Two-point correlation functions of QCD in the Landau gauge

TL;DR

This paper presents a one-loop analytical study of gluon, ghost, and quark propagators in Landau gauge QCD with dynamical quarks, incorporating a gluon mass term to account for Gribov copies, and compares results with lattice data.

Contribution

It introduces a minimal model with a gluon mass term for Landau gauge QCD and compares analytical results with lattice data across multiple quark flavors.

Findings

Gluon and ghost propagators match lattice data within a few percent.

Scalar quark propagator agrees well with lattice results.

Quark renormalization is poorly described, likely due to small two-loop effects.

Abstract

We investigate the gluon, ghost and quark propagators in the Landau gauge with dynamic quarks. We perform a one-loop calculation in a model where the standard Faddeev-Popov Lagrangian is complemented by a mass term for the gluons which is seen as a minimal way of taking into account the effect of the Gribov copies. The analytic results are compared with lattice data obtained in four dimension and for two, three and four quark flavors. The gluon and ghost propagators are reproduced with a few percent accuracy in the whole range of accessible momenta. The scalar part of the quark propagator is found to be in good agreement with the lattice data. However, the quark renormalization is poorly described. We attribute this discrepancy to the fact that the one-loop corrections to this quantity are unusually small so that the two loop contribution can not be discarded. The results are expressed in terms of the coupling, the gluon mass and the light quark mass at 1 GeV.