The anomalous magnetic moment of the muon in the Standard Model

We review the present status of the Standard Model calculation of the anomalousmagnetic moment of the muon. This is performed in a perturbative expansion in thefine-structure constantαand is broken down into pure QED, electroweak, and hadroniccontributions. The pure QED contribution is by far the largest and has been evaluatedup to and includingO(α5) with negligible numerical uncertainty. The electroweakcontribution is suppressed by (mμ/MW)2and only shows up at the level of the seventhsignificant digit. It has been evaluated up to two loops and is known to better than onepercent. Hadronic contributions are the most difficult to calculate and are responsiblefor almost all of the theoretical uncertainty. The leading hadronic contribution appearsatO(α2) and is due to hadronic vacuum polarization, whereas atO(α3) the hadroniclight-by-light scattering contribution appears. Given the low characteristic scale of thisobservable, these contributions have to be calculated with nonperturbative methods, inparticular, dispersion relations and the lattice approach to QCD. The largest part of thisreview is dedicated to a detailed account of recent efforts to improve the calculationof these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result readsaSMμ=116591810(43)×10−11andissmallerthantheBrookhavenmeasurementby3.7σ.Theexperimentaluncertaintywill soon be reduced by up to a factor four by the new experiment currently running atFermilab, and also by the future J-PARC experiment. This and the prospects to furtherreduce the theoretical uncertainty in the near future – which are also discussed here– make this quantity one of the most promising places to look for evidence of new physics.