Off-diagonal gluon mass generation and infrared Abelian dominance in the maximally Abelian gauge in lattice QCD

We study effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge. Using SU(2) lattice QCD, we investigate the propagator and the effective mass of the gluon field in the MA gauge with $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_3$ Landau gauge fixing. The Monte Carlo simulation is performed on the ${12}^3\times 24$ lattice with $2.2<~\beta <~2.4,$ and also on the ${16}^4$ and ${20}^4$ lattices with $2.3<~\beta <~\mathrm{2.4.}$ In the MA gauge, the diagonal gluon component $A_{\mu }^3$ shows long-range propagation, and infrared Abelian dominance is found for the gluon propagator. In the MA gauge, the off-diagonal gluon component $A_{\mu }^{\pm }$ behaves as a massive vector boson with the effective mass $M_{\mathrm{off}}\simeq 1.2\mathrm{GeV}$ in the region of $r\gtrsim 0.2\mathrm{fm},$ and its propagation is limited within a short range. We conjecture that infrared Abelian dominance can be interpreted as infrared inactivity of the off-diagonal gluon due to its large mass generation induced by the MA gauge fixing.