[Paper Review] The anomalous magnetic moment of the muon in the MSSM - recent developments

S. Heinemeyer, Dominik Stöckinger+1 more|ArXiv.org|Jul 15, 2004

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper investigates two-loop supersymmetric contributions to the muon's anomalous magnetic moment in the MSSM, focusing on sfermion and chargino/neutralino loops. It finds these contributions can reach up to 5×10⁻¹⁰—nearly one standard deviation of the experimental uncertainty—significantly altering the MSSM prediction and reducing theoretical uncertainty, especially when experimental constraints are applied.

ABSTRACT

We present recent results of two interesting classes of supersymmetric two-loop contributions to (g-2)_mu. Two-loop diagrams involving either a closed sfermion loop or a closed chargino/neutralino loop can amount to 5*10^{-10}, which is almost one standard deviation of the current experimental uncertainty. We discuss the dependence of these two classes on the unknown supersymmetric parameters and their impact on the supersymmetric prediction of (g-2)_mu.

Motivation & Objective

• To assess the impact of two-loop supersymmetric contributions on the anomalous magnetic moment of the muon in the MSSM.
• To determine how experimental constraints on MSSM parameters affect the size and viability of these two-loop contributions.
• To evaluate whether these two-loop diagrams can resolve the long-standing discrepancy between the experimental value and the Standard Model prediction of (g-2)μ.
• To compare the parameter dependence and phenomenological implications of sfermion-loop versus chargino/neutralino-loop two-loop diagrams.
• To identify the remaining missing two-loop diagrams needed for a complete MSSM calculation of (g-2)μ.

Proposed method

• The authors compute two-loop diagrams involving closed sfermion loops (stops, sbottoms, staus, tau-sneutrinos) using large mass expansion and integral reduction techniques.
• They evaluate two-loop diagrams with closed chargino/neutralino loops, accounting for their dependence on μ, tanβ, M₂, and M_A.
• A full scan over the MSSM parameter space is performed, with increasing experimental constraints applied: M_h > 150 GeV, Δρ, BR(Bs→μ⁺μ⁻), and BR(B→Xsγ).
• The results are compared to one-loop SUSY contributions and the experimental discrepancy of (24.5±9)×10⁻¹⁰.
• Regularization and γ₅ problems in dimensional regularization are addressed using established techniques from previous works.
• The study uses the MSSM as a framework, with all contributions evaluated in the context of a two-Higgs-doublet model-like structure.

Experimental results

Research questions

• RQ1 Can two-loop MSSM contributions involving sfermion loops account for a significant fraction of the observed (g-2)μ discrepancy?
• RQ2 How do experimental constraints on the MSSM parameter space—particularly M_h > 150 GeV—restrict the maximum possible two-loop sfermion contributions to (g-2)μ?
• RQ3 To what extent do chargino/neutralino two-loop diagrams modify the one-loop SUSY prediction for (g-2)μ, especially when smuon and sneutrino masses are heavy?
• RQ4 How do the parameter dependencies of sfermion and chargino/neutralino two-loop diagrams differ, and what are the phenomenological consequences?
• RQ5 What is the impact of these two-loop contributions on the interpretation of the 2–3σ discrepancy between experiment and the Standard Model prediction for (g-2)μ?

Key findings

• The maximum two-loop sfermion-loop contribution to (g-2)μ is reduced from over 15×10⁻¹⁰ to about 5×10⁻¹⁰ when the M_h > 150 GeV constraint is applied.
• Further constraints from Δρ, BR(Bs→μ⁺μ⁻), and BR(B→Xsγ) reduce the maximum sfermion-loop contribution even further.
• The chargino/neutralino two-loop contribution can reach up to 11×10⁻¹⁰ for μ > 0, tanβ = 50, and M_SUSY = 100 GeV, scaling as (tanβ/50) × sign(μ) / (M_SUSY/100 GeV)².
• When smuon and sneutrino masses are heavy (1 TeV), the two-loop chargino/neutralino contributions can dominate over the one-loop ones, modifying the 1σ and 2σ contours in the μ–M₂ plane.
• The two-loop contributions can modify the phenomenological interpretation of the (g-2)μ discrepancy by shifting the allowed parameter space, especially in regions where one-loop contributions are suppressed.
• The remaining missing two-loop diagrams—corrections to the one-loop diagrams with smuon or sneutrino exchange—require a full one-loop renormalization of the MSSM to complete the calculation.