Infrared properties of the gluon mass equation

TL;DR

This paper explores the infrared behavior of the gluon mass equation, demonstrating the equivalence of two different derivations related to non-perturbative massless poles and the Schwinger mechanism.

Contribution

It shows that two seemingly different formulations of the gluon mass equation are fundamentally identical, clarifying their underlying relations.

Findings

The two derivations of the gluon mass equation are equivalent.

The integral equation simplifies in the deep infrared regime.

Relations between different ingredients unify the two approaches.

Abstract

The gauge-invariant generation of a dynamical, momentum-dependent gluon mass is intimately connected with the presence of non-perturbative massless poles in the vertices of the theory, which trigger the well-known Schwinger mechanism. In the deep infrared the integral equation that governs this effective gluon mass assumes a particularly simple form, which may be derived following two seemingly different, but ultimately equivalent procedures. In particular, it may be obtained either as a deviation from a special identity that enforces the masslessness of the gluon in the absence of massless poles, or as a direct consequence of the appearance of a non-vanishing bound-state wave function, associated with the details of the actual formation of these massless poles. In this presentation we demonstrate that, due to profound relations between the various ingredients, the two versions of the gluon mass equation are in fact absolutely identical.