This talk summarizes the recent development in the evaluation of the leading
order hadronic contributions to the running of the QED fine structure constant
\alpha(s), at s=MZ2​, and to the anomalous magnetic moments 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 Ï„ spectral functions in
addition to e^+e^- cross sections, (II), extended use of perturbative QCD and
(III), application of QCD sum rule techniques. The most precise values obtained
are: Δαhad​(M2Z​)=(276.3±1.6)×10−4, yielding
α−1(MZ2​)=128.933±0.021, and aμhad​=(692.4±6.2)×10−10 with which one finds for the complete
Standard Model prediction aμSM​=(11659159.6±6.7)×10−10.
For the electron (g−2)e​, the hadronic contribution is aehad​=(187.5±1.8)×10−14.Comment: 9 pages, Talk given at the ICHEP'98 Conference, Vancouver, Canada,
July 23-29, 199