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 beta = 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 beta = 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 Lambda(L), using asymptotic scaling in the 2-loop and 3-loop approximations for a Lambda(L). In both cases identical ratios for gradient flows versus deconfinement observables are obtained. Differences in the normalization constants with respect to Lambda(L) give a handle on their systematic errors.