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This paper complements a new lattice formulation of SU(2) Yang-Mills theorywritten in terms of new variables in a compact form proposed in the previouspaper. The new variables used in the formulation were once called theCho--Faddeev--Niemi or Cho--Faddeev--Niemi--Shabanov decomposition. Ourformulation enables us to explain the infrared ``Abelian'' dominance, inaddition to magnetic monopole dominance shown in the previous paper, in thegauge invariant way without relying on the specific gauge fixing called themaximal Abelian gauge used in the conventional investigations. In this paper,especially, we demonstrate by numerical simulations that gluon degrees offreedom other than the ``Abelian'' part acquire the mass to be decoupled in thelow-energy region leading to the infrared Abelian dominance.

Compact lattice formulation of Cho-Faddeev-Niemi decomposition: gluon mass generation and infrared Abelian dominance