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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 one-loop correlation functions and the lattice simulations, in three and four 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.
Tissier et al. (Thu,) studied this question.