Evaluation of Α(m

This talk summarizes the recent developments in the evaluation of the leading order hadronic contributions to the running of the QED fine structure constant α(s), at s = M Z, and to the anomalous magnetic moment of the muon (g−2)μ. The accuracy of the theoretical prediction of these observables is limited by the uncertainties on the hadronic contributions. Significant improvement has been achieved in a series of new analyses which is presented historically in three steps: (I), use of τ spectral functions in addition to ee cross sections, (II), extended use of perturbative QCD and (III), application of QCD sum rule techniques. The most precise values obtained are: ∆αhad(M 2 Z)= (276.3 ± 1.6) × 10 , yielding α(M Z) = 128.933 ± 0.021, and a had μ = (692.4 ± 6.2) × 10 −10 with which one finds for the complete Standard Model prediction a μ = (11 659 159.6± 6.7)× 10 . For the electron (g − 2)e, the hadronic contribution is a had e = (187.5 ± 1.8) × 10 .