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.

我们提出了一种新的策略，用于确定使用梯度流进行的有限尺寸缩放研究中的步阶缩放函数\（\ sigma（u）\）。在这种方法中，\（\ sigma（u）\）的确定分为两部分：固定物理尺寸下流动时间的变化和固定流动时间下系统尺寸的变化。使用纯规范理论中的摄动论证和一组模拟，我们证明了这种方法可以更好地控制连续谱外推法。根据这一新建议，我们在纯规范理论中确定高能量下的运行耦合，并重新检查\（\ Lambda \）参数的确定，并特别注意扰动截断的不确定性。