Electroweak Corrections to the Muon Anomalous Magnetic Moment

Abstract

Bosonic two-loop electroweak radiative corrections to the muon's anomalous magnetic moment, $a_{\mu }\equiv \frac{(g_{\mu }-2)}{2}$, are presented. We find $\frac{\Delta a_{\mu }^{\mathrm{EW}}\left(2\mathrm{} \mathrm{loop}\mathrm{bosonic}\right)}{a_{\mu }^{\mathrm{EW}}\left(1\mathrm{} \mathrm{loop}\right)}\approx \left(\frac{\alpha }{\pi }\right)\times [-3.6\mathrm{}\ln (\frac{M_W^2}{m_{\mu }^2})+0.10]\approx -0.11\mathrm{}$ for $M_{\mathrm{Higgs}}\approx 250$ GeV. Combining that result with our previous two-loop fermionic calculation, we obtain an overall 22.6% reduction in $a_{\mu }^{\mathrm{EW}}$ from 195 × ${10}^{-11\mathrm{}}$ to 151(4) × ${10}^{-11\mathrm{}}$. 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.