Opening the Parameter Space of sub-GeV Inelastic Dark Matter through Parity Violation

Sub-GeV dark matter (DM) has emerged as a particularly compelling target in light of the persistent null results from conventional DM searches. While s-wave annihilating DM candidates with masses below the GeV are strongly constrained by indirect-detection bounds, inelastic scenarios can naturally evade these limits. In this work, we show that parity violation can play an important role in inelastic DM models featuring long-lived excited states by inducing small diagonal couplings that significantly relax experimental constraints. A precise determination of the excited-state abundance is essential for assessing the phenomenology of such models. To this end, we solve the integrated Boltzmann equation, fully accounting for up- and down-scattering with electrons and positrons as well as dark-sector conversion processes. Using the resulting abundance, we update the viable parameter space in light of the most recent experimental constraints and demonstrate that parity-violating interactions can reopen broad regions of parameter space that would otherwise be excluded. Moreover, the forthcoming LDMX experiment will probe a significant portion of the parameter space. The framework developed in this work can be readily applied to other exothermic sub-GeV DM scenarios.

💡 Research Summary

The paper investigates a class of sub‑GeV inelastic dark‑matter (iDM) models in which the dark sector contains a Dirac fermion that splits into two nearly degenerate Majorana states, χ (ground state) and χ* (excited state), with a small mass splitting δ ≡ mχ* − mχ. The novelty is the systematic inclusion of parity‑violating interactions in the dark‑photon portal, parametrized by a dimensionless “parity‑violation” parameter δy ≡ (mR − mL)/mL. When δy = 0 the model reduces to the usual parity‑conserving pseudo‑Dirac case, where only off‑diagonal (inelastic) couplings survive. For δy > 0 a diagonal (elastic) coupling α′el = α′ cos²2θ appears alongside the inelastic coupling α′inel = α′ sin²2θ, with θ the mixing angle of the two Majorana states. This small elastic component dramatically changes the thermal history of the excited state.

The authors first lay out the Lagrangian, including a dark‑photon A′ with kinetic mixing ε with the Standard Model hypercharge. They fix a benchmark hierarchy mA′ = 3 mχ (to avoid resonant annihilation) and consider dark‑sector gauge couplings α′ in the range 10⁻³–1, kinetic mixing ε ≈ 10⁻⁶–10⁻⁴, DM masses 10–100 MeV, and splittings δ = 100 keV–500 keV. They impose δ < 2 me to forbid χ* → χ + e⁺e⁻ decays, ensuring that χ* is cosmologically long‑lived.

A central part of the work is the computation of the relic abundance of χ and the fraction f* ≡ nχ*/(nχ + nχ*) of excited states after all chemical processes freeze out. The authors solve the integrated Boltzmann equation for f* including (i) χχ ↔ χχ conversion (driven by α′inel), (ii) up‑ and down‑scattering off electrons/positrons (χe ↔ χe, rates ∝ ε² α′inel), and (iii) the evolution of the dark‑sector temperature Tχ relative to the SM temperature T. They treat kinetic equilibrium between the two sectors self‑consistently, showing that for ε ≳ 10⁻⁵ the dark sector remains thermally coupled until T ≈ δ, after which up‑scattering becomes Boltzmann‑suppressed. In the parity‑conserving limit (δy = 0) this leads to an exponential depletion of χ and f* ≪ 10⁻⁴, which is strongly excluded by CMB constraints on s‑wave annihilation. However, a modest parity‑violating component (δy ∼ 0.1–1) yields a non‑zero elastic coupling that keeps χ ↔ χ* transitions active longer, resulting in a residual excited‑state fraction f* ≈ 10⁻³–10⁻¹ depending on the exact parameters. This fraction is crucial because direct‑detection rates, indirect‑detection (CMB) limits, and self‑interaction bounds all scale with f*.

The decay of the excited state is also analyzed. For δ < 2 me the dominant channels are χ* → χ + 3γ (loop‑induced) and χ* → χ + 2ν (via Z‑mixing). The authors compare two calculations from the literature (Refs.