A low-energy effective Yang-Mills theory for quark and gluon confinement

TL;DR

This paper derives a gauge-invariant low-energy effective Yang-Mills model demonstrating quark and gluon confinement, with the gluon propagator of Gribov-Stingl type, and discusses confinement mechanisms without a mass term.

Contribution

It introduces a gauge-invariant effective model of Yang-Mills theory with a specific gluon propagator form, showing confinement phenomena and exploring mechanisms beyond mass terms.

Findings

Effective gluon propagator matches Gribov-Stingl form.

The model exhibits area law for Wilson loops indicating confinement.

Confinement may occur without a mass term in the effective theory.

Abstract

We derive a gauge-invariant low-energy effective model of the Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type and agrees with it when a mass term which breaks nilpotency of the BRST symmetry is included. We show that the effective model with gluon propagator of the Gribov-Stingl type exhibits both quark and gluon confinement: the Wilson loop average has the area law and the Schwinger function violates reflection positivity. However, we argue that both quark and gluon confinement can be obtained even in the absence of such a mass term.