- Muons, particles akin to electrons, have kept physicists’ heads spinning for more than a decade, because an experimental measurement of their magnetic properties 1 disagrees from theory. Could this be caused by unknown particles or forces?
- A new theoretical calculation of this parameter, involving CNRS physicists and published , has reduced the discrepancy with the experimental measurement. The debate nevertheless continues.

For over 10 years, measurement of the magnetic properties of the muon (an ephemeral cousin of the electron) has exhibited disagreement with theoretical predictions. This suggests a possible gap in the standard model of particle physics 2 , possibly providing a glimpse of a more exotic physics. The first results of Fermilab’s "Muon g-2" experiment, which measures one of these properties known as the muon "magnetic moment," are being revealed on 7 April 2021 .

**While France is not directly participating in this experiment, a CNRS team 3 played a decisive role in calculating the theoretical prediction used as a reference, 4 without which no conclusion would have been possible. **To determine the effect of hadronic vacuum polarisation, which currently limits the accuracy of calculations, the team used measurements made with electron-positron colliders. This exact approach, which depends exclusively on the precision of these measurements, has been developed and improved by this team for 20 years, leading to the disagreement with the experimental measurement of the muon’s magnetic moment.

**A different method was recently used by a team including CNRS researchers 5 , whose result for the calculation of this contribution is being published . This result notably reduces the discrepancy with the current experimental value.** Thus, the standard model may yet have the last word! To achieve this result, 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 supercomputers 6 were needed to meet this great challenge. 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, scientists will have to wait for the results of this new theoretical calculation to be confirmed by other teams, and determine what causes the differences between the two theoretical approaches. CNRS teams are currently working together to meet this challenge. They hope to obtain, by combining approaches, a new theoretical reference 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 g-2" 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 Paris-Saclay), 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 g-2" 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/Aix-Marseille Université/Université de Toulon) in France, the "Budapest-Marseille-Wuppertal" 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 Joliot-Curie at the Very Large Computing Centre (TGCC) of the CEA, by way of the French Very Large-scale Computing Centre (GENCI).

The anomalous magnetic moment of the muon in the Standard Model , T. Aoyama et al. (including Michel Davier and Laurent Lellouch), , 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/s41586-021-03418-1 .