Determination of α_s from the QCD static energy

We compare lattice data for the short-distance part of the static energy in 2+1 flavor quantum chromodynamics (QCD) with perturbative calculations, up to next-to-next-to-next-to leading-logarithmic accuracy. We show that perturbation theory describes very well the lattice data at short distances, and exploit this fact to obtain a determination of the product of the lattice scale r ₀ with the QCD scale Λ_MS̄. With the input of the value of r₀, this provides a determination of the strong coupling α_s at the typical distance scale of the lattice data. We obtain α_s(1.5 GeV)=0.326±0.019, which provides a novel determination of α_s with three-loop accuracy (including resummation of the leading ultrasoft logarithms), and constitutes one of the few low-energy determinations of α_s available. When this value is evolved to the Z-mass scale M_Z, it corresponds to α_s(M_Z)=0.1156-0.0022+0.0021.