Infrared gluon propagator in the Refined Gribov-Zwanziger scenario at one-loop order in the Landau gauge

TL;DR

This paper computes the one-loop corrected gluon propagator within the Refined Gribov-Zwanziger framework in Landau gauge, confirming the stability of key infrared properties and matching lattice data.

Contribution

It provides the first one-loop quantum correction analysis of the RGZ gluon propagator, demonstrating the preservation of its qualitative infrared features.

Findings

Gluon propagator retains finite value at zero momentum

Positivity violation persists after quantum corrections

Complex poles are confirmed for SU(2) and SU(3) gauge groups

Abstract

The Refined Gribov-Zwanziger (RGZ) action in the Landau gauge provides a local and renormalizable framework to account for the existence of infinitesimal Gribov copies in the path integral together with other relevant infrared effects such as the formation of condensates. The properties of the tree-level gluon propagator obtained in this setup has been thoroughly investigated over the past decade. It accommodates important properties seen in lattice simulations such as a finite value at vanishing momentum and positivity violation. Yet a comprehensive study about the stability of such properties against quantum corrections was lacking. In this work, we compute the gluon propagator in the RGZ scenario at one-loop order and implement an appropriate renormalization scheme in order to compare our findings with lattice data. Remarkably, the qualitative properties of the tree-level gluon propagator are preserved. In particular, the fits with lattice data show evidence for positivity violation and the existence of complex poles for SU(2) and SU(3) gauge groups. We comment on the results for the ghost propagator as well.