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Charting the new physics through one-loop effects in the muon magnetic dipole moment

Shi-Ping He

TL;DR

This paper develops a universal, one-loop framework for the muon magnetic dipole moment $a_\mu$ arising from canonical spin-1/2 fermion interactions with scalar or vector mediators. It presents analytic expressions in three representations (PaVe, integral, and a special-function form) and systematically derives mass-hierarchy and degenerate-mass expansions for all relevant loop functions $I_{LL,LR}^{f/S}$ and $L_{LL,LR}^{f/V}$, including their singularity structure. The work also maps between CP and chiral bases, discusses the sign and magnitude of contributions across parameter space, and provides explicit model applications (SM, doubly charged mediators, dark matter, axion-like particles). The results offer practical, compact approximations for predicting new-physics effects in $a_\mu$ and guide constraints on mediator masses and couplings as experimental and theoretical uncertainties evolve. Overall, the framework equips researchers with rigorous tools to assess and design new physics scenarios that address or accommodate the muon $g-2$ results across current and future data.

Abstract

Since the announcement of the muon $g-2$ measurements, numerous studies have been devoted to exploring the new physics through this precision probe. In specific models, the new physics contributions depend on the couplings and mass scales. Approximate formulae are widely adopted when determining the new physics contributions. This manuscript is dedicated to comprehensive analytical results and approximations for the canonical interactions at one-loop level, which is universal for the spin-half fermions and can serve as a useful reference for the magnetic dipole moment calculations. We present the analytic and approximate expressions for the scalar and vector mediator cases, supplemented by explicit examples in specific models to illustrate their applications. For given muon interactions, we can estimate both the sign and magnitude of the contributions conveniently. Furthermore, we investigate the broader physical implications of these results, offering insights into potential new physics.

Charting the new physics through one-loop effects in the muon magnetic dipole moment

TL;DR

This paper develops a universal, one-loop framework for the muon magnetic dipole moment arising from canonical spin-1/2 fermion interactions with scalar or vector mediators. It presents analytic expressions in three representations (PaVe, integral, and a special-function form) and systematically derives mass-hierarchy and degenerate-mass expansions for all relevant loop functions and , including their singularity structure. The work also maps between CP and chiral bases, discusses the sign and magnitude of contributions across parameter space, and provides explicit model applications (SM, doubly charged mediators, dark matter, axion-like particles). The results offer practical, compact approximations for predicting new-physics effects in and guide constraints on mediator masses and couplings as experimental and theoretical uncertainties evolve. Overall, the framework equips researchers with rigorous tools to assess and design new physics scenarios that address or accommodate the muon results across current and future data.

Abstract

Since the announcement of the muon measurements, numerous studies have been devoted to exploring the new physics through this precision probe. In specific models, the new physics contributions depend on the couplings and mass scales. Approximate formulae are widely adopted when determining the new physics contributions. This manuscript is dedicated to comprehensive analytical results and approximations for the canonical interactions at one-loop level, which is universal for the spin-half fermions and can serve as a useful reference for the magnetic dipole moment calculations. We present the analytic and approximate expressions for the scalar and vector mediator cases, supplemented by explicit examples in specific models to illustrate their applications. For given muon interactions, we can estimate both the sign and magnitude of the contributions conveniently. Furthermore, we investigate the broader physical implications of these results, offering insights into potential new physics.
Paper Structure (81 sections, 195 equations, 1 figure, 6 tables)

This paper contains 81 sections, 195 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. The $(g-2)_\mu$ in simplified models
  3. Canonical interactions
  4. Quasi-canonical interactions
  5. Comments on non-canonical contributions
  6. Contributions to $(g-2)_\mu$ for the canonical interactions
  7. General structure of the one-loop contributions
  8. Different representations of the loop functions
  9. Analytic form of the loop functions: scalar mediator case
  10. Analytic form of the loop functions: vector mediator case
  11. Singularities of the loop functions
  12. Expansion of the loop functions: scalar mediator case
  13. Hierarchical mass expansion for the $I_{LL}^f$ and $I_{LR}^f$
  14. Scenario of $m_\mu\ll m_f,m_S$
  15. Scenario of $m_S\ll m_f,m_\mu$
  16. ...and 66 more sections

Figures (1)

  • Figure 1: Typical scalar (upper) and vector (lower) mediator Feynman diagrams which contribute to $(g-2)_\mu$ in the unitary gauge. Here, the diagrams are drawn by JaxoDraw Binosi:2008ig.