QCD (lattice) potential and coupling: How to accurately interpolate between multiloop QCD and the string picture

We present a simple parametrization of the running coupling constant {alpha}{sub {ital V}}({ital q}), defined via the static potential, that interpolates between two-loop QCD in the UV and the string prediction {ital V}({ital r})={sigma}{ital r}{minus}{pi}/12{ital r} in the IR. In addition to the usual {Lambda} parameter and the string tension {sigma}, {alpha}{sub {ital V}}({ital q}) depends on one dimensionless parameter, determining how fast the crossover from UV to IR behavior occurs (in principle we know how to take into account any number of loops by adding more parameters). Using a new {ital Ansatz} for the {ital lattice} potential in terms of the {ital continuum} {alpha}{sub {ital V}}({ital q}), we can fit quenched and unquenched Monte Carlo results for the potential down to {ital one} lattice spacing, and at the same time extract {alpha}{sub {ital V}}({ital q}) to high precision. We compare our {ital Ansatz} with one-loop results for the lattice potential, and use {alpha}{sub {ital V}}({ital q}) from our fits to quantitatively check the accuracy of two-loop evolution, compare with the Lepage-Mackenzie estimate of the coupling extracted from the plaquette, and determine Sommer`s scale {ital r}{sub 0} much more accurately than previously possible. For pure SU(3) we find that {alpha}{sub {ital V}}({ital q}) scales on the percent level for {beta}{ge}6.