A perturbation theory driven analysis of the effective QED coupling at MZ

An evaluation of the effective QED coupling at the scale MZ is presented. It employs the predictions of perturbative QCD for the cross section of electron positron annihilation into hadrons up to order αs2, including the full quark mass dependence, and of order αs3 in the high energy region. This allows to predict the input for the dispersion relations over a large part of the integration region. The perturbative piece is combined with data for the lower energies. The normalization of data from the heavy quark thresholds is deduced from a comparison between data and pQCD below and above the threshold region. The result for the hadronic contribution to the running of the coupling Δα(5)had(MZ2)=(277.5±1.7)×10−4 leads to (α(MZ2))−1=128.927±0.023. Compared to previous analyses which were based on data only the uncertainty is significantly reduced. This is due to our assumption of perturbative QCD to be valid down to 1.8 GeV with the exception of the charm threshold and to our model for the normalization of the data in the region between 3.7 and 5.0 GeV. The error estimate is based on the variation of the renormalization scale μ2 and the parametric uncertainty of αs and the quark masses. The absence of large nonperturbative contributions is assumed.