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We study effective mass generation of off-diagonal gluons and infraredabelian dominance in the maximally abelian (MA) gauge. Using the SU(2) latticeQCD, we investigate the propagator and the effective mass of the gluon field inthe MA gauge with the U(1)$_3$ Landau gauge fixing. The Monte Carlo simulationis performed on the $12^3 \times 24$ lattice with $2.2 \le \beta \le 2.4$, andalso on the $16^4$ and $20^4$ lattices with $2.3 \le \beta \le 2.4$. In the MAgauge, the diagonal gluon component $A_\mu^3$ shows long-range propagation, andinfrared 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 bosonwith the effective mass $M_{\rm off} \simeq 1.2$ GeV in the region of $r \gsim0.2$ fm, and its propagation is limited within short range. We conjecture thatinfrared abelian dominance can be interpreted as infrared inactivity of theoff-diagonal gluon due to its large mass generation induced by the MA gaugefixing.Comment: 31 pages, 7 figures and 2 tables included, changed title, corrected  typos and updated reference, accepted for publication in Physical Review

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