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: $M_{\mathrm{off}}\simeq 1.2\mathrm{GeV}$ in SU(2) QCD, $M_{\mathrm{off}}\simeq 1.1\mathrm{GeV}$ 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''.

Comments: Talk given at 19th International Symposium on Lattice Field Theory (Lattice 2001), Berlin, Germany, 19-24 Aug 2001