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.
Highlights
There are many hadronic quantities from which the strong coupling, αsðpsÞffiffi, can be extracted, at many different energy scales E 1⁄4 s, as long as s is large enough that QCD perturbation theory can be expected to apply
Quoting our results at the τ mass to facilitate comparison to the results obtained from analogous analyses of hadronic τ-decay data, we find αsðm2τ Þ 1⁄4 0.298 Æ 0.016 Æ 0.006 in fixed-order perturbation theory, and αsðm2τ Þ 1⁄4 0.304 Æ 0.018 Æ 0.006 in contour-improved perturbation theory, where the first error is statistical, and the second error reflects our estimate of various systematic effects
II B and II C we review the theoretical representation for large q2 away from the Minkowski axis q2 1⁄4 s, based on the operator product expansion (OPE)
Summary
There are many hadronic quantities from which the strong coupling, αsðpsÞffiffi, can be extracted, at many different energy scales E 1⁄4 s, as long as s is large enough that QCD perturbation theory can be expected to apply. It would be interesting to apply and test the same techniques in a similar setting where no such limit exists This leads us to consider, instead of τ decays, the R-ratio RðsÞ, measured in the process eþe− → hadronsðγÞ, which is directly proportional to the electromagnetic (EM) QCD vector spectral function.. The associated FESR determinations of αs are expected to be much more precise than those obtained by matching the perturbative expression for RðsÞ to the spectral data directly. While resonance effects are still present in the region m2τ ≤ s ≤ 4 GeV2, it turns out that our central value for αs from RðsÞ is much less sensitive to the treatment of residual duality violations than was the case for τ-based analyses, with the modeling of these effects only needed as part of the analysis of systematic errors.
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