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

Abstract

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 $M_{\mathrm{off}}=1.1-1.2\mathrm{GeV}$ in the region of $r=0.3-0.8\mathrm{fm}$, 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 $\exp \{-m_{\mathrm{off}}r\}/r$ with $m_{\mathrm{off}}=1.3-1.4\mathrm{GeV}$ for $r=0.1-0.8\mathrm{fm}$. This also indicates that the spectral function has a negative region.

arXiv admin note: substantial text overlap with arXiv:1207.4377