An analysis of systematic effects in finite size scaling studies using the gradient flow

TL;DR

This paper introduces a new method for determining the step scaling function in finite size scaling studies with gradient flow, improving control over continuum extrapolations and enabling precise high-energy running coupling measurements.

Contribution

A novel two-step approach for calculating the step scaling function in finite size scaling studies using gradient flow, enhancing continuum extrapolation accuracy.

Findings

Improved control over continuum extrapolations.

Accurate determination of the running coupling at high energies.

Re-evaluation of the $oldsymbol{ ext{Lambda}}$-parameter with reduced uncertainties.

Abstract

We propose a new strategy for the determination of the step scaling function $\sigma(u)$ in finite size scaling studies using the Gradient Flow. In this approach the determination of $\sigma(u)$ is broken in two pieces: a change of the flow time at fixed physical size, and a change of the size of the system at fixed flow time. Using both perturbative arguments and a set of simulations in the pure gauge theory we show that this approach leads to a better control over the continuum extrapolations. Following this new proposal we determine the running coupling at high energies in the pure gauge theory and re-examine the determination of the $\Lambda$-parameter, with special care on the perturbative truncation uncertainties.