Precision determination of r₀ΛMS from the QCD static energy

We use the recently obtained theoretical expression for the complete QCD static energy at next-to-next-to-next-to leading-logarithmic accuracy to determine r₀ΛMS by comparison with available lattice data, where r₀ is the lattice scale and ΛMS is the QCD scale. We obtain r₀ΛMS=0.637(+0.032)(-0.030) [corrected] for the zero-flavor case. The procedure we describe can be directly used to obtain r₀ΛMS in the unquenched case, when unquenched lattice data for the static energy at short distances becomes available. Using the value of the strong coupling α(s) as an input, the unquenched result would provide a determination of the lattice scale r₀.