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Final state Sommerfeld effect on dark matter relic abundance

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Xiaoyi Cui, Feng Luo

High Energy Physics - Phenomenology · Submitted 30 Sep 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We find that the impact of the FSS effect on DM relic abundance can be significant, and an electroweak sized long-range interaction is large enough to make a correction well beyond the observational accuracy.

how it is stated · asserted 0.98 read the record →

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arXiv ID2009.14591 (version 1)
Pith IDCULLGYKE, Pith's permanent record of this paper and its review
CitationFeng Luo, Xiaoyi Cui. "Final state Sommerfeld effect on dark matter relic abundance." arXiv:2009.14591 (2020). https://pith.science/paper/CULLGYKE
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The compiled record

The paper's own sentences, arranged. 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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,809 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.75 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

If the annihilation products of dark matter (DM) are non-relativistic and if there is some long-range force between them, there can be Sommerfeld effect for the final state particles. We study this effect on DM relic abundance in the thermal freeze-out scenario. As a proof of concept, we consider the case of a DM pair annihilation into a final state pair, assuming that the mutual interactions between the two final state particles give rise to a Coulomb-like potential, and that the masses of the initial and final state particles are similar, so that both the initial and final state particles are non-relativistic. The size of the final state Sommerfeld (FSS) effect depends on the strength of the potential, as well as on the mass ratio of the final and initial state particles. We find that the impact of the FSS effect on DM relic abundance can be significant, and an electroweak sized long-range interaction is large enough to make a correction well beyond the observational accuracy. Another feature of the FSS effect is that it could be suppressed when its time scale is longer than the lifetime of the final state particles. As a corollary, we also study in the DM coannihilation scenario where the initial state Sommerfeld effect between two coannihilators could be reduced due to their instability, which may need to be taken into account for an accurate calculation of the DM relic abundance.

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 If the annihilation products of dark matter (DM) are non-relativistic and if there is some long-range force between them, there can be Sommerfeld effect for the final state particles. background 1.00 0.06 0.03 hedged possibility 0.94
s1 We study this effect on DM relic abundance in the thermal freeze-out scenario. contribution 1.00 0.88 0.04 asserted 0.68
s2 As a proof of concept, we consider the case of a DM pair annihilation into a final state pair, assuming that the mutual interactions between the two final state particles give rise to a Coulomb-like potential, and that the masses of the initial and final state particles are similar, so that both the initial and final state particles are non-relativistic. method 0.89 0.56 0.03 asserted 0.69
s3 The size of the final state Sommerfeld (FSS) effect depends on the strength of the potential, as well as on the mass ratio of the final and initial state particles. result 0.71 0.33 0.06 asserted 1.00
s4 We find that the impact of the FSS effect on DM relic abundance can be significant, and an electroweak sized long-range interaction is large enough to make a correction well beyond the observational accuracy. result 0.98 0.95 0.80 asserted 0.98
s5 Another feature of the FSS effect is that it could be suppressed when its time scale is longer than the lifetime of the final state particles. result 0.91 0.59 0.05 hedged possibility 0.99
s6 As a corollary, we also study in the DM coannihilation scenario where the initial state Sommerfeld effect between two coannihilators could be reduced due to their instability, which may need to be taken into account for an accurate calculation of the DM relic abundance. contribution 0.80 0.85 0.05 hedged possibility 0.94

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.65.

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not examined
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  • 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

The paper
Original abstract

If the annihilation products of dark matter (DM) are non-relativistic and if there is some long-range force between them, there can be Sommerfeld effect for the final state particles. We study this effect on DM relic abundance in the thermal freeze-out scenario. As a proof of concept, we consider the case of a DM pair annihilation into a final state pair, assuming that the mutual interactions between the two final state particles give rise to a Coulomb-like potential, and that the masses of the initial and final state particles are similar, so that both the initial and final state particles are non-relativistic. The size of the final state Sommerfeld (FSS) effect depends on the strength of the potential, as well as on the mass ratio of the final and initial state particles. We find that the impact of the FSS effect on DM relic abundance can be significant, and an electroweak sized long-range interaction is large enough to make a correction well beyond the observational accuracy. Another feature of the FSS effect is that it could be suppressed when its time scale is longer than the lifetime of the final state particles. As a corollary, we also study in the DM coannihilation scenario where the initial state Sommerfeld effect between two coannihilators could be reduced due to their instability, which may need to be taken into account for an accurate calculation of the DM relic abundance.

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2 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Uses its method or tool 2 papers
  • The first one is the velocity-cut method used in our previous work [ref] .

    Modification of the Sommerfeld effect due to coannihilator decays · Thermally averaged Sommerfeld factors for decaying coannihilators · 0.90

  • Assuming that DM is generated by the $f f →χχ$ reaction and the particle $f$ has a Boltzmann-distributed phase-space distribution, the thermally averaged cross-section can be simplified as follows [ref] : [equation] where $s̃_min = max[1,(m_f/m_χ)^2]$ represents the kinematically allowed velocity, introduced to account for the forbidden case [ref] or final-state SE [ref] .

    Sommerfeld effect in freeze-in dark matter · The thermal average of the SE-modified cross-section · 0.80

Cites it as background 1 paper

What it cites · 35 sentences without a confident label

Cites as background 4 papers
  • We consider the usual situation that the coannihilators and the DM share the same discrete symmetry which makes the DM stable (e.g., the $R$-parity in supersymmetric models [ref] and the $KK$-parity in Universal Extra Dimension models [ref] ), so that a coannihilator can convert to the DM particle or other species of coannihilators through decays or scatterings.

    Is the Lightest Kaluza-Klein Particle a Viable Dark Matter Candidate? · Modification of the initial state Sommerfeld effect in DM coannihilations induced by the coannihilators' instability · 0.92

  • We consider the usual situation that the coannihilators and the DM share the same discrete symmetry which makes the DM stable (e.g., the $R$-parity in supersymmetric models [ref] and the $KK$-parity in Universal Extra Dimension models [ref] ), so that a coannihilator can convert to the DM particle or other species of coannihilators through decays or scatterings.

    Supersymmetric Dark Matter · Modification of the initial state Sommerfeld effect in DM coannihilations induced by the coannihilators' instability · 0.92

  • This scenario has been further developed recently under the names of “Forbidden DM" [ref] and “Impeded DM" [ref] .

    Forbidden Dark Matter · Introduction · 0.81

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