The anomalous magnetic moment of the muon in the Standard Model
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T. Aoyama, N. Asmussen, M. Benayoun et al. The anomalous magnetic moment of the muon in the Standard Model. Physics Reports 887 (2020) 1–166 [https://doi.org/10.1016/j.physrep.2020.07.006]
SponsorshipFermilab Directorate; Fermilab Theoretical Physics Department; Fermilab Distinguished Scholars program; Universities Research Association through a URA Visiting Scholar award; Riken Brookhaven Research Center; Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science KAKEHNHI-17H02906 KAKENHI-15H05742 16K05317 16K05323 16K05338 17H01133 17H02906 18H05226 19K21872 20K03926 20K03960; High Energy Accelerator Research Organization (KEK); U.S.-Japan Science and Technology Cooperation Program in High Energy Physics; Deutsche Forschungsgemeinschaft via the Cluster of Excellence "Precision Physics, Fundamental Interactions and Structure of Matter'' (PRISMA); Collaborative Research Centre "The low-energy frontier of the Standard Model'' SFB 1044; Helmholtz Institute Mainz; United States Department of Energy (DOE) DE-FG02-00ER41132 DE-SC0020106; Centre National de la Recherche Scientifique (CNRS); Conacyt (Ciencia Basica 2015) 250628; Consejo Nacional de Ciencia y Tecnologia (CONACyT) CB2014-22117; Coordinacion de la Investigacion Cientifica (CIC-UMSNH) 4.10; Danmarks Frie Forskningsfond 8021-00122B; German Research Foundation (DFG) CRC 1044 CRC 1044 -204404729 CRC 110 HI 2048/1-1; Prisma Cluster for Excellence PRISMA+ EXC2118/1 STO/876/6-1; European Research Council (ERC) 668679 757646 771971-SIMDAMA 813942; European Union (EU) 754510; European Union (EU) 843134; European Union EuroPLEx Grant H2020-MSCA-ITN-2018-813942; European Union STRONG 2020 project 824093; French National Research Agency (ANR); OCEVU Laboratoire d'Excellence ANR-11-LABX-0060; Fondo SEP-Cinvestav 142; Portuguese Foundation for Science and Technology SFRH/BPD/109443/2015; Generalitat de Catalunya 2017SGR1069; Helmholtz Association (German Federal Ministry of Education and Research); Istituto Nazionale di Fisica Nucleare (INFN); Isaac Newton Trust; Junta de Andalucia A-FQM-467-UGR18; Instituto de Salud Carlos III Spanish Government CICYTFEDER-FPA2017-86989-P; Ministerio de Industria, Economia y Competitividad FPA2016-78220-C3-3-P FPA2017-86989-P PGC2018-094857-B-I00 SEV-2016-0588 SEV-2016-0597; Laboratoires d'Excellence FIRST-TF grants; Ministry of Science and Higher Education of the Russian Federation 14.W03.31.0026; National Research Foundation - South Africa; Natural Sciences and Engineering Research Council of Canada (NSERC) CGIAR; Portuguese Science Foundation (FCT) Investigator Grant IF/00898/2015; Romanian Ministry of Education and Research PN19060101; Russian Science Foundation (RSF) RSF 18-12-00128; Generalitat de Catalunya 2017 SGR 1069; Swedish Research Council 2016-05996 2019-03779; Swiss National Science Foundation (SNSF) PP00P2_176884 PCEFP2_181117; Leverhulme Trust ECF-2019-223; UK Research & Innovation (UKRI) Science & Technology Facilities Council (STFC) ST/N504130/1 ST/P000290/1 ST/P00055X/1 ST/P000630/1 ST/P000711/1 ST/P000746/1 ST/S000879/1 ST/S000925/1; United States Department of Energy (DOE) DE-SC0009919 DE-SC0009998 DE-SC0010005 DE-SC0010120 DE-SC0010339 DE-SC0012391 DE-SC0012704 DE-SC0013682 DE-SC0013895 DE-SC0015655; United States Department of Energy (DOE) DE-FG02-00ER41132 DE-AC02-05CH11231 DE-FG02-97ER41020 DE-AC02-07CH11359; U.S.-Japan Science and Technology Cooperation Program in High Energy Physics, "Incubation Platform for Intensity Frontier"; National Science Foundation (NSF) NSF-PHY-1316222 PHY14-14614 PHY17-19626 PHY19-23131; U.S. National Institute of Standards and Technology (NIST) Precision Measurement Grant 60NANB16D271
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 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 with negligible numerical uncertainty. The electroweak contribution is suppressed by 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 and is due to hadronic vacuum polarization, whereas at 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 and is smaller than the Brookhaven measurement by 3.7. 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.