Mass generation and the problem of seagull divergences

TL;DR

This paper reviews how seagull divergences in gluon mass generation via Schwinger-Dyson equations can be completely eliminated using a special identity in dimensional regularization, enabling consistent dynamical gluon mass generation.

Contribution

It introduces a characteristic identity that removes seagull divergences in gluon mass calculations, facilitating non-perturbative mass generation in QCD.

Findings

Seagull divergences can be eliminated using a specific identity in dimensional regularization.

An Ansatz for the three-gluon vertex allows for dynamical gluon mass generation without divergences.

The method is illustrated with a pedagogical example in scalar QED.

Abstract

The gluon mass generation is a purely non-perturbative effect, and the natural framework to study it in the continuum are the Schwinger-Dyson equations (SDEs) of the theory. At the level of the SDEs the generation of such a mass is associated with the existence of infrared finite solutions for the gluon propagator. From the theoretical point of view, the dynamical gluon mass generation has been traditionally plagued with seagull divergences. In this work, we will review how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. As a pedagogical example, we will first discuss in the context of scalar QED how it is possible to eliminate all seagull divergences, by triggering the aforementioned special identity, which enforces the masslessness of the photon. Then, we will discuss what happens in QCD and present an Ansatz for the three gluon vertex, which completely eliminates all seagull divergences and at same time allows for the possibility of a dynamical gluon mass generation.