Infrared behavior and Gribov ambiguity in SU(2) lattice gauge theory

TL;DR

This study numerically investigates the infrared behavior of ghost and gluon propagators in SU(2) lattice gauge theory, emphasizing the impact of Gribov copies and suggesting a decoupling solution with non-singular gluon propagator.

Contribution

It provides a detailed numerical analysis of Gribov copy effects on propagators, highlighting their importance in the infrared regime and supporting the decoupling solution.

Findings

Gribov copy effects are crucial in the infrared behavior of propagators.

Best copy ghost dressing function approaches a plateau in the infrared.

Gluon propagator tends to decrease with larger lattice sizes, indicating non-singular behavior.

Abstract

For SU(2) lattice gauge theory we study numerically the infrared behavior of the Landau gauge ghost and gluon propagators with the special accent on the Gribov copy dependence. Applying a very efficient gauge fixing procedure and generating up to 80 gauge copies we find that the Gribov copy effect for both propagators is essential in the infrared. In particular, our best copy dressing function of the ghost propagator approaches a plateau in the infrared, while for the random first copy it still grows. Our best copy zero-momentum gluon propagator shows a tendency to decrease with growing lattice size which excludes singular solutions. Our results look compatible with the so-called decoupling solution with a non-singular gluon propagator. However, we do not yet consider the Gribov copy problem to be finally resolved.