The strong coupling from $e^{+}{e}^{-}\to$ hadrons below charm

Abstract

We use a new compilation of the hadronic $R$-ratio from available data for the process $e^{+}{e}^{-}\to \text{mbox}hadrons$ to determine the strong coupling, ${\alpha }_s$. We make use of all data for the $R$-ratio from threshold to a center-of-mass energy of 2 GeV by employing finite-energy sum rules. Data above 2 GeV, for which at present far fewer high-precision experimental data are available, do not provide much additional constraint but are fully consistent with the values for ${\alpha }_s$ we obtain. Quoting our results at the $\tau$ mass to facilitate comparison to the results obtained from analogous 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 reflects our estimate of various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic $\tau$ decays.

Comments: 31 pages, 9 figures