Coscattering: Dark Matter Freeze-Out

• Coscattering is a thermal relic mechanism in which dark matter abundance is set by inelastic scattering with a nearly degenerate partner rather than by direct annihilation.
• It features momentum-selective depletion where chemical processing persists after kinetic decoupling, distinguishing it from standard coannihilation processes.
• The mechanism predicts novel phenomenology including long-lived partner particles and suppressed direct-detection signals due to feeble couplings.

Coscattering is a thermal relic mechanism in which the dark matter abundance is set by the decoupling of an inelastic scattering process rather than by the decoupling of dark-matter self-annihilations. In the canonical setup, a dark matter state $\chi$ is accompanied by a slightly heavier partner $\psi$, and the relevant depletion channel is an endothermic upscattering such as $\chi + X \to \psi + X'$, followed by rapid annihilation or decay of $\psi$ (D'Agnolo et al., 2017). In several model studies this mechanism is also called “conversion-driven freeze-out,” whereas the general cosmological treatment places coscattering within a broader class of conversion/coannihilation dynamics (Sáez, 2024, Sáez et al., 2024, Profumo, 28 Aug 2025). A central conceptual point is that coscattering sharply separates chemical and kinetic aspects of decoupling: chemical processing of the dark matter number density can persist after momentum exchange with the bath has already become inefficient, so that kinetic decoupling can precede chemical freeze-out (Profumo, 28 Aug 2025).

1. Historical formulation and basic definition

The modern formulation of coscattering was introduced as “a fourth exception in the calculation of relic abundances,” distinct from the standard WIMP mechanism and from the classic Griest–Seckel exceptions such as coannihilation, forbidden channels, and pole annihilation (D'Agnolo et al., 2017). Its defining feature is that the process controlling the relic abundance is an inelastic scattering between dark matter and a bath particle, rather than an annihilation process involving two dark-matter particles.

In the original setup, the dark sector contains a lighter state $\chi$, a heavier state $\psi$, and a bath particle $\phi$, with key reactions

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

while $\chi\chi$ and $\chi\psi$ annihilations are suppressed (D'Agnolo et al., 2017). The forward process $\psi$0 is endothermic, so its thermally averaged rate is Boltzmann suppressed by the mass splitting

$\psi$1

As long as $\psi$2 remains efficient, $\psi$3 can be converted into $\psi$4, and the produced $\psi$5 is depleted by rapid annihilation or decay. Once the inelastic scattering rate falls below the Hubble rate, the comoving $\psi$6 abundance freezes (D'Agnolo et al., 2017).

Later work generalized this picture. The “roadmap” treatment of thermal relic freeze-out places coscattering in a unified classification of thermal mechanisms and identifies it as a $\psi$7 process, exemplified by

$\psi$8

with $\psi$9 and $\chi + X \to \psi + X'$0 (Frumkin et al., 2022). In this framework the exponential suppression parameter is

$\chi + X \to \psi + X'$1

which is small for nearly degenerate spectra and leads to slow freeze-out. This slow-freeze behavior is one reason coscattering can support thermal relic masses far above the conventional WIMP unitarity scale in the general analytic treatment (Frumkin et al., 2022).

2. Mechanism and distinction from coannihilation

Coscattering and coannihilation both require a nearly degenerate partner, but they differ in what remains efficient longest. In standard coannihilation, chemical equilibrium between $\chi + X \to \psi + X'$2 and $\chi + X \to \psi + X'$3 is assumed throughout freeze-out, and the relic abundance is controlled by an effective annihilation cross section

$\chi + X \to \psi + X'$4

(Sáez, 2024). In coscattering, by contrast, chemical equilibrium between the dark states breaks down during freeze-out, because the conversion rates become too small: $\chi + X \to \psi + X'$5 while the heavier state can still remain thermalized with the bath (Sáez, 2024).

This difference can be stated in process language. In coannihilation, the abundance is set by annihilations such as $\chi + X \to \psi + X'$6 or $\chi + X \to \psi + X'$7, with fast interconversion enforcing a common chemical potential. In coscattering, the abundance is set by inelastic scatterings like

$\chi + X \to \psi + X'$8

or, in model-dependent realizations,

$\chi + X \to \psi + X'$9

(Sáez, 2024, Sáez et al., 2024, Liu et al., 15 Oct 2025). The heavy state continues to annihilate efficiently, but the lighter dark-matter state can no longer track it once conversions fail.

Several papers explicitly use the synonym “conversion-driven freeze-out” for this regime (Sáez, 2024, Sáez et al., 2024). The broader review, however, treats coscattering as a specific corridor within conversion/coannihilation scenarios, especially when an endothermic upscattering $\psi$0 dominates after ordinary annihilations have already become inefficient (Profumo, 28 Aug 2025). This suggests a useful distinction: “conversion-driven freeze-out” is the wider class, while “coscattering” is often reserved for the momentum-selective inelastic-scattering realization.

3. Chemical equilibrium, kinetic equilibrium, and momentum selectivity

A central result of the 2025 cosmology review is that chemical and kinetic equilibration are distinct and neither implies the other (Profumo, 28 Aug 2025). For a species $\psi$1 with phase-space density $\psi$2, the Boltzmann equation in an FRW background is

$\psi$3

with collision operator decomposed as

$\psi$4

Chemical equilibrium requires the slowest number-changing rate $\psi$5 to satisfy

$\psi$6

whereas kinetic equilibrium requires the transport-weighted momentum-exchange rate $\psi$7 to satisfy

$\psi$8

for the momenta that dominate $\psi$9 and $\chi$0 (Profumo, 28 Aug 2025).

Coscattering is the archetypal counterexample to the lore that chemical and kinetic decoupling are effectively simultaneous. In the conversion/coannihilation/coscattering class, the review identifies the hierarchy

$\chi$1

so that the number density of $\chi$2 is still being processed while elastic scattering is already too weak to maintain a thermal momentum distribution (Profumo, 28 Aug 2025). The paper summarizes this point with the statement that “Chemical equilibrium governs numbers, kinetic equilibrium governs shapes” (Profumo, 28 Aug 2025).

This distinction is especially sharp in coscattering because the dominant process is endothermic. The upscattering

$\chi$3

has a threshold, so only sufficiently energetic $\chi$4 modes can participate. The review therefore describes coscattering as a momentum-selective depletion mechanism: low-momentum modes fall below threshold and stop interacting chemically first, while the high-momentum tail remains chemically active longer (Profumo, 28 Aug 2025). In this regime, the late-time $\chi$5 is neither Maxwellian nor characterized by a single temperature.

The 2019 momentum-dependent analysis in a singlet–triplet model made this structure explicit. There, the relic abundance is set by either coannihilation or, at values of the mixing angle

$\chi$6

by coscattering (Brümmer, 2019). The paper solved the full momentum-dependent Boltzmann equations and showed that lower-momentum modes of $\chi$7 decouple earlier than higher-momentum modes. As a result, a momentum-integrated treatment that enforces kinetic equilibrium can misestimate the relic density by factors of order unity in the coscattering regime (Brümmer, 2019).

4. Boltzmann description and relic-density computation

At the level of integrated number densities, coscattering enters the coupled Boltzmann system through conversion terms that relate $\chi$8 and $\chi$9. In the general conversion/coannihilation treatment, the equations take the schematic form

$\psi$0

$\psi$1

so that, when conversions are fast,

$\psi$2

(Profumo, 28 Aug 2025).

Model studies often work with yields $\psi$3 and inverse temperature $\psi$4. For the dark photon–ALP system, the coupled Boltzmann equations are

$\psi$5

with an analogous equation for $\psi$6 (Sáez, 2024). Here $\psi$7 is the thermally averaged conversion rate per DM particle,

$\psi$8

and the coscattering regime is defined by

$\psi$9

while $\phi$0 remains thermal through its stronger coupling to the Standard Model (Sáez, 2024).

For the two-singlet Higgs-portal model, the coupled equations similarly contain explicit conversion and decay terms,

$\phi$1

with benchmark coscattering behavior occurring for

$\phi$2

where the conversion rate falls below $\phi$3 around the point where $\phi$4 departs from equilibrium (Sáez et al., 2024).

The most precise treatments go beyond integrated equations. In the singlet–triplet model and in the fraternal twin Higgs model, the authors solve momentum-dependent Boltzmann equations for $\phi$5 or $\phi$6, because the inelastic process is threshold-sensitive and different momentum modes freeze out at different times (Brümmer, 2019, Cheng et al., 2018). The fraternal twin Higgs analysis also develops an interpolation procedure for the mixed regime where some momentum modes are controlled by coscattering while others are still effectively coannihilating (Cheng et al., 2018).

5. Model realizations

Coscattering has been realized in a wide range of dark-sector constructions, but their common structure is stable dark matter, a slightly heavier partner, and suppressed direct annihilation of the light state.

In the original “fourth exception” model, the dark sector contains a lighter mostly sterile Majorana fermion $\phi$7, a heavier active state $\phi$8, and a real scalar mediator $\phi$9. The dark-sector Lagrangian includes

$$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$0

with the small mixing parameter $$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$1. In this limit, $$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$2 is unsuppressed, while $$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$3 and $$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$4 are suppressed by powers of $$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$5, naturally producing the coscattering hierarchy (D'Agnolo et al., 2017).

The electroweak-scale singlet–triplet model contains a fermionic SU(2) singlet $$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$6 and a fermionic SU(2) triplet $$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$7, linked by the dimension-5 operator

$$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$8

which induces the mixing angle

$$\chi+\phi \leftrightarrow \psi+\phi, \qquad \psi+\psi \to \phi+\phi,$$9

after electroweak symmetry breaking (Brümmer, 2019). The relic density is controlled by coannihilation at $\chi\chi$0 and by coscattering for $\chi\chi$1 (Brümmer, 2019).

The extended singlet-scalar Higgs portal uses two real scalars $\chi\chi$2 and $\chi\chi$3, both odd under $\chi\chi$4, with scalar-sector Lagrangian

$\chi\chi$5

In the “simplest benchmark scenario,”

$\chi\chi$6

so the relic abundance is dominantly controlled by coscattering and decays (Sáez et al., 2024).

The dark-axion portal model takes a dark photon $\chi\chi$7 as dark matter and an axion-like particle $\chi\chi$8 as the heavier partner, with

$\chi\chi$9

For masses in the electroweak–TeV range and small splitting

$\chi\psi$0

the correct relic density can be obtained in three regimes—coscattering, mediator freeze-out, and coannihilation—with the coscattering region typically at

$\chi\psi$1

(Sáez, 2024).

The fraternal twin Higgs realization identifies dark matter with a twin neutrino $\chi\psi$2, the heavier partner with a twin tau $\chi\psi$3, and the bath mediator with a twin photon $\chi\psi$4. The defining coscattering process is

$\chi\psi$5

and the paper emphasizes that different momentum modes of $\chi\psi$6 can interpolate between coscattering and coannihilation behavior within the same model (Cheng et al., 2018).

Further realizations include inelastic Dirac dark matter with MeV–GeV masses (Filimonova et al., 2022), a scotogenic inverse model with nearly degenerate scalar singlets $\chi\psi$7 and $\chi\psi$8 (Liu et al., 15 Oct 2025), colored-mediator conversion-driven freeze-out where bound-state effects enlarge the multi-TeV parameter space (Garny et al., 2021), and a $\chi\psi$9 $\psi$00-portal model with a neutral light state and a charged heavy partner, where coscattering competes with conversion and coannihilation in both resonance and secluded regimes (Wang et al., 9 Dec 2025).

6. Phenomenology, numerical subtleties, and broader significance

The most immediate cosmological implication of coscattering is that the standard relic-density computation based on a Maxwellian dark-matter distribution can fail. The 2025 cosmology review explicitly warns that when annihilation or production is “sharply momentum-selective,” targeted phase-space evolution is mandatory (Profumo, 28 Aug 2025). Model-specific analyses confirm this: the singlet–triplet study finds that full momentum-dependent Boltzmann equations are needed for a precise relic-density calculation, while the fraternal twin Higgs paper develops an interpolation method for mixed coscattering/coannihilation regimes (Brümmer, 2019, Cheng et al., 2018).

A second generic consequence is the appearance of long-lived partner particles. Because the same small couplings that suppress direct dark-matter annihilation also suppress partner decay widths, the heavy state often becomes a long-lived particle. In the dark-axion portal model, the ALP decay

$\psi$01

has width

$\psi$02

leading to macroscopic decay lengths across the parameter space relevant for coscattering (Sáez, 2024). In the two-scalar Higgs portal, the heavy scalar $\psi$03 can have decay lengths ranging from meters to $\psi$04 km, making displaced-vertex and LLP searches central probes of the mechanism (Sáez et al., 2024). Similar LLP signatures appear in the scotogenic and inelastic Dirac realizations (Liu et al., 15 Oct 2025, Filimonova et al., 2022).

Direct and indirect detection constraints are typically weak in the coscattering region because the stable state is only feebly coupled. The original paper emphasizes suppressed annihilation rates and correspondingly weak indirect-detection limits (D'Agnolo et al., 2017). The scotogenic analysis likewise finds that coscattering points have extremely small $\psi$05, while the $\psi$06-portal model shows that the small mixing angle suppresses both spin-independent scattering and direct annihilation of the light state (Liu et al., 15 Oct 2025, Wang et al., 9 Dec 2025). This does not make coscattering untestable; it shifts the phenomenology toward mediator and partner signatures, cosmological late decays, and specialized collider searches.

Coscattering also has broader conceptual importance because it sharpens a general lesson about relic freeze-out. The unified freeze-out analysis of thermal relics emphasizes that going beyond WIMP-like annihilation typically requires nearly degenerate partner states and often produces slow freeze-out with $\psi$07 in the general parameterization of the rate (Frumkin et al., 2022). The cosmology review extends this lesson by showing that the ordering of chemical and kinetic decoupling is model dependent rather than universal, and that coscattering is one of the clearest cases where kinetic decoupling can occur first (Profumo, 28 Aug 2025).

In this sense, coscattering is not merely a specialized variant of coannihilation. It is a phase-space-sensitive freeze-out mechanism in which endothermic inelastic scattering, rather than annihilation, is the last efficient process controlling the dark-matter abundance. Its characteristic ingredients are a compressed dark spectrum, chemically active but kinetically decoupled dark matter, momentum-selective depletion, and the frequent emergence of long-lived heavy partners (D'Agnolo et al., 2017, Brümmer, 2019, Profumo, 28 Aug 2025).