Determination of α _s from static QCD potential: OPE with renormalon subtraction and lattice QCD

We determine the strong coupling constant α _s from the static QCD potential by matching a theoretical calculation with a lattice QCD computation. We employ a new theoretical formulation based on the operator product expansion, in which renormalons are subtracted from the leading Wilson coefficient. We remove not only the leading renormalon uncertainty of O(Λ _QCD ) but also the first r-dependent uncertainty of O(ΛQCD3r2). The theoretical prediction for the potential turns out to be valid at the static color charge distance Λ _{M S ¯} r≲ 0.8 (r ≲ 0.4 fm), which is significantly larger than ordinary perturbation theory. With lattice data down to Λ _{M S ¯} r∼ 0.09 (r ∼ 0.05 fm), we perform the matching in a wide region of r, which has been difficult in previous determinations of α _s from the potential. Our final result is α _s (M _Z ² ) = 0.1179 _{− 0.0014} ^{+ 0.0015} with 1.3% accuracy. The dominant uncertainty comes from higher order corrections to the perturbative prediction and can be straightforwardly reduced by simulating finer lattices.