Proposal to use laser-accelerated electrons to probe the axion-electron coupling

The axion is a hypothetical particle associated with a possible solution to the strong CP problem and is a leading candidate for dark matter. In this paper we investigate the emission of axions by accelerated electrons. We find the emission probability and energy within the WKB approximation for an electron accelerated by an electromagnetic field. As an application, we estimate the number of axions produced by electrons accelerated using two counter-propagating high-intensity lasers and discuss how they would be converted to photons to be detected. We find that, under realistic experimental conditions, competitive model-independent bounds on the coupling between the axion and the electron could be achieved in such an experiment.

💡 Research Summary

The manuscript proposes a novel laboratory method to probe the axion‑electron coupling constant gₐₑ by exploiting axion emission from electrons accelerated in ultra‑intense laser fields. The authors begin by recalling that the axion, originally introduced to solve the strong CP problem, also serves as a leading dark‑matter candidate. Existing laboratory searches (e.g., CAST, OSQAR) primarily constrain the axion‑photon coupling g_{aγ} and often rely on astrophysical assumptions, leaving the axion‑electron interaction largely untested in a model‑independent way.

To address this gap, the paper develops a semi‑classical description of axion radiation from an accelerated electron. Starting from the Dirac equation with an external electromagnetic potential A^μ, the authors perform a WKB expansion in powers of ℏ. At leading order the electron follows the classical Lorentz force trajectory, while the first‑order correction yields the Thomas‑BMT equation for spin precession. The axion‑electron interaction is introduced via the derivative coupling L_int = −ℏ gₐₑ/(2m) ∂_μ ϕ ψ̄ γ⁵ γ^μ ψ. Using first‑order perturbation theory, they derive the transition amplitude for the process e → e + a, which depends on the electron’s four‑velocity v^μ, four‑acceleration a^μ, and spin state s. Two distinct emission probabilities are obtained: one for spin‑conserving transitions and one for spin‑flip transitions. By averaging over spin, they arrive at a compact expression for the average axion energy emitted per unit proper time, Eq. (20), which resembles the classical Larmor formula but includes additional terms involving the projection of the acceleration onto the axion propagation direction.

The experimental concept involves two counter‑propagating, linearly polarized laser pulses that form a standing wave in the x‑direction with electric field E_z and magnetic field B_y. Electrons from a hydrogen gas jet are placed in the off‑node regions of the standing wave, where they experience both electric and magnetic forces and undergo relativistic oscillations. The authors note that solving the full electron trajectory numerically is possible but computationally intensive; instead they approximate the axion spectrum by that of an electron in a constant magnetic field, which peaks at a characteristic momentum k_a ≈ 4 a₀³ ω₀, where a₀ = eE₀/(mω₀) is the normalized laser strength. The average energy radiated per electron per laser cycle is then expressed as ⟨E⟩ = gₐₑ² ω₀³ m⁻² N(a₀), with N(a₀) determined numerically (e.g., N(30) ≈ 10¹³).

To detect the emitted axions, the proposal relies on the axion‑electron Compton‑like conversion a + e⁻ → γ + e⁻ in a downstream material (e.g., aluminum). The corresponding cross‑section is given by Eq. (25), scaling as Zα gₐₑ⁴ m⁻² f(k_a/m). By multiplying the total number of accelerated electrons (set by the electron density ρ_e, laser pulse energy E_las, pulse duration τ_p, and repetition rate) with the conversion probability, the authors obtain the expected number of photons N_γ (Eq. 27). For a realistic near‑future laser (1 kJ pulse, λ≈1 µm, τ_p=1 ps, a₀≈30, electron density ρ_e=10²⁰ cm⁻³, and a 1 cm conversion target), the calculation yields N_γ < 1 after one week of running unless gₐₑ exceeds ≈ 4 × 10⁻⁵, thereby setting a competitive upper bound. Scaling up to an ambitious 100 kJ, 10⁻¹⁰ s pulse with a 1 MHz repetition rate would improve the sensitivity to gₐₑ ≈ 8 × 10⁻⁸ after a year of data taking.

The paper discusses several approximations and their validity regimes. The WKB treatment requires a₀ ω₀/m ≪ 1, which is satisfied for the chosen parameters (a₀/700)² ≪ 1. The massless axion approximation holds for m_a ≲ 10 keV, well below the typical axion momentum k_a ≈ 10² keV. Plasma effects are neglected under the assumption that the hydrogen jet density is low enough not to modify the laser fields significantly. Background Larmor radiation is shown to be negligible for a₀ ≲ 250. The conversion analysis assumes a model‑independent bound on g_{aγ} (≤ 10⁻⁴ GeV⁻¹) to isolate the gₐₑ dependence.

In conclusion, the authors present a compelling case that laser‑accelerated electrons can serve as a bright source of axions whose detection via axion‑electron scattering yields a model‑independent probe of gₐₑ. The projected sensitivities surpass current laboratory limits derived from reactor experiments and approach astrophysical bounds, especially with next‑generation high‑energy, high‑repetition‑rate laser facilities. The work highlights the synergy between advances in ultra‑intense laser technology and precision particle‑physics searches, and it outlines clear pathways—improved control of electron trajectories, inclusion of plasma dynamics, and optimized conversion targets—to further enhance the experimental reach.