Vacuum condensate of mass dimension 2 as the origin of mass gap and quark confinement

TL;DR

This paper introduces a gauge-invariant vacuum condensate of mass dimension 2 in SU(N) Yang-Mills theory, which can generate an effective gluon mass and has implications for quark confinement.

Contribution

It proposes a new gauge-invariant condensate of mass dimension 2 involving gluons and ghosts, unifying previous condensates and exploring their role in mass gap and confinement.

Findings

Demonstrates the existence of the condensate via operator product expansion.

Shows the condensate can generate an effective gluon mass.

Discusses implications for quark confinement.

Abstract

We propose a vacuum condensate of mass dimension 2 consisting of gluons and ghosts in the framework of the manifestly covariant gauge fixing of the SU(N) Yang-Mills theory. This quantity is both BRST and anti-BRST invariant for any gauge. It includes the ghost condensation $C^a \bar{C}^a$ proposed first in the modified Maximal Abelian gauge and reduces to the gluon condensates $(\mathscr{A}_\mu)^2$ of mass dimension 2 proposed recently in the Landau gauge of the Lorentz gauge fixing. The vacuum condensate of dimensions 2 can provide the effective mass for gluons and ghosts. The possible existence of such condensations is demonstrated by calculating the operator product expansion of the gluon and ghost propagators in both gauges. Its implications to quark confinement are also discussed in consistent with the previous works.