The Landau gauge gluon and ghost propagator in the refined Gribov-Zwanziger framework in 3 dimensions

TL;DR

This paper investigates the Landau gauge gluon and ghost propagators in 3-dimensional refined Gribov-Zwanziger framework, showing infrared behaviors consistent with numerical simulations and extending previous 4D analyses.

Contribution

It extends the refined Gribov-Zwanziger framework to 3 dimensions, analyzing the propagators' infrared behavior and comparing with recent numerical results.

Findings

Ghost propagator behaves like 1/p^2 in infrared

Gluon propagator reaches a finite nonzero value at zero momentum

Gluon propagator violates positivity

Abstract

In previous works, we have constructed a refined version of the Gribov-Zwanziger action in 4 dimensions, by taking into account a novel dynamical effect. In this paper, we explore the 3-dimensional case. Analogously as in 4 dimensions, we obtain a ghost propagator behaving like $1/p^2$ in the infrared, while the gluon propagator reaches a finite nonvanishing value at zero momentum. Simultaneously, a clear violation of positivity by the gluon propagator is also found. This behaviour of the propagators turns out be in agreement with the recent numerical simulations.