  In light of the development of the Gribov issue for pure Euclidean gauge
theories and of the recent lattice measurement of soft breaking of the BRST
invariance in Yang-Mills theories in the Landau gauge, we consider
non-perturbative features in the gauge-interacting matter sector and their
relation with general properties of the Faddeev-Popov operator. A signature for
BRST breaking in the matter sector is proposed and a local and renormalizable
framework is constructed, accommodating this signature and predicting
non-perturbative matter propagators that are consistent with available lattice
data for adjoint scalars and quarks.
