Evaluation of α(M^2_Z) and (g-2)_μ

Abstract

This talk summarizes the recent development in the evaluation of the leading order hadronic contributions to the running of the QED fine structure constant α(s), at $s=M_{\mathrm{Z}}^2$, and to the anomalous magnetic moments of the muon $(g-2{)}_{\mu }$. 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 $\tau$ 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: $\Delta {\alpha }_{had}(M_2^Z)=(276.3\pm 1.6)\times 10^{-4}$, yielding ${\alpha }^{-1}(M_{\mathrm{Z}}^2)=128.933\pm 0.021$, and $a_{\mu }^{\mathrm{had}}=(692.4\pm 6.2)\times 10^{-10}$ with which one finds for the complete Standard Model prediction $a_{\mu }^{\mathrm{SM}}=(11659159.6\pm 6.7)\times 10^{-10}$. For the electron $(g-2{)}_e$, the hadronic contribution is $a_e^{\mathrm{had}}=(187.5\pm 1.8)\times 10^{-14}$.

9 pages, Talk given at the ICHEP'98 Conference, Vancouver, Canada, July 23-29, 1998