Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in Maximally Abelian Gauge in SU(3) Lattice QCD

TL;DR

This study uses SU(3) lattice QCD to analyze off-diagonal gluon mass generation and demonstrates infrared Abelian dominance, revealing that off-diagonal gluons behave as massive particles with short-range propagation.

Contribution

First to analytically extract gauge fields from link-variables in SU(3) lattice QCD, and to study off-diagonal gluon masses and infrared Abelian dominance in the maximally Abelian gauge.

Findings

Off-diagonal gluons have an effective mass of about 1.1-1.2 GeV.

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

Diagonal gluons propagate over larger distances, supporting Abelian dominance.

Abstract

In SU(3) lattice QCD formalism, we propose a method to extract gauge fields from link-variables analytically. With this method, we perform the first study on effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. Using SU(3) lattice QCD, we investigate the propagator and the effective mass of the gluon fields in the MA gauge with U(1)$_3 \timesU(1)_8$ Landau gauge fixing. The Monte Carlo simulation is performed on $16^4$ at $\beta$=5.7, 5.8 and 6.0 at the quenched level. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass $M_{\mathrm{off}} \simeq 1.1-1.2\mathrm{GeV}$ in the region of $r =0.3-0.8$fm, and the propagation is limited within a short range, while the propagation of diagonal gluons remains even in a large range. In this way, infrared Abelian dominance is shown in terms of short-range propagation of off-diagonal gluons. Furthermore, we investigate the functional form of the off-diagonal gluon propagator. The functional form is well described by the four-dimensional Euclidean Yukawa-type function $e^{-m_{\rm off}r}/r$ with $m_{\rm off} \simeq 1.3-1.4\mathrm{GeV}$ for $r = 0.1- 0.8$ fm. This also indicates that the spectral function of off-diagonal gluons has the negative-value region.