Refinements in electroweak contributions to the muon anomalous magnetic   moment
  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 logs are shown to be unaffected. Computation of long-distance contributions is improved by 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 logs are reevaluated. These refinements lead to a reduction in uncertainties and a slight shift in the total electroweak contribution to $a_\mu^{\rm EW} = 154(1)(2)\times 10^{-11}$ where the first error corresponds to hadronic uncertainties and the second is primarily due to the allowed Higgs mass range. 
Andrzej Czarnecki, William J. Marciano and Arkady Vainshtein