Determination of ${\alpha }_s$ from static QCD potential: OPE with renormalon subtraction and lattice QCD

Abstract

We determine the strong coupling constant ${\alpha }_s$ 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 $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ but also the first $r$-dependent uncertainty of $\mathcal{O}({\Lambda }_{\mathrm{QCD}}^3{r}^2)$. The theoretical prediction for the potential turns out to be valid at the static color charge distance ${\Lambda }_{\overline{\mathrm{MS}}}r\lesssim 0.8$ ($r\lesssim 0.4$ fm), which is significantly larger than ordinary perturbation theory. With lattice data down to ${\Lambda }_{\overline{\mathrm{MS}}}r\sim 0.09$ ($r\sim 0.05$ fm), we perform the matching in a wide region of $r$, which has been difficult in previous determinations of ${\alpha }_s$ from the potential. Our final result is ${\alpha }_s(M_Z^2)=0.1179_{-0.0014}^{+0.0015}$ 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.

Version to appear in JHEP, Supplementary analyses added in Appendix F; other modifications are minor, 42 pages

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