[Paper Review] Effective field theory interpretation of lepton magnetic and electric dipole moments

Jason Aebischer, Wouter Dekens+4 more|arXiv (Cornell University)|Feb 17, 2021

Particle physics theoretical and experimental studies146 references74 citations

TL;DR

This paper provides a model-independent analysis of lepton magnetic and electric dipole moments using one-loop effective field theory (EFT) techniques in both SMEFT and LEFT frameworks. It identifies that only a limited set of SMEFT operators—specifically the dipole operators CeW and CeB, and certain semileptonic four-fermion operators—can generate the observed 4.2σ discrepancy in the muon anomalous magnetic moment, with significant contributions from top-quark loops and non-perturbative QCD effects.

ABSTRACT

We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the effective-theory operators. Semileptonic four-fermion operators involving light quarks give sizable non-perturbative contributions to the dipole moments, which are included in our analysis. We find that only a very limited set of the SMEFT operators is able to generate the current deviation of the magnetic moment of the muon from its Standard Model expectation.

Motivation & Objective

• To provide a model-independent interpretation of the observed 4.2σ discrepancy in the muon anomalous magnetic moment (g−2) using effective field theory.
• To identify which higher-dimensional operators in SMEFT and LEFT can generate the observed dipole moment deviations.
• To include one-loop renormalization group evolution, matching from SMEFT to LEFT, and non-perturbative QCD effects from light-quark semileptonic operators.
• To constrain the imaginary parts of Wilson coefficients to remain consistent with stringent electric dipole moment bounds.

Proposed method

• Performs one-loop matching from SMEFT onto LEFT and evolves operators using one-loop anomalous dimensions.
• Computes one-loop contributions to lepton dipole moments via top- and charm-quark loops, including QCD corrections.
• Incorporates non-perturbative effects from semileptonic four-fermion operators using O(1) parameters derived from lattice QCD.
• Uses master formulae in terms of SMEFT and LEFT Wilson coefficients to express ∆aµ and ∆ae as functions of operator coefficients.
• Analyzes leptoquark and two-Higgs-doublet model scenarios as illustrative examples.
• Applies constraints from the muon EDM bound and µ→eγ branching ratio to rule out certain BSM explanations.

Experimental results

Research questions

• RQ1 Which SMEFT and LEFT operators can generate the observed 4.2σ discrepancy in the muon anomalous magnetic moment?
• RQ2 How do one-loop running, matching, and non-perturbative QCD effects modify the contributions to dipole moments?
• RQ3 What constraints do the electron and muon EDM bounds place on the imaginary parts of Wilson coefficients in SMEFT?
• RQ4 Can leptoquark models simultaneously explain the muon and electron g−2 anomalies without violating µ→eγ or EDM constraints?
• RQ5 Which specific combinations of operator coefficients are required to generate ∆aµ ∼ 251×10−11 within EFT?

Key findings

• Only the dipole operators CeW and CeB, and the semileptonic four-fermion operators C(3)lequ2222 and C(3)lequ2233 can generate the observed ∆aµ if new physics is above the electroweak scale.
• Chirally enhanced contributions from top-quark loops in leptoquark models can explain the anomaly with M1 ∼ 1–10 TeV and Yukawa couplings near unity.
• The predicted branching ratio for µ→eγ exceeds the experimental limit of 4.2×10−13 if both ∆ae and ∆aµ are explained by the same leptoquark, ruling out such models.
• The minimal branching ratio for µ→eγ is found to be 1.5×10−4 when ∆ae and ∆aµ are both explained via top-quark loops, exceeding the experimental bound.
• Non-perturbative QCD effects on semileptonic operators contribute significantly and must be included via O(1) parameters determined non-perturbatively.
• The imaginary parts of Wilson coefficients must be suppressed by at least a factor of ∼10^5 to satisfy the electron EDM bound, assuming real parts are of order 10−10.