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

Keywords

• QCD Phenomenology
• Lattice field theory simulation