Inelastic Dark Matter Models

• Inelastic dark matter models are defined by a nonzero mass splitting between ground and excited states, leading to distinct kinematic thresholds in scattering events.
• They utilize various frameworks—composite, magnetic dipole, vector portal, and scalar realizations—to explain experimental anomalies and reconcile direct detection results.
• These models impact cosmology and structure formation through mechanisms like co-annihilation, self-interactions, and phase transition signals observable in colliders and astrophysical surveys.

Inelastic dark matter (iDM) models constitute a broad and technically rich class of theories wherein the dark matter particle accesses multiple internal states, with low-lying excited states that can be accessed via kinematically suppressed transitions. The defining phenomenological feature of such models is the existence of a nonzero mass splitting, typically in the range of tens of keV to several GeV, between a ground state (the actual dark matter candidate) and one or more nearby excited states. Scattering events involving Standard Model (SM) particles then generically require inelastic transitions, distinguishing the recoil spectra, detection signatures, and cosmological behavior from those of canonical elastic dark matter candidates. Over the past two decades, iDM has been invoked to address experimental anomalies and theoretical challenges spanning direct detection, collider searches, small-scale structure, and dark sector cosmology.

1. Model-Building Frameworks and Mass Splitting Mechanisms

Inelastic dark matter arises in a variety of theoretical frameworks, each specifying both the origin of the spectrum and the dominant mediation mechanism for interactions with the SM or within the dark sector.

Composite iDM

The composite inelastic dark matter (CiDM) framework (Alves et al., 2010) realizes the mass splitting via hyperfine interactions in a nonabelian confining sector, analogous to the hydrogen atom. Here, dark matter is a bound mesonic state composed of a heavy fermion ($\Psi_H$) and a light anti-fermion ($\bar{\Psi}_L$). Hyperfine splitting is induced by spin–spin chromomagnetic interactions, with the dominant contribution:

$$\Delta E \simeq \kappa_1^2 \left(1 - \frac{1}{N_c} \right) \frac{\Lambda_d^2}{m_H}$$

where $\Lambda_d$ is the dark confinement scale, $N_c$ the number of colors, and $m_H$ the heavy quark mass. For plausible values ($\Lambda_d \sim \mathcal{O}(100)$ MeV, $m_H \gg \Lambda_d$), this naturally yields splittings $\delta m \sim 100$ keV.

Magnetic Dipole iDM

Magnetic inelastic dark matter (MiDM) models (Chang et al., 2010, Patra et al., 2011) posit that the dark matter particle is a Majorana (or pseudo-Dirac) fermion with only off-diagonal magnetic dipole interactions. The transition operator between mass eigenstates is

$$\mathcal{L} \supset - \frac{\mu_\chi}{2} \bar{\chi}^* \sigma^{\mu\nu} F_{\mu\nu} \chi + \textrm{h.c.}$$

Loop diagrams involving new charged fields generate the transition dipole, and the mass splitting results from perturbations such as small Majorana terms or Higgs-portal-like couplings.

Vector Portal and Axion-Mediated Models

In generalizations, inelastic splitting can arise in models with new vector mediators coupled to baryon or lepton number (Foguel et al., 1 Oct 2024), or via axion-like particles where matrix elements of CP-odd gluonic currents induce spin-dependent, often inelastic, interactions (Bae et al., 2023). The splitting can be generated through spontaneous symmetry breaking (via a dark Higgs or clockwork mechanism), small Majorana terms, or loop-induced operators.

Minimalistic and Scalar Realizations

Recent developments emphasize minimal field content, showing that inelasticity can be induced by a single real scalar—serving both as the dark Higgs and the mediator—without a new gauge boson (Garcia, 4 Nov 2024). Purely inelastic scalar DM models have been constructed where a complex scalar, upon mass matrix diagonalization, results in two real scalars (dark matter and its excited partner) with only off-diagonal Higgs portal couplings (Guo et al., 18 Aug 2025).

2. Scattering Kinematics and Experimental Signatures

A universal feature of iDM is the suppression or kinematic threshold for inelastic transitions:

$$v_\textrm{min}(E_R) = \frac{1}{\sqrt{2 m_N E_R}} \left|\delta m - \frac{m_N E_R}{\mu}\right|$$

where $\delta m$ is the splitting, $m_N$ the target mass, $E_R$ the recoil, and $\mu$ the reduced mass. This leads to several consequences:

• Direct Detection: Only the fastest-moving halo DM can scatter, imparting a distinct cutoff and modulation in the recoils. For $\delta m \sim 100$ keV, a notable fraction of standard direct detection parameter space is opened for signals compatible with DAMA/LIBRA but not with xenon or germanium targets (Alves et al., 2010, Barello et al., 2014, Chang et al., 2010).
• Magnetic iDM: For models exploiting the nuclear magnetic moment (notably iodine and cesium), dipole–dipole interactions are enhanced, allowing strong modulation signals even when electric (charge–dipole) scattering is small (Chang et al., 2010).
• Collider Signatures: For large splittings ($\delta m \gtrsim 100$ MeV), direct detection is kinematically suppressed and colliders become the primary probe. Generic signals include monojet or monophoton + missing energy plus a displaced vertex from the decay of the excited state, often as soft lepton jets or pions (Bai et al., 2011, Izaguirre et al., 2015, Berlin et al., 2018, Kang et al., 2021).
• Multi-Component and Boosted Scenarios: In setups with multiple dark sector species (e.g., boosted dark matter), high-energy signals (MeV-scale electrons, displaced multi-track events) are anticipated, not accessible to conventional nuclear recoil searches (Giudice et al., 2017).

3. Cosmological and Astrophysical Implications

Relic Abundance

Co-annihilation is a dominant mechanism in many iDM models: the relic density is set by $\chi_1 \chi_2 \to$ SM process at freeze-out, with the effective cross section Boltzmann-suppressed for large $\delta m$. The Boltzmann equations may include scattering, decay, and conversion processes (coscattering in the inelastic Dirac DM context (Filimonova et al., 2022)), and, for sub-GeV masses, departures from kinetic equilibrium alter the classic freeze-out paradigm.

Self-Interactions and Structure

Light mediators (e.g., dark photons) generate velocity-dependent self-interactions, potentially resolving small-scale structure anomalies via enhanced $\sigma/m$ at small velocities (Alvarez et al., 2019, Baek, 2021). When inelastic up- or down-scattering is allowed, energy injection or dissipation in halos can modify density profiles, produce large isothermal cores, or even drive core collapse if upscattering followed by rapid decay is efficient (Chua et al., 2020, Alvarez et al., 2019).

Astrophysical Constraints

• Core Formation: Preferred parameter space is defined by requiring self-interaction cross sections per unit mass of $1$–$5$ cm$^2$/g at dwarf galaxy velocities. Too-efficient inelastic cooling (when up-scattering is kinematically allowed and followed by fast decay) is strongly constrained by observations of shallow core profiles (Alvarez et al., 2019).
• Sidereal Modulation and Luminous Signals: For specific splittings ($\delta m \gtrsim 180$ keV), inelastic up-scattering in Earth’s crust followed by decay to photons provides a sidereal modulating, monoenergetic signal for liquid scintillator and gaseous detectors (Eby et al., 2019).

4. Model-Independent Analysis and Operator Formalism

A model-independent non-relativistic effective field theory framework for iDM has been established, generalizing the formalism for elastic scattering. The key innovation is modifying the transverse velocity operator as

$$\vec{v}_\perp^\text{inel} = \vec{v} + \frac{\vec{q}}{2\mu} + \frac{\delta m}{|\vec{q}|^2} \vec{q}$$

ensuring Galilean invariance and correct threshold behavior (Barello et al., 2014). The operator basis for DM–nucleon interactions remains structurally similar to the elastic case but coefficients can be complex, and the velocity and momentum dependence changes the sensitivity of nuclear targets and modulates the annual and threshold effects.

The nuclear response functions and matrix elements must be calculated with these modifications, with accurate knowledge of nuclear form factors (especially the magnetic dipole form factor) essential for robust predictions. Uncertainties in quenching factors (notably for iodine) strongly affect the parameter space for compatibility with DAMA/LIBRA and other experiments.

5. Direct, Indirect, and Complementary Detection

Direct Searches

iDM predictions have successfully accommodated DAMA/LIBRA’s annual modulation via inelastic transitions on iodine, while reconciling null results from xenon, germanium, and fluorine-based experiments, provided mass splittings and operator choices suppress elastic and other inelastic rates (Alves et al., 2010, Barello et al., 2014, Zurowski et al., 2020). Planned experiments with NaI(Tl) targets in both hemispheres (e.g., SABRE) will be able to decisively probe such scenarios within a few years (Zurowski et al., 2020).

Collider and Beam Dump Searches

The collider signature for GeV–TeV iDM with sufficient mass splitting is highly distinctive: high-$p_T$ monojet or monophoton plus missing energy and a displaced vertex from the decay of the excited partner into the ground state and SM fermions or photons. Both prompt and displaced decays, with distance scales ranging from $O(\textrm{mm})$ to tens of meters, can be accessible at the LHC main detectors (ATLAS, CMS), dedicated long-lived particle searches (MATHUSLA, CODEX-b, FASER), and $e^+e^-$ colliders (BaBar, Belle II) (Bai et al., 2011, Izaguirre et al., 2015, Berlin et al., 2018, Kang et al., 2021). Lifetime and decay mode measurements probe the underlying operator and parameter space.

Indirect Astrophysical Signals

Indirect signals from dark matter annihilation or self-interaction (especially those involving inelastic up-scattering followed by decay) can contribute to gamma ray, positron, or antiproton fluxes. MiDM scenarios can account for large-scale cosmic-ray anomalies if their annihilation cross sections are boosted relative to the thermal value (Patra et al., 2011).

Gravitational Wave Signatures

In certain inelastic scalar DM models, the coupling structure (arising from a mixed dark sector scalar potential) can induce a strongly first-order phase transition in the early universe, producing a stochastic gravitational wave background accessible to future space-based detectors (U-DECIGO). This links cosmological, astrophysical, and collider signatures in a unified experimental program (Guo et al., 18 Aug 2025).

6. Open Parameter Space, Future Prospects, and Outstanding Issues

Despite extensive phenomenological coverage, sizable regions of iDM parameter space remain untested:

• Large Splittings: For $\delta m \gtrsim$ few hundred MeV, only collider or cosmic-ray–boosted DM scenarios are sensitive; most direct detection is kinematically forbidden (Bai et al., 2011).
• Small Splittings and Cosmological Constraints: For sub-keV or keV splittings, cosmological constraints from long-lived excited states or late decays (e.g., during BBN) can be severe; minimal models such as inelastic Dirac DM offer freeze-out via coscattering and evade many current limits (Filimonova et al., 2022, Garcia, 4 Nov 2024).
• Model-building Diversity: Generalizations to vector mediators with non-universal (baryon, lepton flavor–dependent) couplings (Foguel et al., 1 Oct 2024) and axion-mediated interactions (Bae et al., 2023) open qualitatively new cosmological and phenomenological regions.
• Detection Strategy Evolution: The need for high-recoil energy windows in present direct detection experiments, time- and direction-tagged searches for luminous inelastic decay products, and planned upgrades in collider displaced vertex tagging are all crucial for progress (Bramante et al., 2016, Eby et al., 2019).

Controversies remain concerning the correct nuclear and atomic physics inputs (e.g., quenching factors, magnetic form factors), and whether observed anomalies such as the XENON1T excess (Baek, 2021) necessarily point toward iDM with light mediators. Robust operator-based analyses and comprehensive global fits remain essential.

7. Comparative Summary Table of Key iDM Model Types

Model Type	Splitting Mechanism	Dominant Experimental Signature
Composite iDM (CiDM) (Alves et al., 2010)	Hyperfine in bound states	Inelastic nuclear recoils (e.g., DAMA modulation)
Magnetic iDM (MiDM) (Chang et al., 2010, Patra et al., 2011)	Transition magnetic dipole (loops)	Nuclear recoils (enhanced for magnetic nuclei), prompt photon emission
Vector-Portal iDM (Izaguirre et al., 2015, Foguel et al., 1 Oct 2024)	Spontaneous symmetry breaking	Collider displaced vertices, monojet/monophoton+MET
Axion-Mediated iDM (Bae et al., 2023)	Clockwork/SUSY axion coupling	Elastic/inelastic direct detection, possible GW+photon signals
Purely Inelastic Scalar DM (Guo et al., 18 Aug 2025)	Higgs portal mixing, rotation	Displaced vertex at LHC, phase transition GWs
Inelastic Dirac DM (Filimonova et al., 2022)	Dark Higgs-induced mixing	Coscattering freeze-out, beam/fixed-target signals
Minimalistic Real-Scalar iDM (Garcia, 4 Nov 2024)	Parity-violating mass term, real scalar	Residual elastic direct detection, possible displaced decays

References are illustrative and not exhaustive within each class; see main text for additional detail.

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In summary, inelastic dark matter models represent a well-motivated, richly structured, and technically subtle sector of particle astrophysics at the intersection of cosmology, direct detection, collider phenomenology, and astrophysical structure formation. The explicit mass splitting, operator structure, and mediation mechanism together yield strong predictions for both kinematic signatures and the viability of different experimental technologies. The ongoing synthesis of non-relativistic EFT, nuclear physics, cosmological modeling, and collider algorithmic advances is essential for decisive tests of these models in the coming decade.