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A non-perturbative version of the BRST quartet mechanism in infrared Landaugauge QCD is proposed for transverse gluons and quarks. Based on the positivityviolation for transverse gluons the content of the respective non-perturbativeBRST quartet is derived. To identify the gluon's BRST-daughter and secondparent state, a truncated Bethe-Salpeter equation for the gluon-(anti-)ghostbound state is investigated. We comment shortly on several equivalent forms ofthis equation. Repeating the same construction for quarks leads to a truncatedBethe-Salpeter equation for a fundamentally charged quark-(anti-)ghost boundstate. It turns out that a cardinal input to this equation is given by thefully dressed quark-gluon vertex, and that it is indispensable to dress thequark-gluon vertex in this equation in order to obtain a consistent truncation.

Ghost-gluon and ghost-quark bound states and their role in BRST quartets