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 ${\alpha }_s$, using finite-energy sum rules. Quoting our results at the $\tau$ mass to facilitate comparison to the results obtained from similar analyses of hadronic $\tau$-decay data, we find ${\alpha }_s(m_{\tau }^2)=0.298\pm 0.016\pm 0.006$ in fixed-order perturbation theory, and ${\alpha }_s(m_{\tau }^2)=0.304\pm 0.018\pm 0.006$ 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 $\tau$ decays. We briefly compare the $R(s)$-based analysis with the $\tau$-based analysis.

Comments: 11 pages, contribution to the International Workshop on Tau Lepton Physics, 2018