Study of the all orders multiplicative renormalizability of a local confining quark action in the Landau gauge

TL;DR

This paper demonstrates that a local quark action coupled via the inverse Faddeev-Popov operator in Landau gauge is multiplicatively renormalizable at all orders, aligning with lattice QCD results in the infrared.

Contribution

It introduces a new local quark action coupled through the inverse Faddeev-Popov operator and proves its all-order multiplicative renormalizability.

Findings

The local action reproduces lattice quark propagator behavior in the infrared.

The action is proven to be multiplicatively renormalizable to all orders.

The approach supports consistent quantization within the Gribov-Zwanziger framework.

Abstract

The inverse of the Faddeev-Popov operator plays a pivotal role within the Gribov-Zwanziger approach to the quantization of Euclidean Yang-Mills theories in Landau gauge. Following a recent proposal [Phys. Rev. D90 (2014) 085010], we show that the inverse of the Faddeev-Popov operator can be consistently coupled to quark fields. Such a coupling gives rise to a local action while reproducing the behaviour of the quark propagator observed in lattice numerical simulations in the non-perturbative infrared region. By using the algebraic renormalization framework, we prove that the aforementioned local action is multiplicatively renormalizable to all orders.