Precision Physics with Muons : A Decade of Theoretical and Experimental Advances

Abstract

The muon has been instrumental in establishing the Standard Model of particle physics and continues to play a key role in exploring the nature of New Physics. A global program is underway to enhance the discovery potential of a wide range of muon probes, with significant increases in sensitivity anticipated over the next decade. In this review, we examine recent experimental advancements in the study of muon decays, the determination of the muon magnetic and electric dipole moments, and the search for charged lepton flavor violating transitions. We explore the implications for scenarios of physics beyond the Standard Model, focusing on models involving light new particles, such as axions or hidden sectors. Opportunities from novel experimental concepts and proposal for new muon facilities are also discussed.

Figures (6)

• Figure 1: The vacuum polarization contribution to the anomalous magnetic moment of the muon. The diagrams show (from left to right) the one-loop QED correction, the one-loop Z-boson exchange, the leading-order hadronic vacuum polarization diagram, and the hadronic light-by-light contribution. Figures adapted from References Keshavarzi:2022kpc (CC-BY).
• Figure 2: view of the muon g-2 experiment at FNAL. Three superconducting coils spanning the circumference of the steel yoke provide a 1.45 T magnetic field, and four electrostatic quadrupoles positioned symmetrically around the ring provide vertical beam confinement. The storage ring is covered by a white insulating blanket. Figure reproduced from https://muon-g-2.fnal.gov with permission from FNAL.
• Figure 3: The experimental values of the muon anomalous magnetic moment (red band) together with theoretical predictions based on lattice QCD calculations (blue band) and data-driven methods (gray band). Figure adapted from Reference Aliberti:2025beg (CC-BY).
• Figure 4: Historical evolution of CLFV searches in muons transitions. Experiments using stopped pion beams in the mid 1950s started to improve upon limits based on cosmic ray measurements, before stopped muon beams allowed further gain in the mid 1970s. The following limits are reported: the branching fractions of the $\mu^+ \rightarrow e^+ \gamma$, $\mu^+ \rightarrow e^+e^-e^+$, and $\mu^+ \rightarrow e^+ \gamma \gamma$ reactions, the ratio of the conversion rate to the total muon capture rate for the $\mu^- N \rightarrow e^- N$ and $\mu^- N \rightarrow e^+ N'$ reactions, and the muoniun-antimuonium conversion probability (the early measurement in Ar gas, indicated by an asterisk, also includes the probability of breaking the antimounium system and forming a muonic Ar atom). Solid symbols indicate past experiments, and open symbols denote the expected reach of future proposals. See References Bernstein:2013hbaParticleDataGroup:2024cfk for details.
• Figure 5: Left: schematic view of the MEG-II experiment together with a simulated event. Right: the Mu3e experiment in the phase I configuration. Figures adapted from References MEGII:2023ltwMu3e:2020gyw (CC-BY-NC-ND).