Effective Mass Generation of Off-diagonal Gluons as the Origin of Infrared Abelian Dominance in the Maximally Abelian Gauge in QCD

We study the origin of the abelian dominance in the maximally abelian (MA) gauge for the long-distance physics in terms of the interaction range mediated by gluons. In the MA gauge, diagonal gluon components behave as neutral gauge fields like photons, and off-diagonal gluon components behave as charged matter fields on the residual abelian gauge symmetry. We study the gluon propagator in the MA gauge with the U(1)$_3$ Landau gauge fixing using the SU(2) lattice QCD with $ 2.2 \le \beta \le 2.4$ and $12^3 \times 24$. We find the abelian dominance for the gluon propagator in the MA gauge in the infrared region. The off-diagonal charged gluon behaves as a massive vector boson with the effective mass $M_{\rm ch} \simeq 0.94$ GeV in the region of $r \gsim 0.2$ fm. The origin of the infrared abelian dominance is physically explained as the generation of the charged gluon mass $M_{\rm ch}$ induced by the MA gauge fixing, and the charged-gluon mass generation predicts general abelian dominances for the long-distance physics in QCD in the MA gauge.