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.
Highlights
In this work we study the main sources of systematic effects in finite-size scaling studies using the GF
We propose a new strategy for the determination of the step scaling function σ (u) in finite size scaling studies using the gradient flow
In this work we have examined the main sources of uncertainties present in finite-size scaling studies using the Gradient Flow: the continuum extrapolation and the statistical uncertainties
Summary
In this work we study the main sources of systematic effects in finite-size scaling studies using the GF. On the contrary, when different finite volume couplings are determined at the same value of the flow time t, the scaling violations are very small. This observation will be supported by a non-perturbative study. It will allow us to propose a new strategy for the determination of the step scaling function by breaking it up into two pieces: first a change in the flow time, without any change in the volume, second a change in the volume without any change in the flow time. We include an analysis of the variance of flow observables, allowing us to predict the dependence of the statistical uncertainties with the flow time t
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