  Due to the nonperturbative masslessness of the ghost field, ghost loops that
contribute to gluon Green's functions in the Landau gauge display infrared
divergences, akin to those one would encounter in a conventional perturbative
treatment. This is in sharp contrast with gluon loops, in which the
perturbative divergences are tamed by the dynamical generation of a gluon mass
acting as an effective infrared cutoff. In this paper, after reviewing the full
nonperturbative origin of this divergence in the two-gluon sector, we discuss
its implications for the three- and four-gluon sector, showing in particular
that some of the form factors characterizing the corresponding Green's
functions are bound to diverge in the infrared.
