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Annihilation feedback on elastic scattering in self-interacting dark matter

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Kalliopi Petraki, Thomas Pignard

High Energy Physics - Phenomenology · Submitted 19 Oct 2026 · 65 references

Pith's verdict: 系统地将单位性约束应用于含湮灭的SIDM，但定量的现象学结果依赖于重正化方案的选择。

T0 · AI review

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arXiv ID2610.27056 (version 1)
Pith IDXM3W5YFH, Pith's permanent record of this paper and its review
CitationKalliopi Petraki, Thomas Pignard. "Annihilation feedback on elastic scattering in self-interacting dark matter." arXiv:2610.27056 (2026). https://pith.science/paper/XM3W5YFH
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The paper

The paper claims

Annihilation feedback must be included in dark-matter self-scattering near Sommerfeld resonances to restore unitarity.

The reading

This paper argues that when dark-matter annihilation is enhanced by a long-range force, its feedback on elastic scattering cannot be ignored. Near Sommerfeld resonances, the feedback suppresses the low-velocity growth of the baseline elastic cross section that would otherwise violate unitarity. Near baseline elastic-scattering zeros, feedback generates a nonzero elastic contribution demanded by unitarity. The authors show this using a Yukawa model and a renormalized non-Hermitian Schrödinger approach, demonstrating that unitarization dramatically reduces the extreme parametric sensitivity of resonant cross sections.

What carries the argument

The key machinery is the non-Hermitian effective potential obtained by adding the absorptive (and dispersive) annihilation kernel to the baseline Yukawa potential. Solving the radial Schrödinger equation with this complex potential resums the annihilation self-energy, producing regulated partial-wave cross sections that automatically satisfy the coupled elastic–inelastic unitarity bound. For s-wave contact-like annihilation, the iteration requires renormalization of the short-distance couplings, achieved via a subtraction at a scale k⋄ = μ α_ϱ.

Extended reading notes

Core claim

The central claim is that including annihilation feedback—through a non-Hermitian optical kernel—restores unitarity and qualitatively changes elastic scattering in self-interacting dark matter. Exactly on an s-wave Sommerfeld resonance, the regulated elastic cross section plateaus at one quarter of the unitarity bound rather than growing without bound. At an elastic antiresonance, annihilation feedback fills in the zero, producing a nonzero elastic floor. Away from these special points the baseline Hermitian calculation remains adequate. These effects arise because the coupled unitarity constraints (via the optical theorem) force elastic and inelastic amplitudes to be treated together.

Load-bearing premise

The results depend on the benchmark choice of setting the dispersive contact coefficient β_0 to zero at the subtraction scale k⋄ = μ α_ϱ; a different short-distance prescription would change the magnitude of the feedback, especially near elastic-scattering zeros.

Editorial extensions

If this is right

  • Resonantly enhanced elastic self-scattering in SIDM models with light mediators is cut off at low velocities by annihilation feedback, capping the cross section at about σ_U/4 per partial wave.
  • Parameter regions that previously gave arbitrarily large low-velocity cross sections (exactly on a Sommerfeld resonance) now yield a finite, velocity-independent plateau, reducing the fine-tuning needed to match dwarf and cluster constraints.
  • Near elastic-scattering zeros (antiresonances), the annihilation-induced elastic floor follows a σ_0 ∝ v_rel^0 scaling, which is shallower than the baseline σ_0 ∝ v_rel^4 and may affect halo transport at very low velocities.
  • The strong sensitivity of baseline cross sections to small variations in the mediator mass or coupling is largely tamed by unitarization, making predictions more robust.
  • Higher partial waves (ℓ ≥ 2) are less affected because centrifugal suppression limits both resonant enhancement and annihilation feedback at low velocities.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the same annihilating channel also couples to other inelastic processes (e.g. radiative bound-state formation), the combined feedback could modify the elastic floor both quantitatively and qualitatively; the present paper treats annihilation alone, while a companion paper addresses bound-state formation.
  • The benchmark renormalization prescription (β_0=0 at k⋄) may underestimate or overestimate the dispersive part of the feedback; a different short-distance coupling could shift the magnitude of the elastic floor, especially near zeros.
  • The restriction to s-wave feedback is justified at lowest order, but for very precise halo-averaged cross sections at sub-km/s velocities, the interplay with d-wave contributions near higher resonances might need inclusion.
Original abstract

Sizable dark-matter self-interactions, motivated by observations of galactic structure, often arise from the exchange of light force mediators. Light mediators can render scattering nonperturbative and make inelastic processes important. Unitarity, via the optical theorem, implies that elastic and inelastic interactions cannot be treated independently: inelasticity induces absorptive contributions to the two-particle self-energy kernel that determines the elastic amplitude, while the resulting incoming-state dynamics also modifies the inelastic amplitudes. We study the feedback of dark-matter annihilation on elastic scattering in the presence of a long-range force. Although annihilation is a short-distance process, it can be strongly enhanced by such a force. We find that its feedback becomes significant near Sommerfeld resonances, where it suppresses the low-velocity growth of the baseline elastic cross section. Near baseline elastic-scattering zeros, it may instead generate a nonzero elastic floor required by unitarity. A companion paper studies the feedback of radiative bound-state formation on elastic scattering, which can generate sizable self-interactions.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-21: 1 request, 6,227 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.44 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.82 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Sizable dark-matter self-interactions, motivated by observations of galactic structure, often arise from the exchange of light force mediators. Light mediators can render scattering nonperturbative and make inelastic processes important. Unitarity, via the optical theorem, implies that elastic and inelastic interactions cannot be treated independently: inelasticity induces absorptive contributions to the two-particle self-energy kernel that determines the elastic amplitude, while the resulting incoming-state dynamics also modifies the inelastic amplitudes. We study the feedback of dark-matter annihilation on elastic scattering in the presence of a long-range force. Although annihilation is a short-distance process, it can be strongly enhanced by such a force. We find that its feedback becomes significant near Sommerfeld resonances, where it suppresses the low-velocity growth of the baseline elastic cross section. Near baseline elastic-scattering zeros, it may instead generate a nonzero elastic floor required by unitarity. A companion paper studies the feedback of radiative bound-state formation on elastic scattering, which can generate sizable self-interactions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Sizable dark-matter self-interactions, motivated by observations of galactic structure, often arise from the exchange of light force mediators. background 1.00 0.04 0.02 asserted 0.72
s1 Light mediators can render scattering nonperturbative and make inelastic processes important. background 1.00 0.06 0.03 hedged possibility 0.71
s2 Unitarity, via the optical theorem, implies that elastic and inelastic interactions cannot be treated independently: inelasticity induces absorptive contributions to the two-particle self-energy kernel that determines the elastic amplitude, while the resulting incoming-state dynamics also modifies the inelastic amplitudes. background 1.00 0.08 0.07 asserted 1.00
s3 We study the feedback of dark-matter annihilation on elastic scattering in the presence of a long-range force. contribution 1.00 0.88 0.05 asserted 0.94
s4 Although annihilation is a short-distance process, it can be strongly enhanced by such a force. background 0.66 0.16 0.05 asserted 0.53
s5 We find that its feedback becomes significant near Sommerfeld resonances, where it suppresses the low-velocity growth of the baseline elastic cross section. result 1.00 0.96 0.55 asserted 1.00
s6 Near baseline elastic-scattering zeros, it may instead generate a nonzero elastic floor required by unitarity. result 0.99 0.85 0.12 hedged possibility 1.00
s7 A companion paper studies the feedback of radiative bound-state formation on elastic scattering, which can generate sizable self-interactions. future work 0.60 0.16 0.03 asserted 0.81

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.70.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Regulated elastic cross section, normalized to the unitarity limit,
Figure 2. One-boson-exchange kernels generating long-range potentials in the model.
Figure 3. Unregulated normalized partial-wave cross sections,
Figure 5. DM annihilation into two scalar mediators,
Figure 6. Contributions to the XX† 2PI kernel. (a) Dispersive long-range contribution generated by ϱ exchange. (b) Dispersive contact contribution generated by the quartic self-coupling. (c)–(f) Optical-kernel contributions generated by annihilation into ϱϱ† . The red dashed lines denote on-shell cuts, which generate absorptive terms, whereas off-shell ϱϱ† intermediate states generate dispersive terms. For the unregulated cross sections in this section, only the long-range contribution (a) is retained, whereas the contributions (a)–(f) are included in the regulated scattering studied in…
Figure 7. Sommerfeld factors as functions of ξ ≡ µ|α|/mmed, for fixed ℓ and ζ ≡ α/vrel. As ξ → ∞, they approach the corresponding Coulomb values, S C ℓ . Left: For ℓ = 0, the potential is attractive, and resonances occur at fixed values of ξ due to bound states at threshold. Right: For ℓ = 1, the potential is repulsive, and the Sommerfeld factor introduces a suppression. There are no bound states, so no resonances occur. 10-3 10-1 101 103 105 100 101 102 103 104 105 106 Attractive potential ξ 10 19.8 20 100 ∞ Resonance n  5 Coulomb ℓ  0 10-3 10-1 101 103 105 10-24 10-20 10-16 10-12 10-8…
Figure 8. Sommerfeld factors as functions of |ζ| = |α|/vrel, for fixed ℓ and ξ = µ|α|/mmed. For attractive potentials, the Yukawa result follows the Coulomb limit for |ζ| ≲ ξ/(ℓ + 1), while finite-range effects become important at larger |ζ|. For repulsive potentials, the exponential Coulomb suppression is more sensitive to screening, which becomes significant at smaller |ζ|. See text for further discussion. 24
Figure 9. Unregulated s-wave annihilation cross sections normalized to the unitarity cross section, as a function of ζ, for λXϱ = 0 and different values of αϱ and ξ = µαϱ/mϱ. Away from the discrete resonance values of ξ, the cross sections remain well below the global inelastic unitarity bound, y Ann ℓ,unreg ⩽ 1/4. Near resonances, they can approach and, at sufficiently small velocities, exceed this bound. For ξ = ξn=1,ℓ=0 ≃ 0.84 and the larger coupling shown, αϱ = 10−1 (left), the global unitarity bound is exceeded below vrel ∼ 50 km s−1 , at velocities characteristic of dwarf galaxies. For…
Figure 10. Comparison of the quantities entering Eq. (
Figure 11. illustrates that annihilation feedback can strongly modify elastic scattering in the immediate vicinity of a Sommerfeld resonance, while rapidly becoming negligible away from it. The effect becomes increasingly pronounced towards lower velocities. We focus on the first s-wave resonance, ξ = ξ1,0; higher resonances exhibit similar behavior. At a point sufficiently detuned from the resonance,
Figure 12. Unregulated and regulated s-wave cross sections, normalized to the unitarity cross section, as functions of |ζ| = αϱ/vrel, for αϱ = 10−1 near the first s-wave resonance. Left: Elastic cross sections. Right: Annihilation cross sections. On resonance, the un￾regulated annihilation cross section grows towards arbitrarily low velocities, increasingly suppressing elastic scattering through feedback. At finite detuning, the Sommerfeld enhancement eventually saturates and the ordinary contact-like scaling is recovered. Regularization strongly reduces the sensitivity to ξ, yielding very…
Figure 13. Total viscosity cross section per unit mass as a function of
Figure 14. Annihilation feedback near the first s-wave elastic antiresonance, for αϱ = 10−1 . Left: Baseline and regulated s-wave elastic cross sections, normalized to the unitarity cross section, as functions of ξ = µαϱ/mϱ for vrel = 10 and 100 km s−1 . Anni￾hilation feedback fills in the baseline zeros. Right: s-wave elastic cross section per unit DM mass as a function of vrel, for mX = 102 GeV, comparing the exact antiresonance with a nearby point whose baseline cross section vanishes at finite velocity. On the antiresonance Exactly on the antiresonance, the leading s-wave threshold…
Figure 15. Halo-averaged XX† Yukawa contribution to the viscosity cross section per unit DM mass, σ V XX† /(2mX), for symmetric DM. We show the DM mass–coupling plane at fixed mediator mass (upper row) and the DM mass–mediator mass plane at fixed coupling (lower row), comparing the baseline result (left) with that including s-wave annihilation feedback using the benchmark prescription of Section 5.3 (right); higher partial waves remain at their baseline values. Red regions exceed the cluster benchmark of Eq. (6.7a), blue regions fall below the dwarf benchmark of Eq. (6.7b), and white regions…
Figure 16. Leading-order short-distance contributions to DM annihilation,
Figure 17. Unregulated partial-wave cross sections as functions of

Showing 16 of the paper's 17 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2610.27056 by the authors.

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