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

Abstract

Abstract 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 $$ \mathcal{O} $$ O (ΛQCD) but also the first r-dependent uncertainty of $$ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}^3{r}^2\right) $$ O Λ Q C D 3 r 2 . The theoretical prediction for the potential turns out to be valid at the static color charge distance $$ {\Lambda}_{\overline{\mathrm{MS}}}r\lesssim 0.8 $$ Λ M S ¯ r ≲ 0.8 (r ≲ 0.4 fm), which is significantly larger than ordinary perturbation theory. With lattice data down to $$ {\Lambda}_{\overline{\mathrm{MS}}}r\sim 0.09 $$ 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.