Electroweak Fermion-loop Contributions to the Muon Anomalous Magnetic Moment

The two-loop electroweak corrections to the anomalous magnetic moment of the muon, generated by fermionic loops, are calculated. An interesting role of the top quark in the anomaly cancellation is observed. New corrections, including terms of order $G_{\mu }\alpha m_t^2$, are computed and a class of diagrams previously thought to vanish are found to be important. The total fermionic correction is $-(23\pm 3)\times {10}^{-11}$ which decreases the electroweak effects on $g-2$, predicted from one-loop calculations, by 12%. We give an updated theoretical prediction for $g-2$ of the muon.