All order renormalizable refined Gribov-Zwanziger model with BRST invariant fermionic horizon function in linear covariant gauges

Abstract

We introduce, within the refined Gribov-Zwanziger setup, a composite Becchi-Rouet-Stora-Tyutin (BRST) invariant fermionic operator coupled to the inverse of the Faddeev-Popov operator. As a result, an effective BRST invariant action in Euclidean space-time is constructed, enabling us to pave the first step towards the study of the behavior of the fermion propagator in the infrared region in the class of the linear covariant gauges. The aforementioned action is proven to be renormalizable to all orders by means of the algebraic renormalization procedure.