Second order gluon polarization for SU(N) theory in linear covariant gauge

TL;DR

This paper computes the second order gluon polarization in SU(N) Yang-Mills theory within linear covariant gauges, providing numerical results and comparing variational methods for improved understanding of gluon propagators.

Contribution

It introduces a generalized perturbation theory approach to evaluate gluon polarization at second order for any space dimension and gauge, including variational method insights.

Findings

Numerical data for gluon propagator in Landau and Feynman gauges

Comparison of variational methods using second-order polarization

Analysis of gauge dependence in gluon polarization

Abstract

The gluon polarization functional is evaluated for a generic linear covariant gauge and for any space dimension in pure Yang-Mills SU(N) theory up to second order in a generalized perturbation theory, where the zeroth order action is freely chosen and can be determined by some variational method. Some numerical data are given for the gluon propagator in Landau gauge and compared with Feynmann gauge. A comparison is given for several variational methods that can be set up by the knowledge of the second-order polarization.