Co-Scattering Mechanism for Dark Matter

• Co-scattering is a mechanism where dark matter converts to heavier states via inelastic scatterings, setting its relic abundance instead of direct annihilation.
• The process exhibits exponential sensitivity to mass splitting and momentum dependence, distinguishing it from traditional WIMP freeze-out models.
• This mechanism offers actionable insights for experiments by predicting unique collider signatures and modified cosmological imprints.

A co-scattering mechanism for dark matter (DM) involves inelastic interactions between the DM particle and states of comparable mass—either within the dark sector or with states from the Standard Model (SM) plasma. Unlike traditional freeze-out via annihilations, the relic abundance is set by the decoupling of these inelastic (often endothermic) scatterings. This mechanism has significant implications: it alters the relationship between DM mass and abundance, modifies cosmological and collider signatures, and extends viable model space to lower-mass DM and feeble couplings. Co-scattering also applies to elastic dark sector interactions, such as momentum-exchange between dark matter and dark energy, affecting structure formation independently of the cosmological background.

1. Definition and General Principles

Co-scattering denotes a class of DM freeze-out scenarios where the chemical decoupling of DM occurs via conversion processes (inelastic scatterings) rather than 2-to-2 annihilations of DM with itself or its coannihilation partners. The general reaction structure has the DM particle (χ) upscattering against a lighter (or comparable mass) state (commonly denoted φ), converting into a heavier state (ψ):

$\chi + \phi \leftrightarrow \psi + \phi,$

with subsequent rapid depletion of ψ via efficient annihilations (e.g., ψψ → φφ). When DM's direct annihilation cross-section is small compared to the conversion process, the relic abundance tracks the freeze-out of this endothermic upscattering. Early thermal histories are dominated by χ-φ scattering, and decoupling occurs once the rate

$$\Gamma_{\chi \to \psi} = n_\phi^{\mathrm{eq}} \langle \sigma_{\chi \to \psi}\, v \rangle$$

falls below the Hubble expansion rate. The mechanism generalizes to scenarios with feeble DM–SM and/or DM–dark sector couplings and small mass splittings.

2. Boltzmann Framework and Key Equations

The number density evolution in co-scattering models is governed by Boltzmann equations that, in the regime where ψ remains efficiently depleted ($n_\psi \sim n_\psi^\mathrm{eq}$), reduce to

$$\dot{n}_\chi + 3 H n_\chi = - n_\phi^{\mathrm{eq}} \langle \sigma_{\chi \to \psi}\, v \rangle (n_\chi - n_\chi^\mathrm{eq}).$$

The coscattering process is endothermic (mψ > mχ), leading to an exponential suppression in the cross section at low T:

$$\langle \sigma_{\chi \to \psi}\, v \rangle \sim (m_\psi^{3/2}/m_\chi^{3/2})\, e^{-x \Delta}\, \langle \sigma_{\psi \to \chi}\, v \rangle, \text{ where } x = m_\chi/T,\, \Delta = (m_\psi - m_\chi)/m_\chi.$$

Freeze-out occurs when

$$n_\phi^{\mathrm{eq}} \langle \sigma_{\chi \to \psi}\, v \rangle \simeq \mathcal{O}(10) \, H,$$

and the relic abundance shows exponential sensitivity to Δ, in contrast to the logarithmic dependence in WIMP freeze-out. Where chemical equilibrium between species cannot be assumed (e.g., very feeble couplings), the full set of coupled Boltzmann equations must include terms for inelastic scatterings and inverse decays,

Term	Description	Expression
Inelastic Scattering	Conversion of frozen DM via upscattering	$\chi + \mathrm{SM} \rightarrow \psi + \mathrm{SM}$
(Inverse) Decay	Conversion via decay of heavier partner	$\psi \rightarrow \chi + \mathrm{SM}$

This complexity is accentuated by the momentum dependence of the process, requiring solution of the momentum-dependent Boltzmann equation for accurate results, particularly in the regime of early kinetic decoupling (D'Agnolo et al., 2017, Brümmer, 2019, Cheng et al., 2018).

3. Phenomenological Regimes and Model Implementations

Co-scattering is realized in a variety of dark matter frameworks:

• Simple Dark Sector Models: A minimal setup involves two states, χ and ψ, stabilized by a discrete symmetry, coupled to a light mediator φ (often a scalar or vector). Inelastic scatterings χ φ ↔ ψ φ control the relic abundance (D'Agnolo et al., 2017).
• Fraternal Twin Higgs: Here, the twin neutrino (ν̂) is the DM candidate, and the twin tau (τ̂) is the co-scattering/co-annihilation partner. The relic density is determined by the interplay between ν̂ → τ̂ (via twin photon mediation) and τ̂ annihilation (Cheng et al., 2018).
• Split Supersymmetry / Singlet–Triplet Fermion Models: Co-scattering dominates when the singlet–triplet mixing angle is extremely small (θ ≲ 10⁻⁵), so that inelastic processes (e.g., χ + SM ↔ ψ + SM) decouple before annihilations (Brümmer, 2019, Alguero et al., 2022).
• EFT Models with Scalar DM: In effective field theories with near-degenerate singlet fermions (N₁, N₂) and a scalar χ, dimension‑5 operators can drive the inelastic conversion that sets the relic abundance (Bélanger et al., 8 Aug 2025).
• Singlet–Doublet Fermion Models: For small singlet–doublet mixing, the relic density is set by co-scattering, not annihilation or co-annihilation (Paul et al., 3 Dec 2024).

The parameter space for co-scattering is sharply defined by both small mass splittings and small couplings, separating it from the standard co-annihilation regime.

4. Characteristic Cosmological and Collider Signatures

4.1 Relic Density Characteristics

Key features include:

• Exponential Sensitivity: The relic density depends exponentially on Δ and the mediator mass, allowing efficient depletion at much lower DM masses (sub-GeV) than in canonical WIMP scenarios. Typical expressions:

$$\Omega_\chi \propto \sigma_{(\psi\to\chi)}^{-1} e^{x_f (r + \Delta - 1)}$$

where $r=m_\phi/m_\chi$ (D'Agnolo et al., 2017).

• Momentum Dependence: The coscattering process's kinetic threshold induces freeze-out that depends on DM momentum, leading to a non-thermal DM distribution distinct from standard assumptions (D'Agnolo et al., 2017, Brümmer, 2019, Cheng et al., 2018).

4.2 Suppressed Standard Signatures

Because the dominant DM abundance is stored in χ, whose annihilation cross section is suppressed, standard indirect signatures (e.g., gamma rays, CMB distortions from annihilation) are weakened. However, the late decay of ψ (e.g., ψ → χ e⁺e⁻) produces energy injection at late times, potentially leading to observable CMB μ/y-type spectral distortions (D'Agnolo et al., 2017).

4.3 Collider and Astrophysical Implications

• Long-Lived Partners: The near mass degeneracy and small couplings render heavier states (e.g., ψ, twin tau, N₂) long-lived, producing displaced vertex or disappearing track signatures, as discussed for the singlet–triplet (Alguero et al., 2022) and EFT models (Bélanger et al., 8 Aug 2025).
• Mono-photon Signatures: Dimension-5 dipole operators inducing N₂ → N₁ + γ open collider channels with hard photons plus missing energy (Bélanger et al., 8 Aug 2025).
• Parameter Space Accessibility: Inclusion of co-scattering effects shifts allowed parameter regions towards those accessible by current/future high-energy collider experiments (ATLAS, HL-LHC, MATHUSLA) via displaced or mono-photon events (Paul et al., 3 Dec 2024, Bélanger et al., 8 Aug 2025).

5. Broader Context and Comparisons

5.1 Co-annihilation and Standard Freeze-out

Mechanism	Dominant process	Sensitivity to mass splitting	Kinetic/chemical decoupling separation
WIMP	$\chi\chi\rightarrow$ SM	Logarithmic	Often separate
Co-annihilation	$\chi\psi\rightarrow$ SM, $\psi\psi$	Logarithmic / polynomial	Can coincide or separate
Co-scattering	$\chi$ + φ → ψ + φ	Exponential ($e^{-x\Delta}$)	Coincident / momentum-dependent

Co-scattering generalizes the co-annihilation framework to regimes with much weaker couplings and mass splittings. Standard freeze-out analyses that integrate out momentum dependence or assume chemical equilibrium between all species become inaccurate in this regime (Brümmer, 2019, Cheng et al., 2018).

5.2 Alternative Contexts

• Dark Matter–Dark Energy Scattering: Elastic momentum exchange between DM and dark energy (with cross section σ_D) slows structure growth without altering background expansion, with allowed σ_D several orders above the Thomson cross section (Simpson, 2010, Kumar et al., 2017).
• Co-Interacting and Self-Resonant DM: Scenarios where co-scattering between different species (with u-channel resonances or Bose-enhanced cross sections) play crucial roles in astrophysical structure, as in the formation of core DM profiles (Liu et al., 2019, Du et al., 12 Mar 2024).

6. Observational and Experimental Constraints

• CMB and Structure: The late decays of upscattered or heavier DM partners inject energy into the intergalactic medium after recombination, leading to μ- and y-type deviations from a perfect blackbody, testable via current (FIRAS) and future (PIXIE) CMB instruments (D'Agnolo et al., 2017).
• Direct Detection: For electron-coupled dark sectors, the low mass and suppressed scattering rate challenge detection with traditional nuclear recoil experiments, yet enhanced sensitivity may arise in electron recoil or low-threshold experiments (Cheng et al., 2018, Knapen, 2023).
• LHC and Future Colliders: Long-lived partner decays and mono-photon signals provide promising avenues for exclusion/tests, with parameter regions defined by co-scattering often overlapping with collider sensitivity thresholds (Paul et al., 3 Dec 2024, Bélanger et al., 8 Aug 2025).

7. Computational and Theoretical Considerations

Properly computing the DM relic density in co-scattering regimes requires solving momentum-dependent Boltzmann equations. The key technical process involves tracking the phase space distribution $f_\chi(p, t)$ as the endothermic threshold splits the freeze-out epoch across momentum modes, necessitating numerical integration along characteristic curves of the evolving distribution (Brümmer, 2019, Cheng et al., 2018):

$$(\partial_t - H\,\vec{p}\cdot\nabla_{\vec{p}})f_\chi(\vec{p}, t) = \frac{1}{E}C[f_\chi](\vec{p}, t).$$

Such approaches, now implemented in advanced tools (e.g., micrOMEGAs (Alguero et al., 2022)), are essential for accurate predictions in the presence of early kinetic decoupling, non-equilibrium effects, or small couplings.

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The co-scattering mechanism offers an expanded landscape for thermal dark matter production, characterized by exponential parameter dependencies, non-equilibrium cosmological histories, and unique experimental signatures in both cosmology and collider environments. Its paper is essential for a complete survey of the dark matter parameter space, especially in regimes of suppressed direct annihilation and near-degenerate dark sector spectra.