Schwinger poles of the three-gluon vertex: symmetry and dynamics

TL;DR

This paper investigates the structure of the three-gluon vertex in QCD, revealing how symmetry constraints and dynamical equations jointly shape the nonperturbative mass generation mechanism via Schwinger poles.

Contribution

It provides a detailed analysis of Schwinger poles in the three-gluon vertex using two methods, establishing their consistent role in gluon mass generation.

Findings

Slavnov-Taylor identity constrains pole residues.

Schwinger-Dyson equations support these constraints.

Symmetry and dynamics are deeply interconnected in this mechanism.

Abstract

The implementation of the Schwinger mechanism endows gluons with a nonperturbative mass through the formation of special massless poles in the fundamental QCD vertices; due to their longitudinal character, these poles do not cause divergences in on-shell amplitudes, but induce detectable effects in the Green's functions of the theory. Particularly important in this theoretical setup is the three-gluon vertex, whose pole content extends beyond the minimal structure required for the generation of a gluon mass. In the present work we analyze these additional pole patterns by means of two distinct, but ultimately equivalent, methods: the Slavnov-Taylor identity satisfied by the three-gluon vertex, and the nonlinear Schwinger-Dyson equation that governs the dynamical evolution of this vertex. Our analysis reveals that the Slavnov-Taylor identity imposes strict model-independent constraints on the associated residues, preventing them from vanishing. Approximate versions of these constraints are subsequently recovered from the Schwinger-Dyson equation, once the elements responsible for the activation of the Schwinger mechanism have been duly incorporated. The excellent coincidence between the two approaches exposes a profound connection between symmetry and dynamics, and serves as a nontrivial self-consistency test of this particular mass generating scenario.