Gluon Propagator in Maximally Abelian Gauge and Abelian Dominance for Long-Range Interaction

We study the gluon propagator in the MA gauge with the lattice QCD Monte Carlo simulation. The simulation is performed using the heat-bath algorithm on the SU(2) lattice with ${12}^3\times 24$ and $\beta =2.3,2.35$. The propagator of the off-diagonal charged gluon behaves as the massive gauge boson and provides the short-range interaction, while the diagonal gluon propagates long distance. This is the origin of the abelian dominance in the long-range physics.