Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

The anomalous magnetic moment of the muon in the Standard Model

Aoyama, T. ; Bijnens, J. LU orcid ; Colangelo, G. ; Davier, M. ; Eidelman, S. I. ; El-Khadra, A. X. ; Hoferichter, M. ; Lehner, C. ; Mibe, T. and Nyffeler, A. , et al. (2020) In Physics Reports 887. p.1-166
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(α5) with negligible numerical uncertainty. The electroweak contribution is suppressed by (mμ∕MW)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... (More)

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(α5) with negligible numerical uncertainty. The electroweak contribution is suppressed by (mμ∕MW)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(α2) and is due to hadronic vacuum polarization, whereas at O(α3) 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 aμSM=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.

(Less)
Please use this url to cite or link to this publication:
author
; ; ; ; ; ; ; ; and , et al. (More)
; ; ; ; ; ; ; ; ; ; ; ; ; and (Less)
author collaboration
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physics Reports
volume
887
pages
166 pages
publisher
Elsevier
external identifiers
  • scopus:85095616279
ISSN
0370-1573
DOI
10.1016/j.physrep.2020.07.006
language
English
LU publication?
yes
id
ce662967-7a54-4c36-91e7-0837ecac0fc7
date added to LUP
2021-02-12 18:01:14
date last changed
2024-04-18 02:37:51
@article{ce662967-7a54-4c36-91e7-0837ecac0fc7,
  abstract     = {{<p>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<sup>5</sup>) with negligible numerical uncertainty. The electroweak contribution is suppressed by (<i>m<sub>μ</sub></i>∕<i>M<sub>W</sub></i>)<sup>2</sup> 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<sup>2</sup>) and is due to hadronic vacuum polarization, whereas at O(α<sup>3</sup>) 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<i><sub>μ</sub></i><sup>SM</sup>=116591810(43)×10<sup>−11</sup> 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.</p>}},
  author       = {{Aoyama, T. and Bijnens, J. and Colangelo, G. and Davier, M. and Eidelman, S. I. and El-Khadra, A. X. and Hoferichter, M. and Lehner, C. and Mibe, T. and Nyffeler, A. and Roberts, B. L. and Teubner, T. and Hermansson-Truedsson, N. and Rodríguez-Sánchez, A. and Zhevlakov, A.S.}},
  issn         = {{0370-1573}},
  language     = {{eng}},
  month        = {{12}},
  pages        = {{1--166}},
  publisher    = {{Elsevier}},
  series       = {{Physics Reports}},
  title        = {{The anomalous magnetic moment of the muon in the Standard Model}},
  url          = {{http://dx.doi.org/10.1016/j.physrep.2020.07.006}},
  doi          = {{10.1016/j.physrep.2020.07.006}},
  volume       = {{887}},
  year         = {{2020}},
}