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.

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