# A non-perturbative study of matter field propagators in Euclidean Yang-Mills theory in linear covariant, Curci-Ferrari and maximal Abelian gauges

## TL;DR

This paper investigates matter field propagators in Euclidean Yang-Mills theory using the Refined Gribov-Zwanziger approach, incorporating Gribov copies effects and providing explicit propagator calculations across various gauges with qualitative lattice agreement.

## Contribution

It extends the Refined Gribov-Zwanziger framework to matter fields, deriving explicit propagators in multiple gauges considering Gribov effects.

## Key findings

- Qualitative agreement with available lattice data
- Explicit propagator expressions for scalar and quark fields
- Incorporation of Gribov copies in matter sector

## Abstract

In this work, we study the propagators of matter fields within the framework of the Refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the Refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST invariant formulation of the Gribov-Zwanziger framework achieved in [Capri et al 2016], the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement.