Lattice evidence for the family of decoupling solutions of Landau gauge Yang-Mills theory

TL;DR

This study demonstrates that the low-momentum behavior of Landau-gauge gluon and ghost propagators on the lattice depends on the Faddeev-Popov operator's eigenvalues, aligning qualitatively with decoupling solutions from continuum methods.

Contribution

It provides lattice evidence that the low-momentum propagator behavior is influenced by Gribov copies, supporting the decoupling solution scenario in Landau gauge Yang-Mills theory.

Findings

Ghost dressing function rises more rapidly for small eigenvalues.

Gluon propagator levels out to lower zero-momentum value for small eigenvalues.

Dependence on Gribov copies is observed below 1 GeV, not above.

Abstract

We show that the low-momentum behavior of the lattice Landau-gauge gluon and ghost propagators is sensitive to the lowest non-trivial eigenvalue (\lambda_1) of the Faddeev-Popov operator. If the gauge fixing favors Gribov copies with small \lambda_1 the ghost dressing function rises more rapidly towards zero momentum than on copies with large \lambda_1. This effect is seen for momenta below 1 GeV, and interestingly also for the gluon propagator at momenta below 0.2 GeV: For large \lambda_1 the gluon propagator levels out to a lower value at zero momentum than for small \lambda_1. For momenta above 1 GeV no dependence on Gribov copies is seen. Although our data is only for a single lattice size and spacing, a comparison to the corresponding (decoupling) solutions from the DSE/FRGE study of Fischer, Maas and Pawlowski [Annals of Physics 324 (2009) 2408] yields already a good qualitative agreement.