α_{S} from F_{π} and Renormalization Group Optimized Perturbation

Abstract

A new version of the so-called optimized perturbation (OPT), implementing consistently renormalization group properties, is used to calculate the nonperturbative ratio $F_\pi/\overline\Lambda$ of the pion decay constant and the basic QCD scale in the $\overline{MS}$ scheme. Using the experimental $F_\pi$ input value it provides a new determination of $\overline\Lambda$ for $n_f=2$ and $n_f=3$, and of the QCD coupling constant $\overline\alpha_S $ at various scales once combined with a standard perturbative evolution. The stability and empirical convergence properties of the RGOPT modified series is demonstrated up to the third order. We examine the difference sources of theoretical uncertainties and obtain $\overline\alpha_S (m_Z) =0.1174 ^{+.0010}_{-.0005} \pm .001 \pm .0005_{evol}$, where the first errors are estimates of the intrinsic theoretical uncertainties of our method, and the second errors come from present uncertainties in $F_\pi/F_0$, where $F_0$ is $F_\pi$ in the exact chiral $SU(3)$ limit.