The strong coupling from $e^+e^-\to$ hadrons

Abstract

We use a new compilation of the hadronic $R$-ratio from available data for the process $e^+e^-\to$ hadrons below the charm mass to determine the strong coupling $α_s$, using finite-energy sum rules. Quoting our results at the $τ$ mass to facilitate comparison to the results obtained from similar analyses of hadronic $τ$-decay data, we find $α_s(m_τ^2)=0.298\pm 0.016\pm 0.006$ in fixed-order perturbation theory, and $α_s(m_τ^2)=0.304\pm 0.018\pm 0.006$ in contour-improved perturbation theory, where the first error is statistical, and the second error combines various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic $τ$ decays. We briefly compare the $R(s)$-based analysis with the $τ$-based analysis.