  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.
