Explicit construction of the pole part of the three-gluon vertex

TL;DR

This paper explicitly constructs a special part of the three-gluon vertex incorporating the Schwinger mechanism, which allows for dynamical gluon mass generation while preserving gauge invariance and BRST symmetry.

Contribution

It provides a detailed construction of the pole part of the three-gluon vertex that embeds the Schwinger mechanism into the gluon propagator's Schwinger-Dyson equation.

Findings

Demonstrates how the vertex contains massless, longitudinally coupled poles.

Ensures gauge invariance and BRST symmetry are maintained with a dynamical gluon mass.

Provides a framework for incorporating the Schwinger mechanism into QCD calculations.

Abstract

We present an explicit construction of the special part of the three gluon vertex, which incorporates the Schwinger mechanism into the Schwinger-Dyson equation of the gluon propagator, enabling the generation of a dynamical gluon mass. This vertex contains massless, longitudinally coupled poles, acting effectively as composite Nambu-Goldstone bosons, generated by the strong QCD dynamics. The basic ingredients required for this construction are the longitudinal nature of this vertex and the Slavnov-Taylor identities that it must satisfy, in order for gauge-invariance and BRST symmetry to remain intact in the presence of a gluon mass.