Exothermic Inelastic Dark Matter (ineDM)
- Exothermic inelastic dark matter (ineDM) involves a heavier excited state down–scattering to a lighter ground state, releasing the mass splitting as extra kinetic energy.
- Detection strategies focus on monoenergetic electron recoils and broadened nuclear recoil spectra via the Migdal effect, enabling sub–GeV dark matter searches.
- Combined analyses of DM–electron and nuclear recoil channels constrain mediator couplings and relic excited state parameters, integrating laboratory, astrophysical, and cosmological limits.
Exothermic inelastic dark matter (“ineDM”; Editor’s term) is a theoretical framework in which dark matter particles scatter off ordinary matter primarily via inelastic transitions that deposit the dark sector mass splitting as extra kinetic energy into the recoiling standard model (SM) particle. In exothermic models, the heavier (“excited”) dark matter state down–scatters to a lighter (“ground”) state, releasing energy. This process leads to distinctive experimental signatures, a nontrivial relationship between astrophysical, direct detection, and cosmological observations, and specific constraints on the allowed parameter space for viable particle models.
1. Theoretical Foundations and Scattering Kinematics
Exothermic inelastic dark matter consists of at least two nearly degenerate dark matter states (typically denoted as X and X′ or χ₁ and χ₂) with a small mass splitting, Am = m_X′ – m_X (alternatively δ), with Am often in the range 0.05–200 keV. Direct detection involves down–scattering, in which the heavier state transitions to the lighter state: X′ + SM → X + SM, depositing Am as additional kinetic energy in the target. The recoil energy spectrum for electron targets is sharply peaked at approximately E_ER ≃ Am, with the distribution width set by the small DM kinetic energy and the detector response (He et al., 5 Mar 2024, He et al., 2020, Graham et al., 2010, Wang et al., 18 Aug 2025).
For nuclear targets, the minimum dark matter velocity required to produce a recoil energy E_R in the inelastic case is: v_min = |δ + (m_A E_R)/μχA| / [√(2 E_R m_A)], where δ < 0 for exothermic transitions, m_A is the target mass, and μχA is the DM–nucleus reduced mass (Graham et al., 2010, Blennow et al., 2015, Geng et al., 2016). The process can yield observable signals even for sub–GeV DM where elastic recoils would be undetectable, owing to the energy boost from Am (He et al., 5 Mar 2024, Wang et al., 18 Aug 2025). The Migdal effect—a process in which the nucleus recoil induces ionization of electrons—provides an additional detection channel, with the total observed electronic energy combining the nuclear recoil (often sub–threshold) with the Migdal-induced ionization (Bell et al., 2021, He et al., 5 Mar 2024, Wang et al., 18 Aug 2025).
The overall event rate for exothermic transitions can be much higher than for endothermic (up–scattering) models, since all DM velocities can contribute (no positive kinetic threshold is required), and the signature is nearly independent of the DM velocity distribution except for detailed modulation effects (Graham et al., 2010, Blennow et al., 2015). The expected shape is a narrow spectral peak in electron recoils (for Am ≲ 10 keV) or an enhanced Migdal-induced ionization rate in nuclear recoils at low E_R (He et al., 5 Mar 2024, Wang et al., 18 Aug 2025).
2. Experimental Signatures and Direct Detection Strategies
Experiments searching for exothermic inelastic dark matter focus on ultra–low–threshold detection of single– or few–electron ionization events or low–energy nuclear recoils. The critical features of ineDM in the laboratory are:
- Monoenergetic electron recoil lines: For DM–electron scattering, most of the deposited energy is Am; for Am ≥ 0.05 keV, this produces a sharp spectral feature above background and detector thresholds (Wang et al., 18 Aug 2025, He et al., 5 Mar 2024, He et al., 2020).
- Broadened nuclear recoil spectrum via Migdal effect: For DM–nucleus scattering, the released energy Am can push many events above threshold only via secondary electron emission (Migdal effect), especially notable for sub–GeV DM (Bell et al., 2021, He et al., 5 Mar 2024, Wang et al., 18 Aug 2025).
- Signal shape sensitivity: The electron recoil peak’s position directly tracks Am, while the Migdal contribution is more broadly distributed and is sensitive to the underlying DM–nucleus interaction strength and scaling.
The PandaX-4T experiment, using low–energy unpaired S2–only data (US2 channel), achieved a detection threshold of ≃0.04 keV (electron recoil), probing DM mass-splitting down to 0.05 keV and dark matter masses to the sub–GeV regime (Wang et al., 18 Aug 2025). For light DM, the electron recoil channel dominates and the signal is a narrow peak at EER ≈ Am; for heavier DM (m_X ≳ 1 GeV), Migdal-induced signals can become more relevant but tend to be less sharply peaked due to the broader kinematics (He et al., 5 Mar 2024).
The sensitivity tables of current xenon experiments are:
| Channel | Mass Range Probed | Detection Threshold | Signal Type |
|---|---|---|---|
| DM–electron (S2–only) | 0.01–10 GeV | ≃0.04 keV (US2) | Peak–like at EER ≈ Am |
| Migdal effect (S2–only) | 1–10 GeV | ≃0.04 keV (US2) | Broader below ≈3 keV |
Crucially, the combined analysis of DM–electron and Migdal signals is necessary, as their relative importance and spectral features are model-dependent and both can contribute significantly in overlapping energy regions (He et al., 5 Mar 2024).
3. Impact of Dark Sector and Mediator Models
The detection rates and spectral features of ineDM depend not only on the value of the mass splitting Am, but also on the DM’s couplings to SM electrons and quarks, as mediated by contact operators or dark photon portals. In the scenario with a dark photon mediator, the cross sections are (Wang et al., 18 Aug 2025): σXe ∝ 4α g_X2 ε2 m_e2 / (m{A′}2 + q2)2, with ε the kinetic mixing parameter and g_X the dark sector coupling. For sub–GeV DM, choice of mediator mass m_{A′}, accessibility of kinetic mixing ε, and the relative charge assignments (q_e, q_n, q_p) to electrons, neutrons, or protons strongly affect the rate in each channel and the optimal search strategy (He et al., 5 Mar 2024).
Without direct coupling to electrons (q_e = 0), the Migdal effect is the only route to a detectable signal, but if both couplings exist, the electron recoil peak dominates for light DM. The dual–channel analysis enables stronger constraints and helps avoid missed detections or misinterpretation of model parameter space (He et al., 5 Mar 2024).
Bounds on mediator parameters, particularly ε, are set by comparing observed low–energy events (typically in the 4–8 electrons ionization range at PandaX-4T) with combined SM backgrounds and the ineDM signal hypothesis. The analysis provides stringent exclusion curves in the (m_X, Am) and (m_X, ε) planes, with current PandaX-4T limits surpassing those from XENON1T S2–only analyses at low mass and small Am (Wang et al., 18 Aug 2025).
4. Astrophysical and Cosmological Implications
The implications for cosmology and celestial objects depend on the relic excited–state (X′) fraction and its decay properties:
- Long-lived excited states: For small mass splittings and suppressed coupling, the excited state lifetime can exceed the age of the universe. In freeze-in scenarios, the primordial excited fraction may persist, enabling down-scattering signals in direct detection (Baryakhtar et al., 2020, Heeba et al., 2023).
- Capture in stars and compact objects: In environments with high DM density and large gravitational potential, e.g., white dwarfs or the Sun, ineDM particles are efficiently captured and can annihilate, depositing energy that affects the cooling and thermal evolution of compact stars. Observational absence of old, cool white dwarfs in high DM density environments could support or rule out ineDM scenarios with efficient capture (Hooper et al., 2010).
- Big Bang Nucleosynthesis and CMB constraints: If excited state decays are slow (late), the injection of Am into the SM plasma at late times can cause spectral distortions or modify ionization during recombination, placing limits on the allowed parameter space for dark sector models (Heeba et al., 2023).
- Structure formation: DM particles given a velocity kick of O(Am/m_X) during down–scattering may modify clustering on small scales and alter the dark matter speed distribution in the Milky Way, potentially impacting direct detection signals and contributing to solutions of small–scale structure anomalies (Chua et al., 2020, Leonard et al., 24 Jan 2024).
5. Model Discrimination, Combined Channel Analysis, and Degeneracies
Precise determination of the DM mass m_X and mass splitting Am in ineDM scenarios is complicated by degeneracies in the recoil spectra, particularly between m_X and Am for a fixed EER peak (Bell et al., 2021, He et al., 2020). Using both the electron recoil channel (with Am–sensitive peak) and the Migdal-induced channel (sensitive to both Am and nuclear response functions) allows for improved parameter extraction and potential discrimination between models with different underlying DM–SM couplings.
Laboratory and cosmological constraints play complementary roles. For example, constraints on the dark photon’s kinetic mixing parameter ε from PandaX-4T probe regions of parameter space that overlap with cosmological bounds from BBN or CMB in freeze-in models (Wang et al., 18 Aug 2025, Heeba et al., 2023). In direct detection, the combination of Migdal and DM–electron searches is necessary to avoid missing parameter regions where either signal alone might be weak, and to avoid misattributing a spectral feature (e.g., the XENON1T excess) (He et al., 2020, He et al., 5 Mar 2024).
6. Future Directions and Experimental Prospects
Lowering detection thresholds and increasing exposure are key for future advances. Sub-keV threshold detectors, improved control of electronic and micro-discharge backgrounds, and enhanced acceptance for few-electron signals will enable extension of parameter sensitivity to even smaller mass splittings and lower DM masses (Wang et al., 18 Aug 2025). Next-generation direct detection experiments (e.g., DARWIN) are expected to probe much of the remaining parameter space for minimalistic exothermic iDM models (Garcia, 4 Nov 2024). Upcoming collider and fixed-target experiments will further test dark photon or other light mediator scenarios associated with ineDM.
Refined theoretical modeling—especially of the atomic response (Migdal effect), choice of mediator, and relic excited state abundance—will remain central for mapping direct detection signals to underlying particle models and for combining laboratory searches with astrophysical and cosmological tests.
The exothermic inelastic dark matter hypothesis provides a framework for reconciling disparate null results and potential signals in direct detection, motivates specific signatures (monoenergetic electron peaks, Migdal-induced recoils), constrains the dark sector's structure via a combination of laboratory, astrophysical, and cosmological data, and suggests clear strategies for future searches that leverage low-threshold detectors and multi-channel data analysis (Wang et al., 18 Aug 2025, He et al., 5 Mar 2024, He et al., 2020, Heeba et al., 2023, Garcia, 4 Nov 2024).
