How to Accurately Extract the Running Coupling of QCD from Lattice Potential Data

By (a) using an expression for the LATTICE potential of QCD in terms of a CONTINUUM running coupling and (b) globally parameterizing this coupling to interpolate between 2- (or higher-) loop QCD in the UV and the flux tube prediction in the IR, we can perfectly fit lattice data for the potential down to ONE lattice spacing and at the same time extract the running coupling to high precision. This allows us to quantitatively check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie estimate of the coupling extracted from the plaquette, and determine the scale $r_0$ ten times more accurately than previously possible. For pure SU(3) we find that the coupling scales on the percent level for $\beta \geq 6$.