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

We determine the strong coupling constant αs 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(ΛQCD) but also the first r-dependent uncertainty of OΛQCD3r2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}^3{r}^2\right) $$\end{document}. The theoretical prediction for the potential turns out to be valid at the static color charge distance ΛMS¯r≲0.8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Lambda}_{\overline{\mathrm{MS}}}r\lesssim 0.8 $$\end{document} (r ≲ 0.4 fm), which is significantly larger than ordinary perturbation theory. With lattice data down to ΛMS¯r∼0.09\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Lambda}_{\overline{\mathrm{MS}}}r\sim 0.09 $$\end{document} (r ∼ 0.05 fm), we perform the matching in a wide region of r, which has been difficult in previous determinations of αs from the potential. Our final result is αs(MZ2) = 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.