Improved Theory of the Muon Anomalous Magnetic Moment

A new theoretical value $a_{\mu }=11\mathrm{}659202\left(20\right)\mathrm{}\times {10}^{-10\mathrm{}}$ is reported for the muon anomalous moment, based on the first complete calculation of the ${\alpha }^4$ QED term and improvements of the ${\alpha }^3$ QED term and various hadronic contributions. The remaining error is mostly due to the experimental inputs needed for evaluation of the hadronic vacuum polarization effect. Further improvement of this error seems possible. Thus the electroweak theory may be tested at the one-loop level if measurement of $a_{\mu }$ is improved by an order of magnitude.