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Asymptotic scaling and continuum limit of pure SU(3) lattice gauge theory

Recently the Yang-Mills gradient flow of pure SU(3) lattice gauge theory has been calculated in the range from $β=6/g_0^2=6.3$ to~7.5 (Asakawa et al.), where $g_0^2$ is the bare coupling constant of the SU(3) Wilson action. Estimates of the deconfining phase transition are available from $β=5.7$ to~6.8 (Francis et al.). Here it is shown that the entire range from 5.7 to 7.5 is well described by a power series of the lattice spacing $a$ times the lambda lattice mass scale $Λ_L$, using asymptotic scaling in the 2-loop and 3-loop approximations for $aΛ_L$. In both cases identical ratios for gradient flows versus deconfinement observables are obtained. Differences in the normalization constants with respect to $Λ_L$ give a handle on their systematic errors.