Electroweak corrections to the muon anomalous magnetic moment

The bosonic two-loop electroweak radiative corrections to the muon's anomalous magnetic moment, $a_\mu\equiv (g_\mu-2)/2$, are presented. We find $\Delta a_\mu^{\rm EW}({\rm 2\,loop\, bosonic})/ a_\mu^{\rm EW}({\rm 1\,loop})\approx {\alpha\over \pi}\left(-3.6 \ln\left({M_W^2\over m_\mu^2}\right) +0.10 \right)\approx -0.11$ for $M_{\rm Higgs}\approx 250$ GeV. Combining that result with our previous two-loop fermionic calculation, we obtain an overall 22.6\% reduction in $a_\mu^{\rm EW}$ from $195\times 10^{-11}$ to $151(4)\times 10^{-11}$. Implications for the full standard model prediction and an upcoming high precision measurement of $a_\mu$ are briefly discussed. We also give the two-loop electroweak corrections to the anomalous magnetic moments of electron and tau lepton; they result in a reduction of the one-loop estimates by 35\% and 15\%, respectively.