The Muon Magnetic Moment and Supersymmetry

TL;DR

The muon anomalous magnetic moment is examined as a precise probe of supersymmetry, with leading one- and two-loop SUSY contributions derived and analyzed. The work highlights strong tan$\beta$-driven enhancements and the critical role of the $\mu$ parameter, providing analytic formulas, numerical benchmarks, and comprehensive scans to map MSSM parameter space. It shows that the observed deviation from the SM can be accommodated by SUSY across broad scenarios, yielding testable upper bounds on superpartner masses and meaningful correlations with $B$ decays, dark matter, Higgs physics, and electroweak precision data. The findings underscore $a_\mu$ as a powerful indirect constraint guiding SUSY phenomenology and guiding expectations for LHC/ILC explorations and dark matter searches.

Abstract

The present review is devoted to the muon magnetic moment and its role in supersymmetry phenomenology. Analytical results for the leading supersymmetric one- and two-loop contributions are provided, numerical examples are given and the dominant tan(beta)sign(mu)/M_SUSY^2 behaviour is qualitatively explained. The consequences of the Brookhaven measurement are discussed. The 2 sigma deviation from the Standard Model prediction implies preferred ranges for supersymmetry parameters, in particular upper and lower mass bounds. Correlations with other observables from collider physics and cosmology are reviewed. We give, wherever possible, an intuitive understanding of each result before providing a detailed discussion.

Figures (18)

• Figure 1: Possibilities for chirality-flips along the line carrying the $\mu$-lepton number.
• Figure 2: Five sample mass-insertion diagrams. Vertices and mass insertions are denoted by dots, and the interaction eigenstates corresponding to each line are displayed explicitly. The external photon has to be attached in all possible ways to the charged internal lines. The one-loop diagrams (C), (N1), (N2) have been discussed also in Moroi1L. The loop functions $F$ in the results are different in the five cases and depend on different masses.
• Figure 3: The two SUSY one-loop diagrams, written in terms of mass eigenstates. The external photon line has to be attached to the charged internal lines.
• Figure 4: Sample two-loop diagrams with closed chargino/neutralino or sfermion loop, contributing to $a_\mu^{\chi,\rm 2L}$ and $a_\mu^{\tilde{f},\rm 2L}$. The diagrams are categorized into classes $(XVH)$, $(XVG)$ and $(XVV)$, where $X=\chi^{\pm,0},\tilde{f}$. $V=\gamma,Z,W^\pm$ denotes gauge bosons, $H=h^0,H^0,A^0,H^\pm$ denotes physical Higgs bosons, and $G=G^{\pm,0}$ denotes Goldstone bosons. See HSW03HSW04 for more details on the possible diagram topologies.
• Figure 5: Sample two-loop diagrams involving only SM- or two-Higgs-doublet model particles and either with or without fermion loop. These diagrams are different in the MSSM and the SM due to the modified Higgs sector, and this difference constitutes the SUSY contributions $a_\mu^{\rm SUSY,ferm,2L}$ and $a_\mu^{\rm SUSY,bos,2L}$.