Electroweak Corrections to the Muon Anomalous Magnetic Moment

Abstract

Bosonic two-loop electroweak radiative corrections to the muon's anomalous magnetic moment, ${a}_{\ensuremath{\mu}}\ensuremath{\equiv}\frac{({g}_{\ensuremath{\mu}}\ensuremath{-}2)}{2}$, are presented. We find $\frac{\ensuremath{\Delta}{a}_{\ensuremath{\mu}}^{\mathrm{EW}}(2 \mathrm{loop}\mathrm{bosonic})}{{a}_{\ensuremath{\mu}}^{\mathrm{EW}}(1 \mathrm{loop})}\ensuremath{\approx}(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})\ifmmode\times\else\texttimes\fi{}[\ensuremath{-}3.6\mathrm{ln}(\frac{{M}_{W}^{2}}{{m}_{\ensuremath{\mu}}^{2}})+0.10]\ensuremath{\approx}\ensuremath{-}0.11$ for ${M}_{\mathrm{Higgs}}\ensuremath{\approx}250$ GeV. Combining that result with our previous two-loop fermionic calculation, we obtain an overall 22.6% reduction in ${a}_{\ensuremath{\mu}}^{\mathrm{EW}}$ from 195 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ to 151(4) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$. Implications for the full standard model prediction and an upcoming high precision measurement of ${a}_{\ensuremath{\mu}}$ 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.