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arxiv: 2604.21976 · v1 · submitted 2026-04-23 · ✦ hep-ph · astro-ph.CO· astro-ph.HE

Recognition: unknown

Cosmic-Ray Signatures of Annihilating and Semi-Annihilating Dark Matter via One-Step Cascades

Francesco D'Eramo , Silvia Manconi , Tommaso Sassi
Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:54 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COastro-ph.HE
keywords dark mattersemi-annihilationannihilationcosmic raysindirect detectiongamma raysdwarf galaxiesmediators
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The pith

Dark matter models including semi-annihilation produce distinctive cosmic-ray signals

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets up a framework for dark matter where three kinds of number-changing processes can shape both the relic density after freeze-out and the cosmic rays produced today. These are direct annihilation to Standard Model particles, annihilation to a mediator that decays, and semi-annihilation that produces another dark matter particle plus a mediator. By treating their relative strengths as adjustable parameters, the resulting spectra of gamma rays, neutrinos, and antimatter are calculated and shown to differ based on which processes dominate. The authors then predict gamma-ray signals from dwarf galaxies and give concrete models where these processes occur together, linking early and late universe behavior.

Core claim

We present a framework in which three classes of dark matter number-changing processes affect both the relic abundance via thermal freeze-out and the generation of indirect cosmic-ray signals today, with semi-annihilation included systematically alongside annihilations. For benchmarks of mediator decays, the injection spectra vary with the relative importance of the processes, and this is applied to gamma-ray fluxes from dwarf spheroidal galaxies, with explicit models showing the interplay.

What carries the argument

Systematic inclusion of semi-annihilation processes with a dark matter particle and metastable mediator in the final state, in addition to direct annihilations and annihilations into mediators.

If this is right

  • The injection spectra for gamma rays, neutrinos, and cosmic-ray antimatter depend on the mix of the three processes.
  • Observable gamma-ray fluxes from dwarf spheroidal galaxies vary accordingly in the GeV-TeV range.
  • Explicit model realizations illustrate how multiple processes together determine the signatures.
  • A consistent link is established between early-universe dynamics and present-day observables.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Observers could use spectral shapes to infer the presence of semi-annihilation in addition to standard annihilation.
  • The framework suggests searching for signals that only appear when semi-annihilation contributes significantly.
  • It may help explain why some models fit data better when mixed processes are allowed.

Load-bearing premise

The setup assumes the presence of these processes with unsuppressed s-wave contributions and treats their relative importance as free parameters that can be varied independently.

What would settle it

Precise measurements of gamma-ray fluxes from dwarf galaxies that fail to match any combination of the predicted spectra for varying process weights would falsify the applicability of this framework.

Figures

Figures reproduced from arXiv: 2604.21976 by Francesco D'Eramo, Silvia Manconi, Tommaso Sassi.

Figure 1
Figure 1. Figure 1: Schematic representation of the three distinct classes of processes responsible for CR production considered in this study: annihilations (1a), one-step annihilations (1b), and one-step semi￾annihilations (1c). All initial states involve two DM (anti-)particles (solid black lines). A mediator that couples to both the dark and visible sectors is exchanged or produced in each process (double red lines). In t… view at source ↗
Figure 2
Figure 2. Figure 2: Relative semi-annihilation contribution η (defined in eq. (2.11b)) as a function of the mass of the DM particle mS for constant values of the total, effective averaged cross section Σeff. All the parameter combinations reproduce the DM abundance observed today. the bath temperature TFO satisfies the condition xFO ≡ mS TFO = ln" 0.p 038 MPl mS Σeff g⋆(xFO) xFO # , (2.9) which leads to the DM relic density Ω… view at source ↗
Figure 3
Figure 3. Figure 3: Single process injection spectra: γ rays. Differential injection spectra of γ rays per single DM collision process when the signal is determined exclusively by: direct annihilation (blue), one-step annihilation (orange) or one-step semi-annihilation (green) processes. Each panel (a,b,c,d) refers to a different final state particle ψSM = (γ, b, τ, e), going clockwise starting from the top-left panel. this i… view at source ↗
Figure 4
Figure 4. Figure 4: Ratio of γ−ray spectra from different single process. Ratio R (see eq. (2.17)) of the differential injection spectra of γ rays per single DM collision process in scenarios where the ID signal is uniquely determined by a single process among the ones illustrated in figure 1. Each panel refers to a different final state particle ψSM = (γ, b, τ, e), going clockwise starting from the top-left panel. the benchm… view at source ↗
Figure 5
Figure 5. Figure 5: Injection spectra from a superposition of processes: γ rays. Differential injection spectra of γ rays per single DM collision process in scenarios where the DM signal is generated by the superpositions of the contributions coming by a mixture of two (yellow, red, magenta) all of the three processes (cyan) under consideration. Each panel refers to a different final state particle ψSM = (γ, b, τ, e), going c… view at source ↗
Figure 6
Figure 6. Figure 6: Single process injection spectra: neutrinos. Same as figure 3 but for the total neutrino production per single DM collision process. deviation produced. Nevertheless, given the sizable modification predicted in particular for photon and electron SM primary states, current and forthcoming neutrino data represent a promising avenue to explore DM interactions beyond standard annihilation. 5 Charged cosmic ray… view at source ↗
Figure 7
Figure 7. Figure 7: Ratio of neutrino spectra from different single processes. Same as figure 4 but for the differential injection spectra of neutrinos per single DM collision process. 5.1 Positrons Charged light antiparticles, such as positrons, coming from DM have been searched for in a number of experiments in the past decades, like PAMELA [68], H.E.S.S [69], and AMS￾02 [70]. The raise of the positron fraction firstly dete… view at source ↗
Figure 8
Figure 8. Figure 8: Injection spectra from a superposition of processes: neutrinos. Same as figure 5 but for the neutrinos per single DM collision process. include semi-annihilations. We start comparing in figure 9 the injection spectra of positrons per single DM pair collision in scenarios where the signal is generated by a single type of scattering process. At this stage, we can see that the shape and the characteristics of… view at source ↗
Figure 9
Figure 9. Figure 9: Single process injection spectra: positrons. Same as figure 3 but for the spectra of positrons per single DM collision. line) is very similar to a line-like emission with a much attenuated tail at low energies, while one-step spectra resemble very much a box-shape, which overwhelms the self-annihilation curve by orders of magnitude in a quite broad energy interval from around 10 GeV up to hundreds of GeV, … view at source ↗
Figure 10
Figure 10. Figure 10: Ratio of positron spectra from different single processes. Same as figure 4 but for the differential injection spectra of positrons per single DM collision process. massive and charged CRs like antiprotons provide a strong, complementary test ground for DM ID. In this case, it is the kinetic energy of the antiproton which is the relevant quantity, and the injection spectra must be computed as function of … view at source ↗
Figure 11
Figure 11. Figure 11: Injection spectra from a superposition of processes: positrons. Same as figure 5 but for the positrons per single DM collision process. and the results we obtained in full generality applying eq. (2.16). Our results are intended to be, eventually, a generalised extension of those presented in the past literature, since they are computed with no initial assumption on the hierarchy between the masses of the… view at source ↗
Figure 12
Figure 12. Figure 12: Single process injection spectra: antiprotons. Same as figure 3 but for the spectra of antiprotons per single DM collision. suppression affects the spectra over the whole energy range, contrary to what observed in all the previously discussed cases. This is further evident in figure 13, where we see that one-step (semi-)annihilation to annihilation rates ratio is always smaller than one and of the order o… view at source ↗
Figure 13
Figure 13. Figure 13: Ratio of antiproton spectra from different single processes. Same as figure 4 but for the differential injection spectra of antiprotons per single DM collision process. antiprotons are presented in figure 14. In this framework, we observe that, as remarked before, if a relevant contribution of DM direct annihilation is present, this is going to shape the major features of the injection spectrum. However, … view at source ↗
Figure 14
Figure 14. Figure 14: Injection spectra from a superposition of processes: antiprotons. Same as figure 5 but for the antiprotons per single DM collision process. can be captured within a small observation aperture of 0.5 ◦ (1◦ ) (see figure (7) and Tab. (4) of the same Ref.). According to the CTAO collaboration analysis in [94], DraI is among the eight optimal targets for ∼ 300 h observation time (ranking 7th(4th) for θ < 0.5 … view at source ↗
Figure 15
Figure 15. Figure 15: γ−ray flux from the dSph DraI generated by DM annihilation (blue lines), one-step annihilation (orange) and one-step semi-annihilation (green). Top panels show fluxes for photophilic dark sectors, while bottom panels refer to leptophilic dark sectors coupling to the heavier generation. Left panels refer to mS = 1 TeV, mϕ = 200 GeV, while right panels to a smaller DM and mediator mass of mS = 10 GeV, mϕ = … view at source ↗
Figure 16
Figure 16. Figure 16: Same as figure 15 but for the case in which the signal is shaped by the superposition of the contributions from different collision processes. The standard annihilation is reported in blue for reference, while colored lines correspond to a mix of annihilation, one-step cascade annihilation and semi-annihilation, as defined by the α, β parameters (see eq. (2.21)). 7 Models The strength of the framework pre… view at source ↗
Figure 17
Figure 17. Figure 17: Upper and lower integration limits of the one-step annihilation injection spectrum for antiprotons (X = p) as a function of xS. We fix ϵS = 0.01 and vary ϵϕ = (0.1, 0.05, 0.01, 0.001) across the four panels. Solid lines correspond to the results of Ref. [17], obtained in the large-hierarchy limit (ϵϕ ≪ 1, ϵS ≪ 1), while dashed lines are computed using the full expressions in eq. (B.9). In each panel, we a… view at source ↗
Figure 18
Figure 18. Figure 18: Comparison of antiproton injection spectra from one-step DM annihilations computed using different approximations. We fix ψSM = b as the primary production channel, set ϵS = 0.01, and vary ϵϕ = (0.1, 0.05, 0.01, 0.001). Solid black lines correspond to the results of Ref. [55], obtained within the large-hierarchy approximation (ϵϕ ≪ 1, ϵS ≪ 1). These results coincide with the dashed yellow lines, obtained … view at source ↗
read the original abstract

We present a framework in which three classes of dark matter number-changing processes can affect both the relic abundance via thermal freeze-out in the early universe and the generation of indirect cosmic-ray signals today. These processes are: (i) direct annihilations into Standard Model final states; (ii) annihilations into metastable on-shell mediators that subsequently decay into Standard Model particles; (iii) semi-annihilation processes featuring a dark matter particle in the final state, accompanied by a metastable mediator. A central element of our analysis is the systematic inclusion of semi-annihilation alongside the more commonly considered channels. This setup is largely model-independent, as we only assume the presence of one or more of these processes with unsuppressed $s$-wave contributions. We analyze representative benchmarks for the dominant decay modes of the mediator and show how the resulting injection spectra for $\gamma$ rays, neutrinos, and cosmic-ray antimatter vary with the relative importance of the three classes of processes. As an application, we evaluate the observable $\gamma$-ray fluxes from dwarf spheroidal galaxies in the GeV-TeV window. Finally, we provide explicit model realizations in which multiple processes coexist, and discuss how their interplay shapes indirect detection signatures. Our results provide a consistent connection between early-universe dynamics and present-day observables, revealing distinctive features that arise when multiple dark matter processes contribute simultaneously.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a largely model-independent framework in which three classes of dark matter number-changing processes—direct annihilation to SM states, annihilation to on-shell metastable mediators that decay to SM particles, and semi-annihilation (with a DM particle in the final state plus mediator)—simultaneously determine the thermal relic abundance via freeze-out and generate present-day injection spectra for gamma rays, neutrinos, and antimatter through one-step cascades. Representative benchmarks are analyzed for different mediator decay modes, gamma-ray fluxes from dwarf spheroidals are computed in the GeV-TeV range, and explicit UV-complete models are constructed in which the three channels coexist with calculable relative strengths.

Significance. If the central mapping holds, the work supplies a practical bridge between early-universe dynamics and indirect-detection observables, with the systematic inclusion of semi-annihilation and the demonstration of distinctive multi-channel spectral features offering a useful tool for interpreting cosmic-ray data. The provision of explicit UV realizations and benchmark spectra adds concrete value for model-building and data analysis in dark-matter phenomenology.

major comments (2)
  1. [Boltzmann equation section] § on the Boltzmann equation and effective cross section: the relic-density calculation must incorporate the semi-annihilation term (which does not deplete the DM number density in the same way as pure annihilation); the manuscript should explicitly display the modified Boltzmann equation and confirm that the same s-wave rates used for freeze-out are directly propagated to the injection spectra without additional assumptions.
  2. [Benchmarks section] Benchmarks and spectra section: the relative weights of the three process classes are varied as independent free parameters; while this is stated as model-independent, the paper must show that these variations remain compatible with the observed relic density for each benchmark point, or clarify whether the relic-density constraint is imposed after the fact.
minor comments (2)
  1. [Notation] Notation for the mediator decay branching ratios should be defined once in a dedicated table or equation block rather than repeated inline.
  2. [Application to dwarfs] The dwarf-galaxy flux plots would benefit from an overlay of current experimental limits (e.g., Fermi-LAT or CTA) to make the phenomenological impact immediate.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive recommendation for minor revision. We address each major comment below and have incorporated the requested clarifications and additions into the revised version.

read point-by-point responses

  1. Referee: [Boltzmann equation section] § on the Boltzmann equation and effective cross section: the relic-density calculation must incorporate the semi-annihilation term (which does not deplete the DM number density in the same way as pure annihilation); the manuscript should explicitly display the modified Boltzmann equation and confirm that the same s-wave rates used for freeze-out are directly propagated to the injection spectra without additional assumptions.

    Authors: We agree that an explicit display of the Boltzmann equation is helpful. In the revised manuscript we now present the full form of the equation governing the DM number density, which includes the semi-annihilation term (proportional to the DM density squared but not depleting the total DM number in the same way as annihilation). We explicitly confirm that the s-wave rates entering the freeze-out calculation are identical to those used for the present-day injection spectra, with no additional assumptions beyond the model-independent framework of the paper. revision: yes

  2. Referee: [Benchmarks section] Benchmarks and spectra section: the relative weights of the three process classes are varied as independent free parameters; while this is stated as model-independent, the paper must show that these variations remain compatible with the observed relic density for each benchmark point, or clarify whether the relic-density constraint is imposed after the fact.

    Authors: We have clarified this point in the revised manuscript. The relative weights of the three process classes are indeed treated as free parameters within the model-independent setup, but for each benchmark the overall normalization is fixed by solving the Boltzmann equation so that the observed relic density is reproduced. We have added a short paragraph and an accompanying table that explicitly lists the effective cross-section scale required for each benchmark to match the Planck value, confirming that all points remain compatible with thermal freeze-out. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper defines a phenomenological framework in which the relative rates of three DM processes (direct annihilation, mediator annihilation, semi-annihilation) are introduced as independent free parameters with unsuppressed s-wave contributions. These parameters enter the Boltzmann equation for the relic abundance and are then reused to compute injection spectra for gamma rays, neutrinos, and antimatter. This is an explicit parametric mapping rather than a derivation that reduces to its own inputs. No self-definitional relations, fitted quantities presented as predictions, load-bearing self-citations, or smuggled ansatze appear. Explicit UV model realizations are provided as illustrations, not as the source of the central results. The analysis is self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The framework rests on standard thermal freeze-out cosmology, the existence of metastable mediators, and the assumption that s-wave contributions are unsuppressed; no new particles beyond the mediator are invented, but the relative branching ratios among the three processes are free parameters.

free parameters (1)
  • relative importance of the three process classes
    Varied across representative benchmarks to show how injection spectra change; no specific fitted values given in abstract.
axioms (2)
  • domain assumption Unsuppressed s-wave contributions for the processes
    Stated as the only assumption beyond the presence of the processes themselves.
  • standard math Standard thermal freeze-out in the early universe
    Implicit in the relic abundance calculation.
invented entities (1)
  • metastable on-shell mediator no independent evidence
    purpose: Intermediate state in annihilation and semi-annihilation channels that subsequently decays to SM particles
    Introduced as part of the three process classes; no independent evidence provided in abstract.

pith-pipeline@v0.9.0 · 5559 in / 1445 out tokens · 20968 ms · 2026-05-09T20:54:40.608960+00:00 · methodology

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