Quark confinement in the Yang-Mills theory with a gauge-invariant gluon mass in view of the gauge-invariant BEH mechanism

TL;DR

This paper investigates a gauge-invariant gluon mass in Yang-Mills theory to understand quark confinement, proposing a gauge-scalar model that preserves gauge symmetry and analyzing its effects through lattice simulations.

Contribution

It introduces a gauge-invariant gluon mass model derived from a gauge-scalar framework, providing new insights into confinement mechanisms without breaking gauge symmetry.

Findings

Numerical simulations show the gluon mass affects the Wilson loop and static potential.

The model offers an alternative understanding of the gauge-covariant decomposition of Yang-Mills fields.

The approach maintains gauge invariance while incorporating a dynamical gluon mass.

Abstract

In order to clarify the mechanism of quark confinement in the Yang-Mills theory with mass gap, we propose to investigate the massive Yang-Mills model, namely, Yang-Mills theory with ``a gauge-invariant gluon mass term'', which is to be deduced from a specific gauge-scalar model with a single radially-fixed scalar field under a suitable constraint called the reduction condition. The gluon mass term simulates the dynamically generated mass to be extracted in the low-energy effective theory of the Yang-Mills theory and plays the role of a new probe to study the phase structure and confinement mechanism. In this talk, we first explain why such a gauge-scalar model is constructed without breaking the gauge symmetry through the gauge-independent description of the Brout-Englert-Higgs mechanism which does not rely on the spontaneous breaking of gauge symmetry. Then we discuss how the numerical simulations for the proposed massive Yang-Mills theory can be performed by taking into account the reduction condition in the complementary gauge-scalar model on a lattice. By using the reweighting method, we have investigated the effect of the gluon mass term to the Wilson loop (the static potential) and the dynamically generated mass. Moreover, we point out that the adjoint case would gives an alternative understanding for the physical meaning of the gauge-covariant decomposition for the Yang-Mills field known as the Cho-Duan-Ge-Faddeev-Niemi decomposition, while the fundamental case would give a novel decomposition which has been overlooked so far.