Using the Landau gauge gluon propagator to set the lattice physical scales and understanding the finite size effects

TL;DR

This paper presents a method to set the physical scale in lattice QCD using the Landau gauge gluon propagator, effectively addressing finite size effects and connecting lattice results with continuum perturbation theory.

Contribution

The paper introduces a new procedure for relative scale setting in lattice QCD using the gluon propagator and models finite size effects with an effective approach inspired by perturbation theory.

Findings

Effective handling of finite size effects in lattice simulations.

Linking lattice results with continuum perturbation theory at high momenta.

Demonstration of the method's extension to other Green functions.

Abstract

A crucial step in extracting physical predictions from lattice QCD simulations is the scale setting, i.e. the determination of the lattice spacing ($a$) in physical units. Herein, the relative scale setting for different $\beta$'s is discussed, using the Landau gauge gluon propagator computed with large statistical ensembles. After setting the relative scales, finite size effects are observed in the ultraviolet regime and handled in an effective description, inspired in perturbation theory. The new devised procedure is efficient in handling the finite size effects, linking the lattice simulations with continuum perturbation theory for the high momenta regime. Furthermore, the procedure can be extended to handle other Green functions computed within lattice QCD simulations.