We compute the coupling αqq defined in terms of the static quark force by simulating the 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 ˉg2(a−1)ˆγ1(a/r)2 corrections to the continuum limit.
We finally investigate the applicability of continuum perturbation theory, extract the pure-gauge Λ-parameter at different values of αqq and different orders of perturbation theory and compare to other methods.