Strong randomness of off-diagonal gluon phases and off-diagonal gluon mass in the maximally abelian gauge in QCD

TL;DR

This paper investigates the abelianization of QCD in the maximally abelian gauge, revealing strong randomness in off-diagonal gluon phases, a large effective gluon mass, and evidence for dual Higgs mechanism via monopole condensation.

Contribution

It demonstrates the large off-diagonal gluon mass and magnetic screening in the MA gauge, and introduces a gauge-invariant way to describe the MA projection using a gluonic Higgs scalar.

Findings

Off-diagonal gluon mass in SU(2) QCD is approximately 1.2 GeV.

Off-diagonal gluon mass in SU(3) QCD is approximately 1.1 GeV.

Evidence of magnetic screening and dual Higgs mechanism in the infrared region.

Abstract

We study abelianization of QCD in the maximally abelian (MA) gauge. In the MA gauge, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to a large off-diagonal gluon mass. Using lattice QCD, we find a large effective off-diagonal gluon mass in the MA gauge: $M_{\rm off} \simeq 1.2 {\rm GeV}$ in SU(2) QCD, $M_{\rm off} \simeq 1.1 {\rm GeV}$ in SU(3) QCD. Due to the large off-diagonal gluon mass in the MA gauge, infrared QCD is well abelianized like nonabelian Higgs theories. We investigate the inter-monopole potential and the dual gluon field $B_\mu$ in the MA gauge, and find longitudinal magnetic screening with $m_B \simeq$ 0.5 GeV in the infrared region, which indicates the dual Higgs mechanism by monopole condensation. We propose a gauge invariant description of the MA projection by introducing the ``gluonic Higgs scalar field''.