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

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 approach the determination of σ(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 Λ -parameter, with special care on the perturbative truncation uncertainties.