Refinements in electroweak contributions to the muon anomalous magnetic moment

Abstract

The effects of strong interactions on the two-loop electroweak radiative corrections to the muon anomalous magnetic moment, $a_{\mu }{=(g}_{\mu }-2)/2,$ are examined. Short-distance logarithms are shown to be unaffected. The computation of long-distance contributions is improved by the use of an effective field theory approach that preserves the chiral properties of QCD and accounts for constraints from the operator product expansion. Small, previously neglected, two-loop contributions, suppressed by a $1-4{\sin }^2{\theta }_W$ factor, are computed and the complete three-loop leading short-distance logarithms are reevaluated. These refinements lead to a reduction in uncertainties and a slight shift in the total electroweak contribution to $a_{\mu }^{\mathrm{EW}}=154\mathrm{}\left(1\right)\mathrm{}\left(2\right)\mathrm{}\times {10}^{-11}$ where the first error corresponds to hadronic uncertainties and the second is primarily due to the allowed Higgs boson mass range.