The Muon Magnetic Moment and Physics Beyond the Standard Model

Abstract

We review the role of the anomalous magnetic moment of the muon a_μas a powerful probe of physics beyond the Standard Model (BSM), taking advantage of the final result of the Fermilab g-2 experiment and the recently updated Standard Model value. This review provides both a comprehensive summary of the current status, as well as an accessible entry point for phenomenologists with interests in dark matter, Higgs and electroweak or neutrino and flavour physics in the context of a wide range of BSM scenarios. It begins with a qualitative overview of the field and a collection of key properties and typical results. It then focuses on model-independent, generic formulas and classifies types of BSM scenarios with or without chiral enhancements. A strong emphasis of the review are the connections to a large number of other observables -- ranging from the muon mass and the muon--Higgs coupling and related dipole observables to dark matter, neutrino masses and high-energy collider observables. Finally, we survey a number of well-motivated BSM scenarios such as dark photons, axion-like particles, the two-Higgs doublet model, supersymmetric models and models with leptoquarks, vector-like leptons or neutrino mass models. We discuss the impact of the updated Standard Model value for a_μand of complementary constraints, exploring the phenomenology and identifying excluded and viable parameter regions.

Figures (50)

• Figure 1.1: One-loop Feynman diagrams illustrating Eqs. (\ref{['mmugeneric']},\ref{['amugeneric']}) and the possibility of chiral enhancements. Each contribution to the muon mass and to $a_\mu\xspace$ must involve one factor of some SM or BSM vev$v^{\text{(B)SM}}$ breaking electroweak symmetry, as well as a chirality flip between $\mu_L$ and $\mu_R$. In order to obtain a contribution to $a_\mu\xspace$, a photon (not shown in the diagrams) needs to couple to any of the charged internal lines. In the first two diagrams, the chirality is flipped at the external line, producing an explicit factor $m_\mu$ in the computation of the diagrams. In these two diagrams, the loop only couples to $\mu_L$ or $\mu_R$, respectively. In the third diagram, the chirality is flipped via the loop, possibly via virtual BSM particles.
• Figure 1.2: 1PI on-shell self-energy of the muon. The crosses correspond to insertions of the interaction vertex with the external field $A_\mu^\text{ext}$. Note that for off-shell momenta the r.h.s. would contain an additional 1PI term without insertions of the external field.
• Figure 1.3: Dyson-Schwinger equation for the two-point Green function, corresponding to Eq. (\ref{['DSE']}).
• Figure 1.4: (a) Schematic of the storage ring and illustration of the muon spin precession in the constant magnetic field. In total, 24 calorimeters distributed evenly around the ring measure the positrons emitted by the decaying muon beam. (b) Fit of the positron count overlayed on top of the measured data in the FNAL run-1d Muong-2:2021vma.
• Figure 1.5: Reprinted from Ref. Muong-2:2025xyk. Summary plot of the experimental values of $a_\mu$ obtained from the FNAL run-1, run-2/3 and run-4/5/6 measurements (red squares) as well as the final BNL E821 result (blue triangle). The FNAL final value Eq. \ref{['Eq:FNALfinalresult']} is indicated by the red circle and the current world average Eq. \ref{['eq:amuExp']} by the purple diamond. The additional results can be found in Eqs. \ref{['amuBNL']} and \ref{['amuExpAdditional']}. The vertical bars indicate the statistical uncertainties, the horizontal lines the total uncertainties.