Particle physics: will muons uncover new fundamental physics?

For over 10 years, measurement of a magnetic property of the muon (a more massive, ephemeral cousin of the electron) has exhibited disagreement with theoretical predictions. This suggests a possible gap in the standard model of particle physics2, possibly providing a glimpse of more exotic physics. The first results of Fermilab’s “Muon g2” experiment, which measures this property known as the muon “magnetic moment,” are being revealed on 7 April 2021.
While no French laboratory participates directly in this new experiment, a CNRS team3 has played a decisive role in calculating the reference theoretical prediction4 required to interpret its results.To determine the effect of hadronic vacuum polarisation, which currently limits the accuracy of calculations, the team used measurements made with electronpositron colliders. This exact approach, whose precision depends exclusively on that of those measurements, has been developed and improved by this team for 20 years, leading to the disagreement with the already existing measurement of the muon’s magnetic moment.
A completely different approach was recently used by a team including CNRS scientists5. The result of their calculation of the hadronic vacuum polarisation contribution is being published in the journal Nature, also on April 7. Notably, this work reduces the discrepancy with the current experimental value of the muon magnetic moment: the standard model may yet have the last word! To reach these conclusions, the scientists calculated this contribution ab initio, which is to say using the standard model’s equations with no additional parameter. With approximately one billion variables involved, multiple massively parallel European supercomputers6 were needed to undertake this very challenging calculation. This is the first time an ab initio calculation has rivalled the precision of the reference approach, which predicts values for the muon magnetic moment that differ from the measured value to a greater degree.
To settle the matter once and for all, the results of this new theoretical calculation will have to be confirmed by other teams and, if they are, scientists will have to determine what causes the differences between the two theoretical approaches. In fact, the two CNRS teams are currently working together on this issue. They hope to obtain, by combining both approaches, a new prediction that is accurate enough to decide the fate of the standard model in coming years, which will see the publication of the final results from Fermilab’s “Muon g2” experiment, as well as those from another experiment with similar objectives in Japan.
 1. Measurement conducted at the Brookhaven National Laboratory (United States) between 1997 and 2001.
 2. The standard model of particle physics is the theory that describes elementary particles and their interactions.
 3. The DHMZ group, consisting of Michel Davier (IJCLab CNRS/Université ParisSaclay), Andreas Hoecker (CERN, Geneva), Bogdan Malaescu (LPNHE, CNRS/Sorbonne Université), and Zhiqing Zhang (IJCLab), has published 10 major articles on the subject that have been cited over 3,000 times.
 4. The theoretical value of reference used by the “Muon g2” experiment was obtained by comparing the results, published in Physics Reports in 2020, obtained by various working groups around the globe. It is very close to the final value published by the DHMZ group in 2019.
 5. In addition to Laurent Lellouch’s team at the Centre for Theoretical Physics (CNRS/AixMarseille Université/Université de Toulon) in France, the “BudapestMarseilleWuppertal” collaboration includes Eötvös Loránd University (Hungary), the University of Wuppertal and the Forschungszentrum Jülich (Germany), and Pennsylvania State University (United States).
 6. In Germany, those of the Forschungszentrum Jülich, the Leibniz Supercomputing Centre (Munich), and the High Performance Computing Center (Stuttgart); in France, Turing and Jean Zay at the Institute for Development and Resources in Intensive Scientific Computing (IDRIS) of the CNRS, and JoliotCurie at the Very Large Computing Centre (TGCC) of the CEA, by way of the French Largescale Computing Centre (GENCI).
The anomalous magnetic moment of the muon in the Standard Model, T. Aoyama et al. (including Michel Davier and Laurent Lellouch), Physics Reports, 3 December 2020. DOI: 10.1016/j.physrep.2020.07.006
Leading hadronic contribution to the muon magnetic moment from lattice QCD, Sz. Borsanyi, Z. Fodor, J. N. Guenther, C. Hoelbling, S. D. Katz, L. Lellouch, T. Lippert, K. Miura, L. Parato, K. K. Szabo, F. Stokes, B. C. Toth, Cs. Torok, L. Varnhorst. Nature, 8 April 2021. DOI: 10.1038/s41586021034181.