An all order renormalizable Refined-Gribov-Zwanziger model with BRST invariant fermionic horizon function in linear covariant gauges

TL;DR

This paper develops a renormalizable, BRST invariant fermionic model within the Refined-Gribov-Zwanziger framework, facilitating the study of fermion behavior in the infrared regime in linear covariant gauges.

Contribution

It introduces a novel BRST invariant fermionic operator and constructs an all-order renormalizable effective action in this context.

Findings

Constructed a BRST invariant fermionic operator coupled to the inverse Faddeev-Popov operator.

Proved the renormalizability of the effective action to all orders.

Enabled future analysis of fermion propagators in the infrared region.

Abstract

We introduce, within the Refined-Gribov-Zwanziger setup, a composite 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 behaviour 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.