Axion-Electron Coupling Strengths

• Axion–electron coupling strengths define the interaction between axions and electrons via specific Lagrangian terms, with values linked to decay constants and model parameters.
• Astrophysical measurements from red-giant and white-dwarf cooling provide stringent bounds on gae, employing precision models and MCMC techniques.
• Laboratory methods, including axio-electric searches and quantum sensing, are rapidly advancing to explore and constrain new regions of the axion parameter space.

The axion–electron coupling strength, denoted $g_{ae}$, quantifies the interaction between axions (pseudo-Nambu–Goldstone bosons postulated in Peccei–Quinn extensions of the Standard Model) and electrons. This coupling is central to both theoretical axion model-building and to a wide range of experimental and observational constraints. The study of $g_{ae}$ interleaves precision astrophysical modeling, quantum field theory, laboratory searches, and advanced statistical methodologies. Below, key aspects of axion–electron coupling strengths are organized for a technically expert readership.

1. Theoretical Formulation and Model Dependence

The axion–electron coupling arises in the low-energy Lagrangian as

$$\mathcal{L}_{\rm int} = -\,i\,g_{ae}\,a\,\bar\psi_e\gamma_5\psi_e$$

for pseudoscalar cases, or, in DFSZ-like models, equivalently via a derivative coupling: $$\mathcal{L}_{ae} = \frac{g_{ae}}{2 m_e}\,\partial_\mu a\,\bar\psi_e\gamma^\mu\gamma_5\psi_e$$ where $a$ is the axion field and $\psi_e$ is the electron Dirac spinor.

The dimensionless coupling $g_{ae}$ is often related to model UV parameters, e.g.,

$g_{ae} = X_e \frac{m_e}{f_a}$

where $X_e$ is a Peccei–Quinn charge determined by Higgs basis and coupling assignments, and $f_a$ is the axion decay constant. In the DFSZ models, explicit formulae tie $g_{ae}$ to Higgs VEVs and PQ charges; in multi-Higgs DFSZ variants, $g_{ae}$ is further modulated by the vacuum alignment and charge composition, enabling continuous interpolation between standard values and complete "electrophobia" (Sun et al., 2020, Björkeroth et al., 2019).

For practical comparison across experimental and astrophysical domains, a dimensionless parameter

$\alpha_{26} \equiv 10^{26}\frac{g_{ae}^2}{4\pi}$

is often adopted, with $g_{ae} \sim 10^{-13}\sqrt{4\pi\alpha_{26}}$ (Dennis et al., 2023). In specific cases (e.g., CP-violating observables), dimensionful pseudoscalar-type couplings are considered (Maison et al., 2021).

2. Astrophysical Constraints: Red-Giant and White-Dwarf Cooling

Energy losses mediated by axion–electron coupling alter the evolution of stellar interiors, notably in the dense degenerate cores of red-giant and white-dwarf stars. The inclusion of axion cooling channels modifies the core mass at ignition and the tip of the red-giant branch (TRGB) luminosity.

• Dominant Production Mechanisms:
  • Electron–ion bremsstrahlung and semi-Compton processes dominate axion production.
  • The energy loss per unit mass in RG cores can be parametrized as

  $$Q_{ae} = Q_{sC} + \left(Q_{b,\,\mathrm{ND}}^{-1} + Q_{b,\,\mathrm{D}}^{-1}\right)^{-1}$$

  with scaling $Q_{ae} \propto g_{ae}^2$, and specific temperature and density dependencies detailed in (Dennis et al., 2023).

• Observational Analysis:

  • The empirical I-band magnitude at the TRGB, $M_I$, is sensitive to new cooling channels.
  • Machine-learning emulators trained on grids of stellar evolution models predict $M_I$ for given values of initial mass, helium fraction, metallicity, and $\alpha_{26}$ with millimag accuracy. This enables Markov Chain Monte Carlo (MCMC) inference marginalized over astrophysical uncertainties (Dennis et al., 2023).
  • Prior generations of analyses (e.g., (Straniero et al., 2020)) quote bounds such as $g_{ae} < 1.48 \times 10^{-13}$ (95% C.L.) from the cumulative likelihood across 22 globular clusters.
  • Including all uncertainties and degeneracies, recent findings show that constraints are dramatically weakened; if all stellar parameters are varied freely, the upper posterior on $\alpha_{26}$ becomes unconstrained up to $\alpha_{26}=2$ ($g_{ae} \lesssim 5 \times 10^{-13}$) (Dennis et al., 2023), reopening parameter space previously believed excluded.
• Additional Environments:
  • White-dwarf cooling sequences and luminosity functions yield comparable constraints: $g_{ae} < 2.6 \times 10^{-13}$ (Carenza et al., 2021).
  • Systematic uncertainties from nuclear rates, opacities, conduction, and convection treatments are subdominant once included via emulator-based MCMC (Dennis et al., 2023).

Comparison Table: Current Key Astrophysical Constraints

Environment	Representative Bound on $g_{ae}$	Reference
TRGB (Globular Clusters)	$< 1.3–2.6 \times 10^{-13}$	(Dennis et al., 2023, Straniero et al., 2020, Straniero et al., 2018)
White Dwarf Cooling	$< 2.6 \times 10^{-13}$	(Carenza et al., 2021)
Solar Observables	$< 2.0 \times 10^{-11}$	(Carenza et al., 2021)

3. Laboratory, Direct Detection, and Model-Independent Probes

Laboratory constraints on $g_{ae}$ are categorized into axio-electric effect searches, electron recoil experiments, nuclear resonance conversion, and novel quantum schemes:

• Axio-electric Effect Searches:
  • Direct detection via axio-electric absorption in semiconductors or noble liquid targets such as XENON100 and EDELWEISS-II yields limits at the $g_{ae}< 7.7 \times 10^{-12}$ (solar axions), $g_{ae} < 2.56 \times 10^{-11}$ (dark matter axions) level [(Collaboration et al., 2014); (Armengaud et al., 2013)].
• Nuclear Resonance Conversion:
  • Resonant absorption in nuclei (e.g., $^169$Tm) sets model-independent constraints on the product $g_{Ae}|g^0_{AN}+g^3_{AN}|\leq 2.1\times10^{-14}$ (Derbin et al., 2011).
• Precision Atomic/Molecular Probes:
  • T, P-odd spin-dependent forces, as in YbOH molecule spectroscopy, give laboratory bounds of $|g_e| < 1.5 \times 10^{-10}$, presently weaker than astrophysical limits but competitive for certain CP-violating variants (Maison et al., 2021).
• Cavity Searches and Chiral Magnetic Effect:
  • Axion-induced chiral magnetic currents in conducting cavities (haloscopes) provide direct probes. The sensitivity scales $P_{ae}/P_{a\gamma}\sim(m_a/\sigma)^2$, so improvement may arise via replacement of copper with carbon-based conductors, enabling possible $g_{ae}$ reach to $10^{-9}$ for $m_a \sim 10\,\mu\mathrm{eV}$ (Hong et al., 28 Jul 2025).
• Quantum Sensing and the "Axion Wind":
  • Ferrimagnetic flux concentrators paired with levitated ferromagnet torque sensors can probe $g_{ae}\sim 10^{-11}$ (1–500 Hz) with sub-fT/√Hz sensitivity, opening a quantum-limited regime—see (Gao et al., 29 Sep 2025).

4. Advanced Laboratory Proposals and Accelerator-Based Strategies

Innovative approaches using high-intensity laser–plasma interactions and precise control of free electrons are being advanced:

• Accelerated Electron Emission:
  • Electrons accelerated in the standing wave of counter-propagating lasers can emit axions via their coupling $g_{ae}$, with WKB and Lorentz-covariant methods yielding the emission amplitude and spectra (Vacalis et al., 23 Oct 2025).
  • Photon regeneration via Compton-like scattering of axions in downstream conversion targets enables laboratory-scale, model-independent sensitivity. For realistic laser parameters, bounds $g_{ae} \lesssim 4.1 \times 10^{-5}$ (current technology) and $g_{ae} \lesssim 8 \times 10^{-8}$ (future capabilities) are plausible for $m_a\ll100$ keV, noting plasma and decay backgrounds are negligible at planned densities and timescales.
• Precision Magnetometry and the Axion Wind:
  • The effective oscillating "pseudomagnetic field" experienced by electron spins in the presence of galactic axion dark matter is proportional to $g_{ae} v \sqrt{2\rho_{\rm DM}}$, yielding fields $|B_a|\sim 4\times 10^{-18} \, {\rm T}$ for $g_{ae} \sim 10^{-10}$ (Gao et al., 29 Sep 2025). Flux concentration boosts practical detection sensitivity well past conventional spin-precession methods.

5. Astrophysical Spectroscopy and Multi-Channel Constraints

Extensions to massive, evolved, or highly luminous astrophysical targets strengthen constraints on $g_{ae}$ in combination with other couplings:

• Betelgeuse and Hard X-ray Limits:
  • Thermal axion or ALP emission from supergiant stars like Betelgeuse, followed by GALactic magnetic field conversion, enables hard X-ray searches. NuSTAR non-detections imply

  $$g_{a\gamma} g_{ae} < (0.4 – 2.8) \times 10^{-24} \, {\rm GeV}^{-1}$$

  for $m_a \leq 5 \times 10^{-11}$ eV, setting some of the strongest current dual-coupling constraints (Xiao et al., 2022).

• CAST and Solar Axion Fluxes:

  • Solar axion telescopes such as CAST (LHC dipole magnet repurposed as helioscope) set limits on combinations $g_{a\gamma}g_{ae}$ via the absence of X-ray signals, with 95% C.L. products such as $$g_{a\gamma}g_{ae} < 7.35\times 10^{-23}\,{\rm GeV}^{-1}$$ for $m_a<10\,{\rm meV}$ [(Altenmüller et al., 9 May 2025); (Barth et al., 2013)]. Constraints on isolated $g_{ae}$ require benchmark values for $g_{a\gamma}$.

6. Parameter Space Overview and Future Prospects

A synthesis of the above methodologies shows:

• Astrophysical bounds are strongest for $g_{ae}\lesssim 1.3\times10^{-13}$ (95% C.L. from globular cluster TRGB and white-dwarf cooling), but these depend sensitively on assumed stellar model uncertainties and can become significantly weaker under data-driven, emulator-based, and fully simultaneous MCMC analyses (Dennis et al., 2023).
• Laboratory searches are rapidly improving and, for certain parameter regimes (ultralight axions, high-frequency couplings, or dual-coupling searches), already match or surpass prior parameter exclusions, with ultimate sensitivity scaling with advances in detector technology, laser energy, and quantum sensing.
• Model dependence: All limits must be interpreted in the context of the realized axion scenario (DFSZ, KSVZ, variant models); e.g., KSVZ has negligible tree-level $g_{ae}$, while DFSZ predicts a scaling with electron mass, Higgs sector, and $f_a$.
• Combined constraints from multiple channels (astrophysics, direct detection, atomic–molecular spectroscopy, axion–electron wind) are essential to survey the viable axion parameter space and distinguish model variants.

7. Summary Table: Representative $g_{ae}$ Limits Across Approaches

Approach/Target	Bound on $g_{ae}$	Mass Range	Reference
TRGB (All uncertainties, modern ML+MCMC)	$\lesssim 5\times10^{-13}$ (no upper bound within prior)	$m_a\ll {\rm keV}$	(Dennis et al., 2023)
TRGB (Fixed stellar parameters)	$<4.2\times10^{-13}$	$m_a\ll {\rm keV}$	(Dennis et al., 2023)
White Dwarf Cooling	$<2.6\times10^{-13}$	$m_a\ll {\rm keV}$	(Carenza et al., 2021)
EDELWEISS-II Direct detection	$<2.6\times10^{-11}$	$m_a<1\,{\rm keV}$	(Armengaud et al., 2013)
XENON100 Direct detection	$<7.7\times10^{-12}$	$m_a<1\,{\rm keV}$	(Collaboration et al., 2014)
Solar (Borexino, reactor $\nu$)	$<2.0-2.4\times10^{-11}$	$m_a\lesssim{\rm keV}$	(Carenza et al., 2021)
Cast (Solar Axion Helioscope)	$<7.4\times10^{-13}$	$m_a < 10\,{\rm meV}$	(Altenmüller et al., 9 May 2025)
Penning trap ($g-2$, ultralight DM)	$<4.5\times10^{-14}(m_a/10^{-18}\,{\rm eV})$	$m_a<3\times10^{-18}\,{\rm eV}$	(Arza et al., 2023)
Ferrite wind (magnetometry, projected)	$<10^{-11}$ (1 d run)	$f=1\text{--}500\,{\rm Hz}$	(Gao et al., 29 Sep 2025)
Accelerated electrons (laser-plasma)	$<8\times10^{-8}$ (projected)	$m_a\ll {\rm 100\,keV}$	(Vacalis et al., 23 Oct 2025)

Constraints are subject to underlying assumptions: model dependence (DFSZ, KSVZ, variants), axion mass, coupling normalization, and degree of astrophysical and laboratory systematics included.

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In sum, the study of axion–electron coupling strengths sits at the intersection of theoretical particle physics, precision astrophysics, and quantum sensing. The current landscape reflects both significant progress in empirical exclusion and substantial room for future improvement for both terrestrial and astrophysical approaches. The inclusion of robust uncertainties and parameter degeneracies substantially influences the interpretation of existing bounds, and future advances in data-driven modeling, combined with next-generation detectors, are poised to further refine or reveal the viable parameter space for axion models.