Features of ghost-gluon and ghost-quark bound states related to BRST quartets

The BRST quartet mechanism in infrared Landau gauge QCD is investigated. Based on the observed positivity violation for transverse gluons Atr the field content of the non-perturbative BRST quartet generated by Atr is derived. To identify the gluonʼs BRST-daughter state as well as the Faddeev-Popov-charge conjugated second parent state, a truncated Bethe-Salpeter equation for the gluon-ghost bound state in the adjoint color representation is derived and studied. This equation is found to be compatible with the so-called scaling solutions of functional approaches. Repeating the same construction for quarks instead of Atr leads in a similar way to a truncated Bethe-Salpeter equation for the quark-ghost bound state in the fundamental representation. Within the scaling solution the infrared divergence of the quark-gluon vertex is exactly the right one to make this Bethe-Salpeter equation infrared consistent.