Quark Propagator at one-loop in the Refined Gribov-Zwanziger framework

TL;DR

This paper investigates the quark propagator at one-loop order within the Refined Gribov-Zwanziger framework, comparing results with lattice data and the Curci-Ferrari model, highlighting areas for further improvement.

Contribution

It introduces the quark sector into the Refined Gribov-Zwanziger framework at one-loop and compares the results with lattice data and existing models.

Findings

Good fit for unquenched gluon propagator

Quark mass function agrees with lattice data

Quark dressing function shows qualitative disagreement in infrared

Abstract

The Refined Gribov-Zwanziger scenario is a local and renormalizable setup in which infinitesimal Gribov copies are eliminated and further non-perturbative effects are accounted for. The gluon propagator that arises from this framework fits lattice data very well in the Landau gauge. We investigate the coupling of quarks to this setting at one-loop order by computing the quark propagator. The fermionic sector is introduced by a minimal coupling and the non-perturbative effects are transmitted to the matter sector through gluonic loops which, in this case, carry information from the elimination of infinitesimal Gribov copies and the formation of condensates. We compare our findings with available lattice data both for the unquenched gluon propagator as well as for the quark propagator in the Landau gauge. Our results are comparable with those obtained in the Curci-Ferrari model at one-loop order. In particular, we are able to fit the unquenched gluon propagator and use the fixed parameters to predict the quark mass function and find good agreement with lattice data. However, the quark dressing function does not agree, even at a qualitative level, with lattice data in the infrared. This is agreement with the analogue computation in Curci-Ferrari model. Inspired by the developments in the Curci-Ferrari results, such a disagreement is likely to be cured by the inclusion of two-loops corrections. Finally, we compare the present minimal coupling with a non-perturbative matter coupling proposed in the Refined Gribov-Zwanziger literature.