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Due to the nonperturbative masslessness of the ghost field, ghost loops thatcontribute to gluon Green's functions in the Landau gauge display infrareddivergences, akin to those one would encounter in a conventional perturbativetreatment. This is in sharp contrast with gluon loops, in which theperturbative divergences are tamed by the dynamical generation of a gluon massacting as an effective infrared cutoff. In this paper, after reviewing the fullnonperturbative origin of this divergence in the two-gluon sector, we discussits implications for the three- and four-gluon sector, showing in particularthat some of the form factors characterizing the corresponding Green'sfunctions are bound to diverge in the infrared.

The two-, three- and four-gluon sector of QCD in the Landau gauge