Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge

TL;DR

This paper investigates the infrared behavior of the Landau gauge Gribov-Zwanziger action using Dyson-Schwinger equations, identifying consistent scaling solutions and analyzing the role of auxiliary fields and mixed propagators.

Contribution

It provides a detailed infrared analysis of the Gribov-Zwanziger action, including the effects of auxiliary fields and mixed propagators, and determines the scaling relations and parameters.

Findings

Two consistent infrared scaling solutions identified.

Mixed propagators are suppressed in all loops.

The infrared exponent $\\kappa$ is found to be 0.595.

Abstract

The low momentum behavior of the Landau gauge Gribov-Zwanziger action is investigated using the respective Dyson-Schwinger equations. Because of the mixing of the gluon and the auxiliary fields four scenarios can be distinguished for the infrared behavior. Two of them lead to inconsistencies and can be discarded. Another one corresponds to the case where the auxiliary fields behave exactly like the Faddeev-Popov ghosts and the same scaling relation as in standard Landau gauge, $\ka_A+2\ka_c=0$, is valid. Even the parameter $\ka$ is found to be the same, 0.595. The mixed propagators, which appear, are suppressed in all loops, and their anomalous infrared exponent can also be determined. A fourth case provides an even stricter scaling relation that includes also the mixed propagators, but possesses the same qualitative feature, i.e. the propagators of the Faddeev-Popov ghost and the auxiliary fields are infrared enhanced and the mixed and the gluon propagators are infrared suppressed. In this case the system of equations to obtain the parameter $\ka$ is non-linear in all variables.