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 $A_{\mathrm {tr}}$ the field content of the non-perturbative BRST quartet generated by $A_{\mathrm {tr}}$ is derived. To identify the gluon's 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 colour 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 $A_{\mathrm {tr}}$ 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.