$H(4)$ tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts

TL;DR

This paper investigates lattice tensor representations to analyze the Landau gauge gluon propagator in SU(3) Yang-Mills theory, quantifying lattice artefacts and confirming continuum relations in 4D.

Contribution

It introduces a comprehensive analysis of tensor bases to assess lattice artefacts and validates continuum relations for the gluon propagator on the lattice.

Findings

Quantified deviations due to lattice artefacts.

Confirmed a unique form factor describes the propagator.

Validated continuum relations with lattice data.

Abstract

The use of lattice tensor representations is explored to investigate the lattice Landau gauge gluon propagator for the pure SU(3) Yang-Mills gauge theory in 4D. The analysis of several tensor bases allows to quantify the completeness of the various tensor bases considered, the deviations of the lattice results from the continuum theory due to the lattice artefacts and estimate the theoretical uncertainty in the propagator. Furthermore, our analysis tests continuum based relations with the lattice data and show that the lattice Landau gauge gluon propagator is described by a unique form factor, as in the continuum formulation.