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

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 off ⋍ 1.2GeV in SU(2) QCD, M off ⋍ 1.1GeV 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 μ in the MA gauge, and find longitudinal magnetic screening with m B ⋍ 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”.