Semi-Annihilation in Dark Matter

• Semi-annihilation is a process where two dark-sector particles interact to produce one dark particle plus a mediator, modifying the net dark matter count.
• It alters thermal freeze-out by introducing new terms in the Boltzmann equations, with effective depletion controlled by both annihilation and semi-annihilation channels.
• Distinct observational signatures, including multiple gamma-ray lines and boosted neutrino spectra, enable novel indirect-detection probes of dark-sector dynamics.

Semi-annihilation is a dark-matter number-changing process in which two stable dark-sector particles react to produce one stable dark-sector particle plus an unstable state or a Standard Model particle, schematically $\psi_i\psi_j\to\psi_k\phi$ or $\chi\chi\to\chi X$. Unlike ordinary annihilation, which removes two dark particles from the thermal bath, semi-annihilation changes the total dark-matter number by one unit. It is forbidden in the standard $\mathbb Z_2$-stabilized WIMP setup but becomes allowed when the stabilizing symmetry is larger than $\mathbb Z_2$, notably $\mathbb Z_3$, $\mathbb Z_4$, or more general hidden-sector “baryon” and “flavor” symmetries (D'Eramo et al., 2010, D'Eramo, 2011).

1. Definition, symmetry origin, and distinction from related processes

The defining reaction is

$\psi_i\psi_j\to\psi_k\phi,$

with $\psi_i,\psi_j,\psi_k$ stable dark-sector states and $\phi$ an unstable state, either a Standard Model particle or a mediator that later decays to the Standard Model. In ordinary annihilation, by contrast, two dark particles disappear into non-dark final states,

$\psi\bar\psi\to \text{SM SM},$

while decay involves one unstable particle,

$\chi\chi\to\chi X$0

Semi-annihilation is also distinct from conversion processes such as $\chi\chi\to\chi X$1, which reshuffle species without necessarily reducing the total dark-particle number by one, and from coannihilation in the usual Griest–Seckel sense, which still removes two dark-sector particles into visible states (D'Eramo et al., 2010, D'Eramo, 2011).

Its symmetry origin is central. Under a simple $\chi\chi\to\chi X$2, any allowed interaction contains an even number of dark fields, so processes with an odd number of external dark-sector legs are forbidden. Larger stabilizing symmetries permit them. The simplest example is a single-species $\chi\chi\to\chi X$3 model, in which

$\chi\chi\to\chi X$4

is symmetry-allowed while $\chi\chi\to\chi X$5 remains stable. More generally, semi-annihilation arises naturally in multicomponent sectors with conserved quantum numbers analogous to baryon number or flavor, including QCD-like hidden sectors and models of non-Abelian gauge-boson dark matter (D'Eramo, 2011, Bélanger et al., 2012).

Kinematic consistency requires that the process not open crossed decays of the stable states. The basic condition is

$\chi\chi\to\chi X$6

together with crossed-channel analogues. This is the mechanism by which semi-annihilation can be present while all dark-sector states remain cosmologically stable (D'Eramo et al., 2012, D'Eramo et al., 2010).

The early literature explicitly treated semi-annihilation as a distinct extension of standard relic-density lore. In that formulation, it was compared with the classic “exceptions” to the simplest freeze-out picture and described as a kind of “fourth exception” because it modifies both the Boltzmann structure and the indirect-detection phenomenology (D'Eramo, 2011).

2. Boltzmann dynamics and freeze-out

For a single $\chi\chi\to\chi X$7-stabilized complex scalar $\chi\chi\to\chi X$8, the number density obeys

$\chi\chi\to\chi X$9

The factor of $\mathbb Z_2$0 is characteristic: each semi-annihilation removes only one net dark particle. In the same setup, the relic density depends on the effective depletion combination

$\mathbb Z_2$1

so thermal production can be completely controlled by semi-annihilation (D'Eramo, 2011).

In scalar $\mathbb Z_2$2 models with $\mathbb Z_2$3, the same structure reappears in abundance form. Writing $\mathbb Z_2$4, one may define

$\mathbb Z_2$5

so that

$\mathbb Z_2$6

This modifies the freeze-out condition itself: the paper emphasizes that decoupling begins earlier and ends later than in the standard annihilation-only case (Bélanger et al., 2012).

In genuine multicomponent sectors there is generally no reduction to a single effective Lee–Weinberg equation. The full coupled Boltzmann system must be solved numerically because semi-annihilation competes with ordinary annihilation, species conversion, and, where relevant, dark-partner decays. An early numerical result was that semi-annihilation can remain efficient in regions where conversion is phase-space suppressed, so it is not merely another name for inter-species conversion (D'Eramo et al., 2010, D'Eramo, 2011).

Later model studies made the same point in concrete settings. In the Majoron-coupled $\mathbb Z_2$7 scalar model, the dominant process is

$\mathbb Z_2$8

with

$\mathbb Z_2$9

for $\mathbb Z_2$0. There the total density obeys

$\mathbb Z_2$1

and reproducing $\mathbb Z_2$2 requires roughly

$\mathbb Z_2$3

The relic abundance is therefore set by freeze-out through semi-annihilation rather than by ordinary annihilation (Miyagi et al., 2022).

A systematic model-building conclusion emerged for inert scalar multiplets: with one inert multiplet, efficient renormalizable semi-annihilation is not viable; with two multiplets, semi-annihilation can be efficient, but only a narrow class of technically natural models survives, centered on the $\mathbb Z_2$4 configuration with $\mathbb Z_2$5, $\mathbb Z_2$6, and $\mathbb Z_2$7 (Beauchesne et al., 2024).

3. Kinematics and indirect-detection signatures

Semi-annihilation changes not only the freeze-out equation but also the observable kinematics. For monochromatic gamma rays from

$\mathbb Z_2$8

the photon energy is

$\mathbb Z_2$9

This differs from ordinary annihilation into $\mathbb Z_3$0, for which $\mathbb Z_3$1. In the degenerate limit $\mathbb Z_3$2,

$\mathbb Z_3$3

so a $\mathbb Z_3$4 GeV semi-annihilation line implies

$\mathbb Z_3$5

whereas an ordinary $\mathbb Z_3$6 interpretation would point to $\mathbb Z_3$7 GeV (D'Eramo et al., 2012).

The parametric suppression is also different. For neutral dark matter,

$\mathbb Z_3$8

Semi-annihilation into a single photon is therefore enhanced relative to ordinary annihilation into photon pairs by replacing one power of $\mathbb Z_3$9 with a dark-sector coupling (D'Eramo et al., 2012).

A distinctive consequence is line multiplicity. With $\mathbb Z_4$0 dark species, ordinary annihilation gives $\mathbb Z_4$1 possible line energies through $\mathbb Z_4$2, while semi-annihilation allows one line for each allowed $\mathbb Z_4$3 channel, up to

$\mathbb Z_4$4

that is, parametrically $\mathbb Z_4$5. This was proposed as “dark sector spectroscopy.” In the simplest degenerate case, the identified smoking-gun signature is a strong $\mathbb Z_4$6 GeV semi-annihilation line accompanied by a weaker annihilation line at $\mathbb Z_4$7 GeV (D'Eramo et al., 2012).

Semi-annihilation can also produce correlated boosted-dark-matter signals. In the solar process

$\mathbb Z_4$8

nonrelativistic initial states give

$\mathbb Z_4$9

so the total flux from the Sun contains two narrow spectral features near the dark-matter mass. This “double peak” structure was identified as a distinctive signature for future large-volume neutrino detectors such as DUNE and Hyper-Kamiokande (Toma, 2021).

4. Representative model realizations

Semi-annihilation is realized in a wide range of ultraviolet and effective constructions. The following examples recur across the literature.

Framework	Characteristic channel	Distinctive feature
$\psi_i\psi_j\to\psi_k\phi,$0 scalar portal	$\psi_i\psi_j\to\psi_k\phi,$1	Simplest one-species realization
Gamma-line semi-annihilation	$\psi_i\psi_j\to\psi_k\phi,$2	Multiple gamma lines and dark-sector spectroscopy
$\psi_i\psi_j\to\psi_k\phi,$3 scalar-plus-wino sector	$\psi_i\psi_j\to\psi_k\phi,$4, $\psi_i\psi_j\to\psi_k\phi,$5	Semi-annihilation plus Sommerfeld dynamics
Majoron-coupled scalar DM	$\psi_i\psi_j\to\psi_k\phi,$6	Halo self-heating and box-shaped neutrino spectrum
Two inert electroweak multiplets	$\psi_i\psi_j\to\psi_k\phi,$7	Only one technically natural class clearly survives
Topological freeze-out	$\psi_i\psi_j\to\psi_k\phi,$8	Gauged Skyrme current and purely $\psi_i\psi_j\to\psi_k\phi,$9-wave semi-annihilation

The $\psi_i,\psi_j,\psi_k$0 gamma-line study constructed two explicit models. One was a non-Abelian vector dark-matter model with messenger fermions, in which the low-energy interaction is a non-Abelian Euler–Heisenberg-type operator and the leading semi-annihilation process $\psi_i,\psi_j,\psi_k$1 arises from box diagrams. The other was a retrofitted Rayleigh dark-matter model in which adding a dark vector $\psi_i,\psi_j,\psi_k$2 opens the semi-annihilation-like channel

$\psi_i,\psi_j,\psi_k$3

thereby reproducing a $\psi_i,\psi_j,\psi_k$4 GeV line with heavier dark matter and smaller couplings than the original annihilating RayDM setup (D'Eramo et al., 2012).

A minimal gauge-charged fermionic realization is the $\psi_i,\psi_j,\psi_k$5-symmetric scalar singlet plus wino-like $\psi_i,\psi_j,\psi_k$6 triplet. There the dark sector contains a real scalar $\psi_i,\psi_j,\psi_k$7 and a Dirac fermion triplet $\psi_i,\psi_j,\psi_k$8, with semi-annihilation channels

$\psi_i,\psi_j,\psi_k$9

and conversion

$\phi$0

This model was used to show that semi-annihilation and dark-matter exchange can deplete the fermion relic density enough to allow $\phi$1 TeV, a region excluded for a pure wino (Spray et al., 2015).

The systematic inert-multiplet analysis reached a narrower conclusion. One inert multiplet never yields efficient renormalizable semi-annihilation. With two multiplets, the favored model is the $\phi$2 case with $\phi$3 an odd-dimensional $\phi$4 multiplet, $\phi$5 an even-dimensional $\phi$6 multiplet, and $\phi$7. In that setup the unsuppressed renormalizable operator

$\phi$8

drives the dominant Higgs-emission semi-annihilation channels (Beauchesne et al., 2024).

Recent work has also embedded semi-annihilation into confining and neutrino-mass models. In “Topological Freeze-out by Semi-Annihilation,” gauging dark baryon number in a QCD-like dark sector produces the low-energy topological interaction

$\phi$9

which induces

$\psi\bar\psi\to \text{SM SM},$0

and dominates freeze-out (Davighi et al., 5 Jun 2025). In a $\psi\bar\psi\to \text{SM SM},$1 radiative neutrino-mass model, a Dirac fermion $\psi\bar\psi\to \text{SM SM},$2 semi-annihilates through

$\psi\bar\psi\to \text{SM SM},$3

with the same couplings entering a two-loop neutrino-mass diagram; the phenomenology favors an $\psi\bar\psi\to \text{SM SM},$4 MeV mediator and proton elastic-scattering cross sections of $\psi\bar\psi\to \text{SM SM},$5 for boosted-dark-matter searches (Fujiwara et al., 1 Jun 2026).

5. Thermal, halo, and cosmological consequences

Semi-annihilation can continue to affect the dark sector after chemical freeze-out because it injects kinetic energy into the surviving dark particle. In the self-heating scenario based on

$\psi\bar\psi\to \text{SM SM},$6

semi-annihilation alone can maintain kinetic equilibrium until nearly the end of freeze-out, and after freeze-out the dark-matter temperature scales as

$\psi\bar\psi\to \text{SM SM},$7

as long as self-scattering remains efficient, rather than the standard nonrelativistic scaling $\psi\bar\psi\to \text{SM SM},$8. This was proposed as a mechanism that suppresses structure formation at subgalactic scales like keV warm dark matter but with GeV-scale self-heating dark matter (Kamada et al., 2017).

The Majoron-coupled $\psi\bar\psi\to \text{SM SM},$9 model developed this idea in a concrete particle-physics setting. There the process

$\chi\chi\to\chi X$00

injects recoil energy into the halo, and with only modest elastic self-interaction,

$\chi\chi\to\chi X$01

can induce halo core formation. The same paper stresses that this mechanism is expected to be more effective in dwarf-sized halos than in larger halos on the same timescale (Miyagi et al., 2022).

Semi-annihilation can also create distinctive neutrino spectra through on-shell mediators. In the same Majoron framework, $\chi\chi\to\chi X$02 yields a box-shaped neutrino spectrum because the Majoron is produced on shell and boosted. Hyper-Kamiokande can probe the relevant signal for light dark matter, roughly in the range

$\chi\chi\to\chi X$03

and with a boost factor of $\chi\chi\to\chi X$04 in the present-day semi-annihilation rate the reach can extend up to $\chi\chi\to\chi X$05 MeV (Miyagi et al., 2022).

Resonant enhancement adds another layer of cosmological structure. In models with an $\chi\chi\to\chi X$06-channel resonance near threshold, the late-time semi-annihilation signal can be enhanced by up to five orders of magnitude over the thermal relic cross section. The relic density then depends sensitively on the dark-matter temperature evolution, and self-heating allows number-changing processes to remain effective long after kinetic decoupling of the dark and visible sectors (Cai et al., 2018).

Not all semi-annihilation mechanisms share this behavior. In the topological freeze-out scenario, the process

$\chi\chi\to\chi X$07

is purely $\chi\chi\to\chi X$08-wave. That removes the usual late-time indirect-detection problem: the relic-setting channel is velocity suppressed in the present universe while still efficient during freeze-out (Davighi et al., 5 Jun 2025).

6. Effective-operator systematics and search constraints

A model-independent effective-operator analysis of $\chi\chi\to\chi X$09 semi-annihilation up to dimension $\chi\chi\to\chi X$10, plus leading dimension-$\chi\chi\to\chi X$11 terms, found that the dark-matter-only theory space is highly constrained. Under the assumptions of gauge-singlet scalar and/or fermion dark matter, there are $\chi\chi\to\chi X$12 operators in total when only dark matter is light, and only $\chi\chi\to\chi X$13 for single-component dark sectors. Once light unstable dark partners are included, the operator basis becomes much larger and all Standard Model final states become possible (Cai et al., 2016).

That same analysis emphasized a structural phenomenological point: semi-annihilation contributes to thermal freeze-out but is largely irrelevant for direct detection and collider searches in the dark-matter-only EFT, so the irreducible probes are indirect detection and astrophysical observations. For semi-annihilation to electrons and light quarks, the thermal relic cross sections can be excluded up to about $\chi\chi\to\chi X$14 GeV; for $\chi\chi\to\chi X$15 final states the exclusion reaches roughly $\chi\chi\to\chi X$16 GeV; for Higgs, gauge-boson, and neutrino final states the limits are generally weaker than the thermal relic contour except near threshold (Cai et al., 2016).

Light semi-annihilating dark matter in the MeV–GeV range is constrained by diffuse X-ray and gamma-ray observations. In the $\chi\chi\to\chi X$17 scalar model with

$\chi\chi\to\chi X$18

current data from COMPTEL, EGRET, INTEGRAL, and Fermi Gamma-ray Space Telescope, together with the projected e-ASTROGAM reach, were translated into bounds on the semi-annihilation cross section in the range

$\chi\chi\to\chi X$19

depending on $\chi\chi\to\chi X$20 and $\chi\chi\to\chi X$21. EGRET provides the strongest current constraint in that analysis, while e-ASTROGAM could probe the whole parameter space studied (Guo et al., 2023).

For inert scalar multiplets, the indirect-detection picture is highly representation dependent. The dedicated analysis of semi-annihilation in these models found that all studied gauge combinations can reproduce the relic density, but for all cases except $\chi\chi\to\chi X$22, HESS excludes thermal relic solutions for cuspy Galactic profiles unless the profile contains a sufficiently large core. The exceptional $\chi\chi\to\chi X$23 model remains viable even for very cuspy halos because its semi-annihilation channel is Sommerfeld-suppressed rather than enhanced (Beauchesne et al., 2024).

This suggests a broad contemporary picture. Semi-annihilation is no longer treated merely as a discrete-symmetry curiosity; it functions as a general organizing principle for dark sectors whose stabilization symmetries exceed $\chi\chi\to\chi X$24. Its characteristic signatures include modified Boltzmann equations, kinematic decoupling of line energy from dark-matter mass, boosted-dark-matter final states, mediator-induced box spectra, and representation-dependent Sommerfeld behavior. At the same time, the surviving viable parameter space is strongly conditioned by the symmetry structure, the mediator spectrum, and the velocity dependence of the semi-annihilation channel itself (D'Eramo et al., 2012, Cai et al., 2016).