Perturbative approach to the infrared gluon propagator in the maximal Abelian gauge

TL;DR

This paper investigates the infrared behavior of gluon and ghost propagators in the maximal Abelian gauge using a perturbative approach with a mass-like term, comparing results with lattice data.

Contribution

It extends the perturbative mass approach to the maximal Abelian gauge, providing a systematic analysis and comparison with lattice results for the first time.

Findings

Infrared gluon propagators agree with lattice data

Perturbative approach effectively models gauge-dependent quantities

Results support the validity of the mass-like term in this gauge

Abstract

The inclusion of a mass-like term for the gluon in Yang-Mills theories quantized in the Landau gauge has proven to be an effective way of reproducing lattice results for gauge-fixed correlation functions within perturbative computations. Since those quantities are gauge dependent, it is natural to question how general this prescription is for describing the infrared behavior of gluon and Faddeev-Popov ghost propagators in different gauges. In this work, we provide a systematic investigation of this issue in the maximal Abelian gauge, which cannot be deformed into the Landau gauge and has been investigated in gauge-fixed lattice simulations. We compute the one-loop non-Abelian and diagonal gluon propagators and perform fits to lattice data in the case of $SU(2)$. Our results show that the transverse component of the non-Abelian gluon propagator as well as the diagonal gluon propagator, are in good agreement with lattice data in the infrared.