The two-, three- and four-gluon sector of QCD in the Landau gauge

TL;DR

This paper investigates the infrared divergences in gluon Green's functions in Landau gauge QCD, highlighting the contrasting behaviors of ghost and gluon loops and their implications for multi-gluon sectors.

Contribution

It provides a detailed analysis of the nonperturbative origin of infrared divergences in ghost loops and explores their effects on three- and four-gluon Green's functions.

Findings

Ghost loops cause infrared divergences in gluon Green's functions.

Gluon loops are regulated by dynamical gluon mass generation.

Certain form factors in multi-gluon sectors diverge in the infrared.

Abstract

Due to the nonperturbative masslessness of the ghost field, ghost loops that contribute to gluon Green's functions in the Landau gauge display infrared divergences, akin to those one would encounter in a conventional perturbative treatment. This is in sharp contrast with gluon loops, in which the perturbative divergences are tamed by the dynamical generation of a gluon mass acting as an effective infrared cutoff. In this paper, after reviewing the full nonperturbative origin of this divergence in the two-gluon sector, we discuss its implications for the three- and four-gluon sector, showing in particular that some of the form factors characterizing the corresponding Green's functions are bound to diverge in the infrared.