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In SU(3) lattice QCD, we improve a method to extract gauge fields from linkvariables analytically. With this method, we perform the first study on theeffective mass generation of off-diagonal gluons and infrared Abelian dominancein the maximally Abelian (MA) gauge in the SU(3) case. We investigate thepropagator and the effective mass of the off-diagonal gluon field in the MAgauge with ${\rm U(1)}_3 \times {\rm U(1)}_8$ Landau gauge fixing in SU(3)quenched lattice QCD on $16^4$ at $\beta$=5.7, 5.8 and 6.0. The off-diagonalgluon component behaves as a massive vector boson with the approximateeffective mass $M_{\rm off} = 1.1 - 1.2 {\rm GeV}$ in the region of $r = 0.3 -0.8 {\rm fm}$, and its propagation is limited within a short range. We thusshow the origin of infrared Abelian dominance in terms of short-rangepropagation of off-diagonal gluons. We also investigate the functional form ofthe off-diagonal gluon propagator. We find that the functional form is welldescribed by the four-dimensional Euclidean Yukawa-type function ${\rmexp}\{-m_{\rm off} r\}/r$ with $m_{\rm off} = 1.3 -1.4 {\rm GeV}$ for $r = 0.1-0.8{\rm fm}$. This also indicates that the spectral function has a negativeregion.

Analytical derivation of gauge fields from link variables in SU(3) lattice QCD and its application in maximally Abelian gauge