Gluon masses without seagull divergences

The study of dynamical gluon mass generation at the level of Schwinger-Dyson equation involves a delicate interplay between various field-theoretic mechanisms The underlying local gauge invariance remains intact by resorting to the well-known Schwinger mechanism, which is assumed to be realized by longitudinally coupled bound state poles, produced by the non-perturbative dynamics of the theory. These poles are subsequently included into the Schwinger-Dyson equation of the gluon propagator through the three-gluon vertex, generating a non-vanishing gluon mass, which, however, is expressed in terms of divergent seagull integrals. In this talk we explain how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger this identity depends, in turn, on the details of the three-gluon vertex employed, and in particular, on the exact way the bound state poles are incorporated. A concrete example of a vertex that triggers the aforementioned identity is constructed, the ensuing cancellation of all seagull divergences is explicitly demonstrated, and a finite gluon mass is obtained. Due to the multitude of conditions that must be simultaneously satisfied, this construction appears to be exclusively realized within the PT-BFM framework. The resulting system of integral equations gives rise to a gluon mass that displays power-law running and an effective charge which, due to the presence of the gluon mass, freezes in the infrared at a finite (non-vanishing) value.