Lattice artefacts on the Landau gauge gluon propagator from hypercubic tensor representations

TL;DR

This paper investigates how hypercubic lattice symmetries affect the Landau gauge gluon propagator in SU(3) Yang-Mills theory, quantifying deviations from continuum expectations and identifying configurations with minimal artifacts.

Contribution

It introduces a tensor basis approach respecting lattice symmetries to analyze lattice artifacts and estimates the uncertainty in the gluon propagator due to hypercubic effects.

Findings

Lattice correlation functions differ from continuum due to hypercubic symmetry.

A unique form factor describes the lattice Landau gauge gluon propagator.

Certain kinematic configurations minimize lattice artifacts.

Abstract

Lattice tensor representations are used to investigate the lattice Landau gauge gluon propagator for the 4-dimensional pure SU(3) Yang-Mills gauge theory. Due to the different symmetry structure of hypercubic lattices compared to the continuum space-time, lattice correlation functions are described by different tensor structures. Therefore, form factors describing lattice correlation functions have, in principle, non-trivial relations with the continuum counterparts. The use of several tensor bases respecting lattice symmetries, and the analysis of its completeness allows to quantify the deviations of the lattice results from the continuum theory, and also estimate the theoretical uncertainty in the propagator. Furthermore, our analysis tests continuum based relations with the lattice data and shows that the lattice Landau gauge gluon propagator is suitably described by a unique form factor, as in the continuum formulation. Additionally, we identified classes of kinematic configurations where these deviations are minimal and the continuum description of lattice tensors is improved.