Improved gradient flow for step scaling function and scale setting

TL;DR

This paper presents an empirical non-perturbative improvement method for the gradient flow renormalized coupling, reducing lattice artifacts in step scaling and scale setting for lattice gauge theories, demonstrated on SU(3) systems and QCD.

Contribution

The paper introduces a simple, non-perturbative improvement technique to reduce lattice artifacts in gradient flow calculations, applicable to various lattice gauge theories.

Findings

Reduced lattice artifacts in step scaling functions

Improved accuracy in scale setting for lattice QCD

Effective application to SU(3) flavor systems

Abstract

The gradient flow renormalized coupling offers a simple and relatively inexpensive way to calculate the step scaling function and the lattice scale, but both applications can be hindered by large lattice artifacts. Recently we introduced an empirical non-perturbative improvement that can reduce, even remove $\mathcal{O}(a^2)$ lattice artifacts. The method is easy to implement and can be applied to any lattice gauge theory of interest both in step scaling studies and for scale setting. In this talk I will briefly review this improvement method and discuss its application for determining the discrete $\beta$ function of the 8 and 12 flavor SU(3) systems and for improved scale setting in 2+1+1 flavor QCD