SU(2) lattice gluon propagator: continuum limit, finite-volume effects and infrared mass scale m_IR

TL;DR

This study investigates the SU(2) lattice gluon propagator, analyzing finite-volume effects, continuum limit behavior, and the infrared mass scale, revealing non-perturbative features and the importance of Gribov copies in the deep infrared region.

Contribution

It provides a detailed analysis of the SU(2) gluon propagator's scaling, finite-volume effects, and Gribov copy dependence, including the estimation of the infrared mass scale.

Findings

Continuum limit approached for momenta above 0.6 GeV

Finite-volume and Gribov copy effects are small above 0.6 GeV

Infrared behavior fits a Gaussian, estimating m_IR ~ 0.7 GeV

Abstract

We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU(2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from $(3.0 \mathrm{fm})^4$ to $(7.3 \mathrm{fm})^4$. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (non-perturbative) multiplicative renormalizability and the approach to the {\it continuum limit} for the renormalized gluon propagator $D_{ren}(p)$ at momenta $|p| \ageq 0.6$ GeV >. The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found the Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple pole-like behavior $\sim (p^2+m_g^2)^{-1}$ for momenta $|p| \aleq 0.6$ GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume $(5.0 \mathrm{fm})^4$ - we estimate a corresponding infrared (mass) scale to be $m_\mathrm{IR} \sim 0.7 $ GeV.