Axion-Like Electrophilic Portal for Pion Dark Matter

We investigate a scenario where Strongly Interacting Massive Particle (SIMP) dark matter interacts with an axion-like particle (ALP) that couples exclusively to electrons. This minimal setup provides interactions which enforce thermal equilibrium between dark matter and the SM in the early Universe. We analyze the cosmological evolution of the dark sector and the constraints arising from dark matter annihilations, ALP laboratory searches and astrophysical observations. Our results show that the allowed parameter space is wider than previous studies and an ALP with mass $m_a \sim {\cal O}(10)~\text{MeV}$ can act as a viable portal between the visible and dark sectors. Interestingly, this mass range overlaps with the parameter space suggested by the reported $X_{17}$ anomaly. Furthermore, the introduction of non-vanishing $θ$ angle in the dark sector of the model opens up the parameter space to heavy ALP masses.

💡 Research Summary

The paper presents a novel realization of Strongly Interacting Massive Particle (SIMP) dark matter in which the dark sector consists of a QCD‑like confining gauge theory based on an Sp(2N_c) group. The fermionic matter content yields pseudo‑Goldstone bosons—dark pions—after chiral symmetry breaking. These dark pions acquire masses of order 100 MeV–1 GeV and interact through the Wess‑Zumino‑Witten (WZW) term, which drives 3 → 2 annihilations that set the relic abundance when the temperature falls to T ≈ m_π/20.

A crucial requirement for SIMP models is that the dark sector remains in thermal contact with the Standard Model (SM) bath at least until the 3 → 2 processes freeze out. The authors introduce an axion‑like particle (ALP) that couples exclusively to electrons, described by the Lagrangian
L_a = ½(∂a)² − ½m_a²a² − g_{ae} a \bar e γ₅ e.
Because the ALP does not couple directly to photons at tree level, the usual astrophysical bounds on ALP‑photon interactions are largely avoided. For m_a ≳ 1 MeV the ALP decays promptly to e⁺e⁻ (Γ ∝ g_{ae}² m_a) and thus does not interfere with Big‑Bang Nucleosynthesis or the Cosmic Microwave Background.

The ALP also interacts with the dark pions through the term (m_π²/4f_a²) a² π^aπ^a, which yields (i) elastic π a ↔ π a scattering that keeps the dark pions and the ALP at a common temperature, and (ii) the annihilation channel π π → aa when kinematically allowed. The elastic scattering rate must exceed the 3 → 2 rate to maintain kinetic equilibrium; this condition translates into a lower bound on the decay constant f_a (or equivalently on g_{ae}) that is compatible with existing laboratory limits.

The authors perform a detailed parameter‑space scan, imposing (1) the relic‑density requirement from the WZW‑driven 3 → 2 process, (2) the kinetic‑equilibrium condition, (3) constraints from beam‑dump experiments, electron‑g‑2, and astrophysical observations (e.g., white‑dwarf cooling), and (4) the requirement that the ALP decay before ≈ 1 s. They find that a wide region with ALP masses m_a ≈ 10–100 MeV and couplings g_{ae} ≈ 10⁻¹⁰–10⁻⁸ satisfies all constraints. Notably, the mass window around 17 MeV overlaps with the tentative X₁₇ resonance reported by the PADME experiment and other nuclear‑transition anomalies, suggesting that the electrophilic ALP could simultaneously serve as the SIMP portal and the X₁₇ mediator.

An additional novelty is the exploration of a non‑zero topological θ‑angle in the dark sector. While the SM θ is experimentally constrained to be tiny, the dark Sp(2N_c) theory has no such bound. A non‑zero θ induces an extra a G \tilde G coupling, which modifies the ALP‑pion interactions and opens up a second viable region where the ALP is heavier than the dark pion (m_a ≫ m_π). In this regime, thermal equilibrium is achieved via the θ‑induced interactions rather than the π a elastic scattering, extending the allowed ALP mass up to the GeV scale.

In summary, the paper demonstrates that an electron‑only coupled ALP provides a minimal and robust portal for SIMP dark pions. It widens the viable parameter space compared to previous photon‑coupled ALP or dark‑photon mediators, accommodates the X₁₇ anomaly, and remains consistent with all current laboratory and astrophysical bounds. Future dedicated searches for electrophilic ALPs (e.g., NA64‑e, LDMX, DarkLight) and refined measurements of low‑energy nuclear transitions will be decisive in testing this framework.