  We investigate the 2-point correlation functions of Yang-Mills theory in the
Landau gauge by means of a massive extension of the Faddeev-Popov action. This
model is based on some phenomenological arguments and constraints on the
ultraviolet behavior of the theory. We show that the running coupling constant
remains finite at all energy scales (no Landau pole) for $d>2$ and argue that
the relevant parameter of perturbation theory is significantly smaller than 1
at all energies. Perturbative results at low orders are therefore expected to
be satisfactory and we indeed find a very good agreement between 1-loop
correlation functions and the lattice simulations, in 3 and 4 dimensions.
Dimension 2 is shown to play the role of an upper critical dimension, which
explains why the lattice predictions are qualitatively different from those in
higher dimensions.
