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We determine the strong coupling constant $\alpha_s$ from the static QCDpotential by matching a theoretical calculation with a lattice QCD computation.We employ a new theoretical formulation based on the operator productexpansion, in which renormalons are subtracted from the leading Wilsoncoefficient. We remove not only the leading renormalon uncertainty of$\mathcal{O}(\Lambda_{\rm QCD})$ but also the first $r$-dependent uncertaintyof $\mathcal{O}(\Lambda_{\rm QCD}^3 r^2)$. The theoretical prediction for thepotential turns out to be valid at the static color charge distance$\Lambda_{\rm \overline{MS}} r \lesssim 0.8$ ($r \lesssim 0.4$ fm), which issignificantly larger than ordinary perturbation theory. With lattice data downto $\Lambda_{\rm \overline{MS}} r \sim 0.09$ ($r \sim 0.05$ fm), we perform thematching in a wide region of $r$, which has been difficult in previousdeterminations of $\alpha_s$ from the potential. Our final result is$\alpha_s(M_Z^2) = 0.1179^{+0.0015}_{-0.0014}$ with 1.3 % accuracy. Thedominant uncertainty comes from higher order corrections to the perturbativeprediction and can be straightforwardly reduced by simulating finer lattices.

Determination of $\alpha_s$ from static QCD potential: OPE with renormalon subtraction and lattice QCD