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

TL;DR

This paper analytically derives gauge fields from link variables in SU(3) lattice QCD and studies the effective mass and propagation of off-diagonal gluons in the maximally Abelian gauge, revealing short-range behavior and infrared dominance.

Contribution

It introduces an improved analytical method to extract gauge fields from link variables in SU(3) lattice QCD and applies it to study off-diagonal gluon mass and propagation in the MA gauge.

Findings

Off-diagonal gluons behave as massive vectors with ~1.1-1.2 GeV mass.

Off-diagonal gluon propagator fits Yukawa-type function.

Propagation of off-diagonal gluons is limited to short range.

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 ${\rm U(1)}_3 \times {\rm U(1)}_8$ Landau gauge fixing in SU(3) quenched lattice QCD on $16^4$ at $\beta$=5.7, 5.8 and 6.0. The off-diagonal gluon component behaves as a massive vector boson with the approximate effective 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 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.