## Abstract

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant α and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including O(α^{5}) with negligible numerical uncertainty. The electroweak contribution is suppressed by (m_{μ}∕M_{W})^{2} and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at O(α^{2}) and is due to hadronic vacuum polarization, whereas at O(α^{3}) the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads a_{μ}^{SM}=116591810(43)×10^{−11} and is smaller than the Brookhaven measurement by 3.7σ. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce 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.

Original language | English |
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Pages (from-to) | 1-166 |

Number of pages | 166 |

Journal | Physics Reports |

Volume | 887 |

DOIs | |

Publication status | Published - 3 Dec 2020 |

## Keywords

- PION FORM-FACTOR
- 6TH-ORDER RADIATIVE-CORRECTIONS
- HADRONIC CROSS-SECTION
- BY-LIGHT CONTRIBUTION
- VACUUM POLARIZATION INSERTIONS
- FINE-STRUCTURE CONSTANT
- VIRTUALITY 2-PHOTON INTERACTIONS
- PHOTON SCATTERING CONTRIBUTION
- MONTE-CARLO GENERATOR
- RANGE 600-1380 MEV