Predictions forg−2of the muon andαQED(MZ2)

We calculate $g-2$ of the muon and the QED coupling $\alpha {(M}_Z^2),$ by improving the determination of the hadronic vacuum polarization contributions and their uncertainties. We include the recently reanalyzed CMD-2 data on $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}.$ We carefully combine a wide variety of data for the $e^{+}{e}^{-}$ production of hadrons and obtain the optimum form of $R\left(s\right)\mathrm{}\equiv {\sigma }_{\mathrm{had}}^0\mathrm{}\left(s\right)/{\sigma }_{\mathrm{pt}}\mathrm{}\left(s\right),$ together with its uncertainty. Our results for the hadronic contributions to $g-2$ of the muon are $a_{\mu }^{\mathrm{h}\mathrm{a}\mathrm{d},\mathrm{L}\mathrm{O}}=(692.4\mathrm{}\pm {5.9}_{\exp }\pm {2.4}_{\mathrm{rad}})\times {10}^{-10}$ and $a_{\mu }^{\mathrm{h}\mathrm{a}\mathrm{d},\mathrm{N}\mathrm{L}\mathrm{O}}=(-9.8\pm {0.1}_{\exp }\pm {0.0}_{\mathrm{rad}})\times {10}^{-10},$ and for the QED coupling $\Delta {\alpha }_{\mathrm{had}}^{\mathrm{}\left(5\right)\mathrm{}}{(M}_Z^2)=(275.5\mathrm{}\pm {1.9}_{\exp }\pm {1.3}_{\mathrm{rad}})\times {10}^{-4}.$ These yield $\left(g-2\right)/2=0.00116591763\left(74\right),$ which is about $2.4\sigma$ below the present world average measurement, and $\alpha {(M}_Z^2{)}^{-1}=128.954\mathrm{}\pm \mathrm{0.031.}$ We compare our $g-2$ value with other predictions and, in particular, make a detailed comparison with the latest determination of $g-2$ by Davier et al.