Electroweak corrections to the muon anomalous magnetic moment

Abstract

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 $\Delta a_{\mu }^{\mathrm{EW}}(2\mathrm{loop}\mathrm{bosonic})/a_{\mu }^{\mathrm{EW}}(1\mathrm{loop})\approx \frac{\alpha }{\pi }\left(-3.6\ln \left(\frac{M_W^2}{m_{\mu }^2}\right)+0.10\right)\approx -0.11$ 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 $195\times 10^{-11}$ 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.

Comments: Revtex, 10 pages. Corrected version, submitted to Phys. Rev. Lett. Two-loop electroweak corrections to anomalous magnetic moments of electron and tau are included