Improved gradient flow for step scaling function and scale setting

Understand

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