Lattice QCD Study for Gluon Propagator and Gluon Spectral Function

TL;DR

This study investigates the gluon propagator in lattice QCD, revealing a Yukawa-type behavior in the infrared, an effective gluon mass around 600 MeV, and a spectral function mostly negative, suggesting dimensional reduction effects.

Contribution

It provides a detailed analysis of the gluon propagator and spectral function in lattice QCD, proposing a Yukawa-type model and exploring effective dimensional reduction in the infrared regime.

Findings

Gluon propagator fits Yukawa-type function in infrared

Effective gluon mass estimated at ~600 MeV

Gluon spectral function is mostly negative with a delta peak

Abstract

We study the gluon propagator in the Landau gauge in SU(3) lattice QCD at $\beta$=5.7, 5.8 and 6.0 at the quenched level. The Euclidean Landau-gauge gluon propagator $D(r)\equiv D_{\mu\mu}^{aa}(x)/24$ is found to be well described by four-dimensional Yukawa-type function $e^{-mr}/r$ in the infrared and intermediate region of $r \equiv (x_\mu x_\mu)^{1/2}$ = 0.1 $\sim$ 1.0fm. The infrared effective gluon mass is obtained as $m \simeq$ 600MeV. Associated with the 4D Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff}(t)$, and the spectral function $\rho(\omega)$ of the gluon field. Remarkably, the obtained gluon spectral function $\rho(\omega)$ is almost negative definite, except for a positive $\delta$-functional peak at $\omega=m$. Since the Yukawa-type propagation indicates a three-dimensional space-time character, we consider a hypothesis of an effective dimensional reduction by generalized Parisi-Sourlas mechanism in a stochastic color-magnetic vacuum of infrared QCD.