Gluon Propagators in Linear Covariant Gauge

TL;DR

This paper discusses the challenges of implementing the linear covariant gauge in lattice QCD, exploring discretization methods and the limit of the gauge parameter to address convergence issues.

Contribution

It analyzes various discretization strategies and the approach of taking the gauge parameter to zero to improve numerical implementation of the linear covariant gauge.

Findings

Different discretizations can mitigate convergence problems.

Large N_c groups offer alternative implementation options.

Studying the xi → 0 limit connects to Landau gauge results.

Abstract

The implementation of the linear covariant gauge on the lattice faces a conceptual problem: using the standard compact discretization, the gluon field is bounded, while the four-divergence of the gluon field satisfies a Gaussian distribution, i.e. it is unbounded. This can give rise to convergence problems when a numerical implementation is attempted. In order to overcome this problem, one can use different discretizations for the gluon field or consider an SU(N_c) group with sufficiently large N_c. One can also consider small values of the gauge parameter xi and study numerically the limiting case of xi \to 0, i.e. the Landau gauge. These different approaches will be discussed here.