Particle physics: will muons uncover new fundamental physics?

  • Muons, particles akin to electrons, have kept physicists' heads spinning for more than a decade, because an experimental measurement of their magnetic properties1 disagrees with theory. Could this be caused by unknown particles or forces?
  • A new theoretical calculation of these properties, involving CNRS physicists and published in the journal Nature, reduces the discrepancy with the experimental measurement. The debate continues nevertheless. 

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 g-2” 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 electron-positron 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 g-2” experiment, as well as those from another experiment with similar objectives in Japan.


Representation of the calculation of the hadronic vacuum polarization effect on muon magnetism. The muon (µ) spins like a top, turning into a tiny magnet surrounded by a magnetic field. It follows a trajectory along which it interacts with the magnet from the “Muon g-2” experiment, as well as with virtual particles from the quantum vacuum. Thus it polarises the hadronic vacuum, leading in turn to a modification of its own magnetic moment. The background of 0s and 1s, along with the square tiling, call to mind a supercomputer calculation, which is one of the approaches described here.
© Dani Zemba, Pennsylvania State University.


  • 1Measurement conducted at the Brookhaven National Laboratory (United States) between 1997 and 2001.
  • 2The standard model of particle physics is the theory that describes elementary particles and their interactions.
  • 3The 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.
  • 4The 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.
  • 5In 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).
  • 6In 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 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), 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/s41586-021-03418-1.


Michel Davier
Université Paris-Saclay researcher
Laurent Lellouch
CNRS researcher
Véronique Etienne
CNRS press officer