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

In SU(3) lattice QCD, we improve a method to extract gauge fields from link variables analytically. With this method, we perform the first study on the effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. We investigate the propagator and the effective mass of the off-diagonal gluon field in the MA gauge with ${\mathrm{U}(1)}_3\times {\mathrm{U}(1)}_8$ Landau gauge fixing in SU(3) quenched lattice QCD on ${16}^4$ at $\beta$=5.7, 5.8 and 6.0. The off-diagonal gluon component behaves as a massive vector boson with the approximate effective mass $M_{\mathrm{o}\mathrm{f}\mathrm{f}}=1.1-1.2\mathrm{G}\mathrm{e}\mathrm{V}$ in the region of $r = 0.3 - 0.8 {\rm fm}$, and its propagation is limited within a short range. We thus show the origin of infrared Abelian dominance in terms of short-range propagation of off-diagonal gluons. We also investigate the functional form of the off-diagonal gluon propagator. We find that the functional form is well described by the four-dimensional Euclidean Yukawa-type function ${\rm exp}{-m_{\rm off} r}/r$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 negative region.