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In light of the development of the Gribov issue for pure Euclidean gaugetheories and of the recent lattice measurement of soft breaking of the BRSTinvariance in Yang-Mills theories in the Landau gauge, we considernon-perturbative features in the gauge-interacting matter sector and theirrelation with general properties of the Faddeev-Popov operator. A signature forBRST breaking in the matter sector is proposed and a local and renormalizableframework is constructed, accommodating this signature and predictingnon-perturbative matter propagators that are consistent with available latticedata for adjoint scalars and quarks.

Properties of the Faddeev-Popov operator in the Landau gauge, matter confinement and soft BRST breaking