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

Abstract

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.