# Dependence of the propagators on the sampling of Gribov copies inside the first Gribov region of Landau gauge

## TL;DR

This study investigates how different non-perturbative gauge choices within the first Gribov region affect the behavior of propagators and running coupling in SU(2) Yang-Mills theory across multiple dimensions using lattice simulations.

## Contribution

The paper constructs various gauges inside the first Gribov region and analyzes their impact on propagators and coupling, revealing gauge dependence and lattice artifact effects.

## Key findings

- Gluon propagator is largely insensitive to gauge choice.
- Ghost propagator and running coupling show significant dependence on gauge.
- Lattice artifacts have a larger influence than in minimal Landau gauge.

## Abstract

Beyond perturbation theory the number of gauge copies drastically increases due to the Gribov-Singer ambiguity. Any way of treating them defines, in principle, a new, non-perturbative gauge, and the gauge-dependent correlation functions can vary between them. Herein various such gauges will be constructed as completions of the Landau gauge inside the first Gribov region. The dependence of the propagators and the running coupling on these gauges will be studied for SU(2) Yang-Mills theory in two, three, and four dimensions using lattice gauge theory, and for a wide range of lattice parameters. While the gluon propagator is rather insensitive to the choice, the ghost propagator and the running coupling show a stronger dependence. It is also found that the influence of lattice artifacts is larger than in minimal Landau gauge.