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

TL;DR

This paper determines the strong coupling constant $_s$ from $e^+e^- o$ hadrons data below 2 GeV using finite-energy sum rules, achieving results consistent with tau decay analyses and previous experiments.

Contribution

It introduces a new compilation of the hadronic $R$-ratio data below 2 GeV and applies finite-energy sum rules to extract $_s$, providing a precise determination consistent with tau decay results.

Findings

_s(m_ au^2)=0.298 extpm 0.016 extpm 0.006 in fixed-order perturbation theory

_s(m_ au^2)=0.304 extpm 0.018 extpm 0.006 in contour-improved perturbation theory

Results agree with recent tau decay analyses and OPAL/ALEPH data.

Abstract

We use a new compilation of the hadronic $R$-ratio from available data for the process $e^+e^-\to\mbox{hadrons}$ 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.