The Veneziano ghost, glost and gauge copies in QCD

In this short note, we come back to the recent proposal put forward by Kharzeev and Levin [PRL 114 (2015) 24, 242001], in which they phenomenologically couple the non-perturbative Veneziano ghost to the perturbative gluon, leading to a modified gluon propagator (the "glost") of the Gribov type, with complex poles. As such, a possible link was made between the QCD topological \theta-vacuum (Veneziano ghost) and color confinement (no physically observable gluons). We discuss some subtleties concerning gauge (BRST) invariance of this proposal, related to the choice of Feynman gauge. We furthermore provide an example in the Landau gauge of a similar phenomenological vertex that also describes the necessary Veneziano ghost but does not affect the Landau gauge gluon propagator.