New results on the hadronic contributions to α(MZ2) and to (g−2)μ

We reevaluate the dispersion integrals of the leading order hadronic contributions to the running of the QED fine structure constant α(s) at s=MZ2, and to the anomalous magnetic moments of the muon and the electron. Finite-energy QCD sum rule techniques complete the data from e+e− annihilation and τ decays at low energy and at the cc̄ threshold. Global quark-hadron duality is assumed in order to resolve the integrals using the Operator Product Expansion wherever it is applicable. We obtain Δαhad(MZ2) =(276.3±1.6)×10−4 yielding α−1(MZ2)=128.933±0.021, and aμhad=(692.4±6.2)×10−10 with which we find for the complete Standard Model prediction aμSM=(11 659 159.6±6.7)×10−10. For the electron, the hadronic contribution reads aehad=(187.5±1.8)×10−14. The following formulae express our results on the running of α at MZ2 as a function of the input value for αs(MZ2) and its error:Δαhad(MZ2)=(249.8+221αs(MZ2)±1.5±221Δαs(MZ2))×10−4 ,α−1(MZ2)=129.297−3.03αs(MZ2)±0.020±3Δαs(MZ2) .