Evaluation of $\alpha (M_{\mathrm{Z}}^2)$ and $(g-2{)}_{\mu }$

Abstract

This talk summarizes the recent developments in the evaluation of the leading order hadronic contributions to the running of the QED fine structure constant $\alpha (s)$, at $s=M_{\mathrm{Z}}^2$, and to the anomalous magnetic moment 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: $\Delta {\alpha }_{\mathrm{had}}(M_{\mathrm{Z}}^2)$, $=(276.3\pm 1.6)\times 10^{-4}$, 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 $a_e^{\mathrm{had}}=(187.5\pm 1.8)\times 10^{-14}$.

Comments: 13 pages