Spin-Resolved Decay of Axion-Like Particles into Electron--Positron Pairs in Strong Electromagnetic Fields

The gist The investigation derives a compact analytic spin-resolved differential rate for an axion-like particle decaying into an electron–positron pair in an intense laser field, which retains finite ALP-mass effects and lepton spin degrees of freedom across the vacuum threshold.

Formalism and Interaction Model

The study employs the Baier–Katkov quasiclassical operator formalism within the locally constant field approximation to derive a compact analytic rate retaining finite ALP-mass effects and the lepton spin degrees of freedom. The interaction is described by the pseudoscalar coupling LI = −i gae ϕ ψγ¯ 5ψ (1). The analysis considers an ultrarelativistic ALP with energy ω, mass ma, and m2a/ω2 ≪ 1, in an intense laser background characterized by a large classical nonlinearity parameter a0 = geA0/me ≫ 1. The locally constant field approximation (LCFA) is justified parametrically through the adiabatic limit ωL → 0, for which a0 → ∞ while χa remains fixed.

Spin-Resolved Decay Rate Derivation

The spin-resolved differential decay rate in the LCFA is given by dΓ/dε+ = g 2ae/16π3ωZ dτ dα dβ F(τ, α, β) e−i(aτ3+bτ) (2). The spin-dependent prefactor F is given by a complex expression involving the dimensionless variables α and β, and the spin vectors ζ+ and ζ−. The phase in Eq. (2) has a cubic structure characteristic of LCFA processes. The parameter ∆ encodes the effect of the finite ALP mass and has a simple kinematic origin, where for a fixed positron energy fraction δ+ = ε+/ω, vacuum decay into an electron–positron pair requires m2a/m2e δ+(1−δ+) ≥ 1.

Kinematic Regimes and Unified Representation

The analytical evaluation of the integral in Eq. (2) leads to two regimes identified by the sign of ∆. In the vacuum-forbidden kinematic regime (∆ > 0), the rate is expressed using modified Bessel functions Kν via Eq. (7). In the vacuum-allowed kinematic regime (∆ < 0), where ε+ is inside a specific kinematic window, the integral splits into inner and outer regions, yielding ordinary Bessel functions Jν via Eq. (9). These two regimes are unified into a single compact expression using Airy functions in Eq. (10). This unified form provides a uniform analytic continuation across ∆ = 0, connecting the vacuum-forbidden and vacuum-allowed kinematic regions.

Mass Effects and Oscillatory Signatures

The finite ALP mass introduces the parameter ∆, which governs the transition between regimes. For ma > 2me, the vacuum decay channel opens over a finite energy interval and contributes to the same final state as the field-assisted process. The coherent interplay between vacuum and field-assisted contributions produces oscillatory modulations in the energy spectrum, total rate, and spin asymmetry when ma > 2me. These oscillations are traced to the two-realsaddle structure arising from coherent interference between the two real formation-time saddles.

Spin Entanglement Analysis

The reduced two-qubit spin density matrix is constructed using coefficients derived from the Airy function representation in Eq. (26). The concurrence C and the spin correlator cΣ are calculated from this density matrix, which are shown to encode qualitatively distinct correlation patterns across the (χa, δm) plane. In the strong-field limit χa >> 1, the state is triplet-like with finite entanglement C → 1/2. Deep in the vacuum-dominated regime (X >> 1), the reduced spin state evolves toward a separable triplet-like mixture, where cΣ → 1.

Conclusion on Signatures

The results indicate that the concurrence and spin correlations of the produced pair may provide complementary, process-specific information on ALP-mediated pair production. The quantum state of the produced pair carries a direct imprint of the underlying production mechanism, with triplet-like entanglement in strong fields and nearly singlet-like entanglement near the vacuum threshold. This framework offers both a spin-resolved description of ALP decay in strong electromagnetic fields and a practical way to track the quantum state of the produced electron–positron pair. The compact analytical form makes it well suited for implementation in semiclassical Monte Carlo simulations of strong-field particle cascades.

How it works

** The study uses the Baier–Katkov quasiclassical operator formalism and the locally constant field approximation to derive a compact analytic rate retaining finite ALP-mass effects and the lepton spin degrees of freedom. This method allows for a unified description across the vacuum threshold. The resulting differential rate is expressed in terms of Airy functions, providing a uniform analytic continuation across the threshold at ∆ = 0. This compact form is convenient for Monte Carlo implementations. The analysis shows that for ma 2me, the coherent interplay between vacuum and field-assisted contributions produces oscillatory modulations in the energy spectrum, total rate, and spin asymmetry. **

** The spin correlations are analyzed by constructing the reduced two-particle spin density matrix from Eq. (10). The concurrence C is used as a measure of entanglement, distinguishing singlet-like from triplet-like correlations using the spin correlator cΣ. In the strong-field limit, the state is entirely supported in the triplet sector with C → 1/2. Deep in the vacuum-dominated regime, the reduced spin state becomes triplet-like but separable. **

** The net positron polarization is defined along the B direction, and it is nonvanishing only along B while T and N components vanish identically. Above threshold, the net polarization drops and develops a strongly nonmonotonic fringe pattern originating from the negative-argument oscillation of the Airy function in Eq. (10). This strong spin polarization points to nontrivial two-particle spin correlations. **

** The numerical mapping across the parameter space shows that the concurrence grows as δm increases from zero toward the threshold, and then decreases while cΣ evolves toward a triplet-like value in the vacuum-dominated regime. The fringe patterns observed in integrated observables are identified as the entanglement counterpart of the vacuum–field interference oscillations in the rate. **

** The framework successfully maps the kinematic variable X, which interpolates continuously from singlet-like to triplet-like character as X increases, interpolating between field-induced and vacuum-dominated descriptions. The near-threshold limit X → 1 corresponds to a maximally entangled singlet state, while the large mass limit X >> 1 corresponds to a triplet-like but separable mixture. **

** The analysis confirms that the net polarization is nonvanishing only along B, and the spin–spin correlator cΣ = ⟨σ+ ·σ−⟩ determines the expectation value of the total spin squared.

1. Use spin-resolved differential rates to distinguish between different production mechanisms; The pseudoscalar coupling ψγ¯ 5ψ generates spin-correlation patterns that differ from those in photon-induced pair creation. This allows the improved AI system to differentiate between ALP decay and standard QED pair production signatures in experimental data.

2. Implement a unified Airy-function representation for the decay rate; Equation (10) provides a uniform analytic continuation across ∆ = 0, connecting the vacuum-forbidden and vacuum-allowed kinematic regions. This enables the AI to model ALP searches consistently across different laser field strengths and particle masses without needing separate analytical treatments.

3. Analyze spin correlations and entanglement as signatures of finite mass and threshold effects; These results identify spin-resolved spectra and entanglement as signatures of finite-mass and threshold effects in strong-field ALP searches. The improved AI can use these metrics (concurrence, spin correlator cΣ) to directly probe the underlying physics governing ALP production.

4. Develop a numerical tool for extracting reduced two-qubit spin density matrices; From the spin-resolved differential rate in Eq. (10), we construct the reduced two-qubit spin density matrix of the produced e+e− pair and quantify the entanglement it encodes. This allows the AI to quantify quantum state information directly from simulated or measured decay spectra, moving beyond simple rate measurements.

5. Predict net positron polarization based on production regime; Below threshold, where pair creation is purely field-induced, the positron is nearly fully polarized in the weak-field limit. The system can predict whether a given experimental setup will yield a high net polarization based on whether it operates above or below the vacuum decay threshold.

6. Map entanglement structure across parameter space; The concurrence C and the spin–spin correlator cΣ are shown in Figs. 7(a1) and (a2). The improved AI can visualize how entanglement evolves as a function of laser intensity (χa) and ALP mass (δm), identifying specific regions where singlet-like entanglement occurs near threshold.