0.8925 (β=2.3), and 0.9489 (β=2.4), indicating a smooth approach to the continuum limit.
• The results support the decoupling solution for the gluon propagator in the infrared, consistent with SU(3) lattice studies, and suggest that Gribov effects diminish with increasing volume.