Scaling, decoupling and transversality of the gluon propagator

Abstract

In this note we discuss a couple of technical issues relevant to solving the Dyson-Schwinger equation for the gluon propagator in Landau gauge Yang-Mills theory. In the deep infrared functional methods extract a one-parameter family of solutions generically showing a massive behavior referred to as 'decoupling' but also including the so-called 'scaling' solution with a conformal infrared behavior as a limiting case. We emphasize that the latter cannot be ruled out by technical arguments related to the removal of quadratic divergencies and transversality.