Yang Mills short distance potential and perturbation theory

Abstract

We compute the coupling $\alpha_\mathrm{qq}$ defined in terms of the static quark force by simulating the $\mathrm{SU}(3)$ Yang-Mills theory at lattice spacings down to $10^{-2}$~fm, keeping the volume large. In order to systematically improve the approach to the continuum, we subtract the leading cutoff effects in Symanzik's effective theory, resumming the leading $\log(a/r)$-term by renormalization group improvement. Subsequently we extrapolate with $\bar g^2(a^{-1})^{\hat \gamma_1}\,(a/r)^2$ corrections to the continuum limit. We finally investigate the applicability of continuum perturbation theory, extract the pure-gauge $\Lambda$-parameter at different values of $\alpha_\mathrm{qq}$ and different orders of perturbation theory and compare to other methods.