Asymmetric dark matter from semi-annihilation: unitarity constraints and long-lived final states

Peter Mat\'ak; Tom\'a\v{s} Bla\v{z}ek; Viktor Zaujec

REVIEW 3 major objections 4 minor 48 references

Asymmetric dark matter from semi-annihilation: unitarity constraints and long-lived final states

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A missing diagram erases the claimed semi-annihilation dark-matter asymmetry.

desk verdict A genuinely useful correction to a flawed published mechanism, with a clear central argument and honest caveats, though the numerical results rest on unquantified omissions that a referee should ask to be pinned down. read the letter →

arxiv 2412.01470 v2 pith:2UMXY3EZ submitted 2024-12-02 hep-ph

Tomáš Blažek , Peter Maták , Viktor Zaujec This is my paper · ORCID

classification hep-ph PACS 95.35.+d98.80.Cq

keywords asymmetricdarkmattersemi-annihilationCPTsymmetryunitarityconstraintslong-livedparticlesrelicdensityBoltzmannequationsholomorphiccuttingrules

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the asymmetric dark matter mechanism based on semi-annihilation, as formulated in an earlier model, is undone by CPT symmetry and S-matrix unitarity: a semi-annihilation asymmetry in a single final-state channel must be exactly cancelled by the same initial-state reactions into other channels, and the earlier model's nonzero result came from omitting one leading-order diagram. The authors then show how a genuine asymmetry can be built, by including two distinct final-state species (two scalars or two Majorana fermions) that are long-lived and slowly decay to the Standard Model. Solving the Boltzmann equations for the modified models, they find that the dark sector becomes almost fully asymmetric and can match the observed dark matter relic density. This matters because it converts a previously accepted dark matter production mechanism into a constrained one, with explicit conditions a successful model has to satisfy.

What carries the argument

The machinery is S-matrix unitarity and CPT, expressed as $\sum_f \Delta|T_{fi}|^2=0$ (Eq. 2.1): for any fixed initial state, the rate asymmetries into all final states sum to zero, so an asymmetry in one process must be balanced by an opposite asymmetry in another. Equivalently, at the diagrammatic level, asymmetries are generated by forward-scattering diagrams with holomorphic cuts (Eq. 2.3), and unitarity-compatible asymmetries can be systematically enumerated by cutting vacuum diagrams and using rephasing invariants, combinations of couplings invariant under field redefinitions whose arrow-reversal structure reveals whether they are irreducibly complex. This two-channel requirement is the load-bearing mechanism; the paper then uses vacuum-diagram arrow reversal to show that the single-channel model has no asymmetry, and constructs two-channel scalar and fermion models with long-lived final states whose Boltzmann evolution is solved numerically.

What would settle it

Compute the full set of unitarity-related reactions in the modified scalar and fermionic models, including $\chi\chi\to\chi^\dagger\chi^\dagger\chi$, $3\chi\to\chi^\dagger\phi\chi$, and $\chi\phi_2\to\chi\phi_1$, and include their interference terms in the Boltzmann equations; if those contributions are as large as the semi-annihilation asymmetry of Eq. (3.3), the reported relic-density curves would change and the parameter choices would no longer reproduce the observed abundance. Alternatively, restoring the omitted leading-order diagram $T_3$ in the model of Ref. [30] should make the originally claimed asymmetry vanish exactly.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a non-zero semi-annihilation asymmetry requires at least two distinct final states for a fixed initial state; for a single final state the unitarity identity $\sum_f \Delta|T_{fi}|^2=0$ forces the asymmetry to vanish. For the $Z(3)$-symmetric scalar model of Ref. [30], the authors identify the omitted tree-level diagram (their $T_3$) whose interference with loop diagrams cancels the apparent asymmetry, and they show that higher-order vacuum-diagram contributions that do produce asymmetries are not suppressed and must be included. The corrected models introduce two real scalars or two Majorana fermions that are long-lived, so that their densities depart from equilibrium and the two semi-annihilation channels $\chi\chi\to\chi^\dagger\phi_1$ and $\chi\chi\to\chi^\dagger\phi_2$ (or their fermionic analogues) have opposite, non-cancelling asymmetries. Numerical solution of the coupled Boltzmann equations then yields a total dark sector asymmetry and a relic density compatible with observation, with the produced asymmetry enhancing the relic density by orders of magnitude compared with annihilation-only estimates.

Load-bearing premise

The numerical results assume that the leading semi-annihilation diagrams plotted in the paper are the only important source of asymmetry, even though the paper shows that in the earlier model additional equal-strength higher-order processes were not negligible.

Editorial extensions

If this is right

The earlier single-scalar semi-annihilation scenario cannot produce an asymmetry by itself; any computation of this type must include all leading-order interference diagrams, including the omitted diagram $T_3$.
A viable asymmetric semi-annihilation model needs at least two distinct final-state channels for the same initial state, so that opposite asymmetries can coexist without violating unitarity.
If the additional final-state particles are long-lived and feebly coupled, the dark sector can reach a state of almost complete asymmetry, raising the final relic density by up to three orders of magnitude relative to annihilation-only estimates.
Asymmetric semi-annihilation can reproduce the observed dark matter abundance for parameter choices with feeble dimensionless couplings in the scalar model, or with order-one couplings suppressed by a high-energy scale $\Lambda$ in the fermionic model.
The Boltzmann analysis must include not only connected reaction topologies but also higher-order cuts of vacuum diagrams; in the original model these are unsuppressed and contribute to $3\chi\to\chi^\dagger\phi\chi$, $\chi^\dagger\phi\chi\to\chi^\dagger\chi$, and $\chi^\dagger\chi\to 3\chi$.

Reading between the lines

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

The unitarity identity used here is process-independent, so the same two-channel check can be applied to other asymmetric freeze-in, freeze-out, or semi-annihilation constructions; single-process asymmetries in those constructions may similarly vanish once omitted diagrams are restored.
The authors' own neglect of the $\chi\phi_2\to\chi\phi_1$ asymmetry and of higher-order vacuum contributions in their modified models implies that their relic-density curves are a leading-order estimate; including those terms could shift the required couplings.
The long-lived $\phi_i$ and $\psi_i$ states are promising displaced-vertex or decay-in-flight signatures, and measuring their lifetimes and final states would directly test the mechanism.
A direct corollary of the two-channel condition is that an observed cosmic asymmetry in dark matter cannot be traced to a single dominant CP-violating reaction; searches should target pairs of channels with opposite rate asymmetries.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know this paper for one reason: it identifies a real error in a previous semi-annihilation asymmetric dark matter paper and shows, using S-matrix unitarity and holomorphic cutting rules, that the asymmetry vanishes once the missing T3 diagram is included. The diagrammatic cancellation argument is clear and, as far as I can see, correct. That alone makes the paper worth reading.

The new constructive part is a systematic way to avoid the problem: you need at least two distinct final-state channels for a non-zero asymmetry. The two-species scalar and fermionic models they build are sensible, and the Boltzmann analysis shows that large dark matter asymmetries can be generated when the final-state particles are long-lived. The paper is honest about what it does and does not do. It explicitly says it neglects the χφ2→χφ1 asymmetry after Eq. (3.8), and it mentions the existence of higher-order vacuum diagrams in Section 2.2 without trying to hide them.

The soft spots are real, though. The most important is that the paper never quantifies the higher-order vacuum-diagram asymmetries in the new models. In the original model it shows that such contributions are equally unsuppressed—no extra phase-space or Boltzmann suppression—and the modified models share the same qualitative ingredients. Without an estimate or an argument that those diagrams are subleading, the numerical relic densities in Figs. 3 and 4 can shift. This is not a fatal flaw, because the central mechanism does not depend on those numbers being exact, but it is exactly what a referee should ask for. Second, the neglected χφ2→χφ1 asymmetry uses the same λ12 that drives the source, and the paper gives no reason it is negligible. Third, the fermionic cross-sections are not derived in the text; the reader is told FeynCalc was used. That is a reproducibility gap, not a sign of error, but it should be filled.

On the citation side, the self-citations are legitimate—the cutting-rule formalism is their own, and the core result does not depend on their earlier conclusions. The paper is not a takedown; it is a correction with a positive construction. I believe the central argument holds up, and the gaps are fixable in revision.

Who is this for? Anyone working on asymmetric dark matter or on CP-violating processes in the early universe. It deserves a serious referee. My recommendation: send it to peer review, and ask the authors to quantify the omitted higher-order and washout contributions, and to show the fermionic amplitudes. Then it can be a solid contribution.

Referee Report

3 major / 4 minor

Summary. The paper studies asymmetric dark matter generated through semi-annihilation, with emphasis on unitarity and CPT constraints. It argues that the earlier model of Ref. [30] omitted a leading-order diagram and therefore obtained a spurious asymmetry; using S-matrix unitarity and holomorphic cutting rules, it shows that the asymmetry cancels when all diagrams are included, and that a nonzero semi-annihilation asymmetry requires at least two distinct final-state channels. The paper then proposes a scalar model and a fermionic effective model, each with two long-lived final-state species, writes down Boltzmann equations for the dark-matter asymmetry and abundances, and numerically demonstrates that the observed relic density can be reproduced when one of the final-state species is out of equilibrium. The central unitarity argument is physically sound and clearly presented; the numerical results, however, rely on approximations whose size is not quantified.

Significance. If the numerical proof-of-principle holds, the paper resolves a real inconsistency in the existing literature and gives a viable route to asymmetric dark matter from semi-annihilation. The unitarity argument is a genuine strength: it uses Eq. (2.1) to show that asymmetries must cancel pairwise, identifies the omitted diagram in Ref. [30], and provides a systematic cutting-rule procedure for finding all relevant terms. The paper also gives explicit Boltzmann equations and explores both scalar and fermionic realizations, which makes the mechanism concrete. The main weakness is that several contributions that could affect the relic-density predictions—higher-order vacuum-diagram cuts, the asymmetry of χφ2→χφ1, and the fermionic cross-section derivation—are not shown or bounded. The conclusion is therefore conditional on these terms being subdominant.

major comments (3)

[Sec. 2.2, Eq. (2.7) vs Sec. 3.1, Eq. (3.1)] The paper demonstrates that in the original model, higher-order vacuum-diagram cuts produce asymmetries with no extra phase-space or Boltzmann suppression (Eq. (2.7)). The modified scalar model of Eq. (3.1) retains the same qualitative ingredients—λ1, λ2, λ12, and a large λ3—so the same class of cut vacuum diagrams can contribute to χχ→χ†φ1/2 and to multi-particle channels at comparable kinematic order. The paper does not enumerate or bound these contributions for the new models. If they are comparable to Eq. (3.3), the relic densities and the sign-flip behaviour in Fig. 3(b) would shift; the manuscript needs an estimate or a symmetry/scale argument showing these terms are subdominant.
[Sec. 3.1, after Eq. (3.8)] The sentence after Eq. (3.8) explicitly states that the asymmetry of χφ2→χφ1 is neglected. This process involves the same coupling λ12 that drives the asymmetry source in Eq. (3.3), so its CP-odd part can feed directly into the evolution of Δ. No estimate or suppression argument is given. Since the washout term in Eq. (3.6) already controls the final asymmetry, the neglected process could plausibly alter the numerical curves in Fig. 3. The authors should either include this asymmetry in the Boltzmann equations or quantify why it is negligible.
[Sec. 3.2, fermionic model] For the fermionic model, the paper states that spin sums were evaluated using FeynCalc but does not display the amplitudes or the resulting thermally averaged cross-sections. The two-phase structure proportional to sinδ1 and sinδ2, which is central to Fig. 4, is therefore not independently verifiable from the text. The authors should provide at least the key steps of the cross-section calculation or an explicit expression for Δ⟨σv⟩ in the fermionic case, so that the dependence on both phases can be checked.

minor comments (4)

[Sec. 1] The phrase 'CP Tsymmetry' appears with an unwanted space; it should read 'CPT symmetry'.
[Sec. 2.2] There is a typographical error: 'arrise' should be 'arise'.
[Eq. (2.3)] The notation iTiniTnf iTf i is not defined before use; the index conventions for the T-matrix elements and the meaning of the sums over n, k should be specified.
[Sec. 3.1, Eqs. (3.5)-(3.8)] The factors of 1/2 and 1/4 in the semi-annihilation terms of the Boltzmann equations are not derived; a brief explanation of how they arise from the reaction topologies would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central asymmetry claims follow from standard S-matrix unitarity and explicit diagrammatic cancellations; self-citations are formal, not load-bearing.

full rationale

The paper's central unitarity statement, Eq. (2.1), is taken from Refs. [32,33] (Kolb-Wolfram and Dolgov) and is an external benchmark, not an input defined in terms of the paper's conclusions. The claimed cancellation in the earlier model of Ref. [30] is exhibited explicitly: the paper lists T1-T3 and L1-L3 diagrams, notes that TiL*_i is real, and shows that TiL*_j cancels TjL*_i, with the T3/L*_1 pair displayed in Eqs. (2.4)-(2.5). This is a direct calculation of the omitted diagrams, not an assumption equivalent to the result. The new-model asymmetry in Eq. (3.3) is a one-loop interference integral whose sign relation between chi chi -> chi-dagger phi1 and chi chi -> chi-dagger phi2 follows from the formula's symmetry; it is not a fitted parameter renamed as a prediction. The Boltzmann equations (3.5)-(3.8) are standard rate equations, and the model parameters are scanned or tuned as an existence proof of the mechanism; the statement in Fig. 4 (left) that parameters were tuned to reproduce the observed density is an explicit fit, not a prediction masquerading as a derivation. Self-citations to Refs. [36] and [41-43] supply the holomorphic cutting-rule formalism and vacuum-diagram enumeration, but the load-bearing cancellation is demonstrated diagram by diagram and the unitarity constraint is externally sourced; these citations are therefore not load-bearing. The unquantified higher-order vacuum-diagram contributions (Eq. (2.7)) and the neglected asymmetry of chi phi2 -> chi phi1 are physical-completeness or correctness risks, not circular steps, because nothing in the derivation defines those terms to equal the final relic density by construction.

Assumptions & free parameters 9 free parameters · 5 assumptions · 3 invented entities

The ledger shows that the demonstration of the corrected mechanism depends on a set of small couplings, specific masses, tiny decay widths, and a high effective scale Λ, all chosen by hand to match the observed DM relic density. These are not predictions but inputs to an existence proof. The general unitarity constraints are the sole external benchmark supporting the no-go claim. The long-lived φ1/φ2 and ψ1/ψ2 fields, and the heat-bath scalar φ3, are new model entities with no independent evidence.

free parameters (9)

|λ1|, |λ2| (scalar model couplings) = 3e-7, 1e-6 (Fig. 3a); 1e-6, 2e-6 (Fig. 3b)
Chosen to keep φ1/φ2 out of equilibrium and to match the observed DM relic density; no external constraint.
λ12 (scalar coupling) = 1e-6 (Fig. 3a); 3e-6 (Fig. 3b)
Controls the size of the semi-annihilation asymmetry; tuned to match the relic density.
λ3 (heat-bath coupling) = 6.0
Large coupling to φ3 that annihilates the symmetric DM component; value chosen to ensure efficient annihilation.
m, m1, m2 (masses) = 200 GeV, 260 GeV or 0, 400 GeV
Mass spectrum selected to allow the relevant phase space and decay hierarchy.
Γ1/m1, Γ2/m2 (decay widths) = 2e-17, 3e-16 (Fig. 3b); 1e-15, 4e-15 (Fig. 4)
Tiny widths make φ1/φ2 long-lived, keeping them out of equilibrium; fitted to produce total asymmetry.
Im[λ1λ2*]/|λ1λ2| (CP phase) = 0.8
Sets the magnitude of the asymmetry; chosen as a representative large value.
Λ (fermionic effective scale) = 4e5 GeV
Suppresses the four-fermion operators; chosen to yield the observed DM density with O(1) couplings.
sin δ1, sin δ2 (fermionic phases) = 0.8/0.0 or 0.0/0.8
Scanned to show the effect of the two independent phases on the final relic density.
y (Yukawa to φ3) = 3.0
Strength of the annihilation channel removing the symmetric component; from figure caption.

assumptions (5)

standard math S-matrix unitarity and CPT symmetry: for any initial state, the sum of CP asymmetries over all final states vanishes.
Used in Eq. (2.1) to prove that a single semiannihilation channel cannot carry an asymmetry. This is a standard QFT result.
domain assumption The holomorphic cutting rules of Ref. [36] give a valid diagrammatic expansion of the unitarity relation, and the vacuum-diagram analysis correctly identifies all asymmetry contributions.
The paper relies on this technique (Section 2.1) to classify diagrams. It is the authors' own prior method, assumed applicable here.
domain assumption Classical Maxwell-Boltzmann statistics and standard Boltzmann equations are adequate for the early-universe relic density calculation.
The authors use these equations throughout Section 3 and mention quantum-statistics and thermal-mass corrections only in passing (Section 2.2).
ad hoc to paper The two final-state species (φ1/φ2 or ψ1/ψ2) are long-lived, with constant decay widths Γ1, Γ2 to Standard Model states, and their back-reaction on the asymmetry is negligible.
The long-lived nature is essential for the out-of-equilibrium condition, but the decay channels are not specified, so this is a model assumption.
ad hoc to paper In the effective fermionic model, the operators in Eq. (3.9) are the only relevant ones at the scale Λ; all other higher-dimensional operators are negligible.
No complete operator analysis is provided in Section 3.2, so this is an unverified assumption.

invented entities (3)

φ1, φ2 (real scalar fields)
purpose: Provide two distinct final-state channels for semi-annihilation, enabling a nonzero asymmetry that satisfies unitarity; they are long-lived and decay slowly into SM states.
Introduced as dark-sector fields. No direct observational signature is proposed; their existence is inferred only from the model's consistency, not from any external data.
ψ1, ψ2 (Majorana fermion fields)
purpose: Analogous to φ1, φ2 in the effective fermionic model; provide two final-state channels and two independent CP phases (δ1, δ2) that drive the asymmetry.
Theoretical fields with no independent evidence; the paper does not predict observable signals beyond the assumed slow decays.
φ3 (massless scalar or Yukawa-coupled scalar)
purpose: Acts as a heat bath, giving a large annihilation cross section for the symmetric DM component so that only the asymmetric part survives.
Model-building device to remove symmetric DM; no independent evidence or unique prediction.

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Cite this review

Pith. "Pith review of Asymmetric dark matter from semi-annihilation: unitarity constraints and long-lived final states." pith.science (2026). https://pith.science/paper/2UMXY3EZ

@misc{pith2026241201470,
  author       = {Pith},
  title        = {Pith review of: Asymmetric dark matter from semi-annihilation: unitarity constraints and long-lived final states},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2UMXY3EZ}},
  note         = {Machine review of arXiv:2412.01470}
}

abstract

This work presents an asymmetric dark matter model with relic density determined by the freeze-out of asymmetric semi-annihilations into long-lived particles slowly decaying into the Standard Model states. We carefully consider the $CPT$ symmetry and unitarity constraints to the asymmetries entering the Boltzmann equation. The main idea of the paper is to point out a critical inconsistency in the previous literature, where these constraints are violated. We present a systematic approach to avoid the inconsistency.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 21 canonical work pages

[30]

Ghosh, D

A. Ghosh, D. Ghosh and S. Mukhopadhyay, Asymmetric dark matter from semi-annihilation , Journal of High Energy Physics 2020 (2020) 149 [ 2004.07705]

arXiv 2020
[1]

Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh

A.D. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32

work page 1967
[2]

Blennow, B

M. Blennow, B. Dasgupta, E. Fernandez-Martinez and N. Rius, Aidnogenesis via leptogenesis and dark sphalerons , Journal of High Energy Physics 2011 (2011) 14 [ 1009.3159]

arXiv 2011
[3]

Haba and S

N. Haba and S. Matsumoto, Baryogenesis from Dark Sector , Progress of Theoretical Physics 125 (2011) 1311 [ 1008.2487]

arXiv 2011
[4]

Davoudiasl, D.E

H. Davoudiasl, D.E. Morrissey, K. Sigurdson and S. Tulin, Unified origin for baryonic visible matter and antibaryonic dark matter , Phys. Rev. Lett. 105 (2010) 211304 [ 1008.2399]

arXiv 2010
[5]

P.-H. Gu, M. Lindner, U. Sarkar and X. Zhang, Weakly interacting dark matter and baryogenesis, Phys. Rev. D 83 (2011) 055008 [ 1009.2690]

arXiv 2011
[6]

Falkowski, J.T

A. Falkowski, J.T. Ruderman and T. Volansky, Asymmetric dark matter from leptogenesis , Journal of High Energy Physics 2011 (2011) 106 [ 1101.4936]

arXiv 2011
[7]

Asymmetric Inelastic Inert Doublet Dark Matter from Triplet Scalar Leptogenesis

C. Arina and N. Sahu, Asymmetric inelastic inert doublet dark matter from triplet scalar leptogenesis, Nuclear Physics B 854 (2012) 666 [ 1108.3967]

work page Pith review arXiv 2012

Show all 48 references

[8]

W.-Z. Feng, A. Mazumdar and P. Nath, Baryogenesis from dark matter , Phys. Rev. D 88 (2013) 036014 [ 1302.0012]

2013 arXiv
[9]

Borah, S

D. Borah, S. Mahapatra, P.K. Paul, N. Sahu and P. Shukla, Asymmetric self-interacting dark matter with a canonical seesaw model , Phys. Rev. D 110 (2024) 035033 [ 2404.14912]

2024 arXiv
[10]

Farrar and G

G.R. Farrar and G. Zaharijas, Dark matter and the baryon asymmetry of the universe , Phys. Rev. Lett. 96 (2006) 041302

2006
[11]

Baldes, N.F

I. Baldes, N.F. Bell, K. Petraki and R.R. Volkas, Particle-antiparticle asymmetries from annihilations, Phys. Rev. Lett. 113 (2014) 181601 [ 1407.4566]

2014 arXiv
[12]

N.F. Bell, S. Horiuchi and I.M. Shoemaker, Annihilating asymmetric dark matter , Phys. Rev. D 91 (2015) 023505 [ 1408.5142]

2015 arXiv
[13]

Ghosh, D

A. Ghosh, D. Ghosh and S. Mukhopadhyay, Cosmology of complex scalar dark matter: Interplay of self-scattering and annihilation , Phys. Rev. D 104 (2021) 123543 [ 2103.14009]

2021 arXiv
[14]

D’Eramo and J

F. D’Eramo and J. Thaler, Semi-annihilation of dark matter , Journal of High Energy Physics 2010 (2010) 109 [ 1003.5912]

2010 arXiv
[15]

D’Eramo, M

F. D’Eramo, M. McCullough and J. Thaler, Multiple gamma lines from semi-annihilation , 1210.7817. – 10 –

arXiv
[16]

Cai and A

Y. Cai and A. Spray, Fermionic semi-annihilating dark matter , Journal of High Energy Physics 2016 (2016) 87 [ 1509.08481]

2016 arXiv
[17]

Cai and A

Y. Cai and A. Spray, A systematic effective operator analysis of semi-annihilating dark matter, Journal of High Energy Physics 2017 (2017) 120 [ 1611.09360]

2017 arXiv
[18]

Kamada, H.J

A. Kamada, H.J. Kim, H. Kim and T. Sekiguchi, Self-heating dark matter via semiannihilation, Phys. Rev. Lett. 120 (2018) 131802 [ 1707.09238]

2018 arXiv
[19]

Cai, Radiative neutrino model with semiannihilating dark matter , Phys

H. Cai, Radiative neutrino model with semiannihilating dark matter , Phys. Rev. D 101 (2020) 035006 [ 1907.11595]

2020 arXiv
[20]

Bandyopadhyay, D

P. Bandyopadhyay, D. Choudhury and D. Sachdeva, Semiannihilation of fermionic dark matter, Phys. Rev. D 107 (2023) 015020 [ 2206.05811]

2023 arXiv
[21]

J. Guo, L. Wu and B. Zhu, Mev gamma-ray constraints for light dark matter from semi-annihilation, Physics Letters B 840 (2023) 137853 [ 2302.06159]

2023 arXiv
[22]

Benincasa, A

N. Benincasa, A. Hryczuk, K. Kannike and M. Laletin, Phase transitions and gravitational waves in a model of Z(3) scalar dark matter , Journal of High Energy Physics 2024 (2024) 207 [2312.04627]

2024 arXiv
[23]

Beauchesne and C.-W

H. Beauchesne and C.-W. Chiang, Dark matter semi-annihilation for inert scalar multiplets , Journal of High Energy Physics 2024 (2024) 164 [ 2403.01729]

2024 arXiv
[24]

Kuzmin, A Simultaneous solution to baryogenesis and dark matter problems , Phys

V.A. Kuzmin, A Simultaneous solution to baryogenesis and dark matter problems , Phys. Part. Nucl. 29 (1998) 257 [ hep-ph/9701269]

1998 arXiv
[25]

Kitano and I

R. Kitano and I. Low, Dark matter from baryon asymmetry , Phys. Rev. D 71 (2005) 023510 [hep-ph/0411133]

2005 arXiv
[26]

Kaplan, M.A

D.E. Kaplan, M.A. Luty and K.M. Zurek, Asymmetric dark matter , Phys. Rev. D 79 (2009) 115016 [0901.4117]

2009 arXiv
[27]

Petraki and R.R

K. Petraki and R.R. Volkas, Review of asymmetric dark matter , International Journal of Modern Physics A 28 (2013) 1330028 [ 1305.4939]

2013 arXiv
[28]

Zurek, Asymmetric dark matter: Theories, signatures, and constraints , Physics Reports 537 (2014) 91 [ 1308.0338]

K.M. Zurek, Asymmetric dark matter: Theories, signatures, and constraints , Physics Reports 537 (2014) 91 [ 1308.0338]

2014 arXiv
[29]

Iminniyaz, M

H. Iminniyaz, M. Drees and X. Chen, Relic abundance of asymmetric dark matter , Journal of Cosmology and Astroparticle Physics 2011 (2011) 003 [ 1104.5548]

2011 arXiv
[31]

Ghosh, D

A. Ghosh, D. Ghosh and S. Mukhopadhyay, Revisiting the role of CP-conserving processes in cosmological particle–antiparticle asymmetries, The European Physical Journal C 81 (2021) 1038 [2103.03650]

2021 arXiv
[32]

Kolb and S

E.W. Kolb and S. Wolfram, Baryon number generation in the early universe , Nuclear Physics B 172 (1980) 224

1980
[33]

Dolgov, Baryon asymmetry of the universe and violation of the thermodynamics equilibrium

A.D. Dolgov, Baryon asymmetry of the universe and violation of the thermodynamics equilibrium. (in Russian) , Pisma Zh. Eksp. Teor. Fiz. 29 (1979) 254

1979
[34]

Hook, Unitarity constraints on asymmetric freeze-in , Phys

A. Hook, Unitarity constraints on asymmetric freeze-in , Phys. Rev. D 84 (2011) 055003 [1105.3728]. – 11 –

2011 arXiv
[35]

Bhattacharya, R

A. Bhattacharya, R. Gandhi and S. Mukhopadhyay, Revisiting the implications of CPT and unitarity for baryogenesis and leptogenesis , Phys. Rev. D 89 (2014) 116014 [ 1109.1832]

2014 arXiv
[36]

Blaˇ zek and P

T. Blaˇ zek and P. Mat´ ak,CP asymmetries and higher-order unitarity relations , Phys. Rev. D 103 (2021) L091302 [ 2102.05914]

2021 arXiv
[37]

Coster and H.P

J. Coster and H.P. Stapp, Physical-region discontinuity equation, Journal of Mathematical Physics 11 (1970) 2743

1970
[38]

Bourjaily, H

J.L. Bourjaily, H. Hannesdottir, A.J. McLeod, M.D. Schwartz and C. Vergu, Sequential discontinuities of feynman integrals and the monodromy group , Journal of High Energy Physics 2021 (2021) 205 [ 2007.13747]

2021 arXiv
[39]

Hannesdottir and S

H.S. Hannesdottir and S. Mizera, What is the i ε for the S-matrix? , SpringerBriefs in Physics, Springer (1, 2023), 10.1007/978-3-031-18258-7, [ 2204.02988]

2023 arXiv
[40]

Roulet, L

E. Roulet, L. Covi and F. Vissani, On the CP asymmetries in majorana neutrino decays , Physics Letters B 424 (1998) 101 [ hep-ph/9712468]

1998 arXiv
[41]

Blaˇ zek and P

T. Blaˇ zek and P. Mat´ ak,Cutting rules on a cylinder: a simplified diagrammatic approach to quantum kinetic theory , The European Physical Journal C 81 (2021) 1050 [ 2104.06395]

2021 arXiv
[42]

Blaˇ zek and P

T. Blaˇ zek and P. Mat´ ak,Mass-derivative relations for leptogenesis , The European Physical Journal C 82 (2022) 214 [ 2111.03419]

2022 arXiv
[43]

Blaˇ zek, P

T. Blaˇ zek, P. Mat´ ak and V. Zaujec,Mass-derivative relations and unitarity constraints for CP asymmetries at finite temperature , J. Cosmol. Astropart. Phys. 2022 (2022) 042 [2209.03829]

2022 arXiv
[44]

Botella, M

F.J. Botella, M. Nebot and O. Vives, Invariant approach to flavour-dependent CP-violating phases in the MSSM , Journal of High Energy Physics 2006 (2006) 106 [ hep-ph/0407349]

2006 arXiv
[45]

Gondolo and G

P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: Improved analysis , Nucl. Phys. B 360 (1991) 145

1991
[46]

Shtabovenko, R

V. Shtabovenko, R. Mertig and F. Orellana, FeynCalc 9.3: New features and improvements , Computer Physics Communications 256 (2020) 107478 [ 2001.04407]

2020 arXiv
[47]

Shtabovenko, R

V. Shtabovenko, R. Mertig and F. Orellana, New developments in FeynCalc 9.0 , Computer Physics Communications 207 (2016) 432 [ 1601.01167]

2016 arXiv
[48]

Mertig, M

R. Mertig, M. B¨ ohm and A. Denner, Feyn Calc - Computer-algebraic calculation of Feynman amplitudes, Computer Physics Communications 64 (1991) 345. – 12 –

1991

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [30]

Ghosh, D

A. Ghosh, D. Ghosh and S. Mukhopadhyay, Asymmetric dark matter from semi-annihilation , Journal of High Energy Physics 2020 (2020) 149 [ 2004.07705]

arXiv 2020

[2] [1]

Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh

A.D. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32

work page 1967

[3] [2]

Blennow, B

M. Blennow, B. Dasgupta, E. Fernandez-Martinez and N. Rius, Aidnogenesis via leptogenesis and dark sphalerons , Journal of High Energy Physics 2011 (2011) 14 [ 1009.3159]

arXiv 2011

[4] [3]

Haba and S

N. Haba and S. Matsumoto, Baryogenesis from Dark Sector , Progress of Theoretical Physics 125 (2011) 1311 [ 1008.2487]

arXiv 2011

[5] [4]

Davoudiasl, D.E

H. Davoudiasl, D.E. Morrissey, K. Sigurdson and S. Tulin, Unified origin for baryonic visible matter and antibaryonic dark matter , Phys. Rev. Lett. 105 (2010) 211304 [ 1008.2399]

arXiv 2010

[6] [5]

P.-H. Gu, M. Lindner, U. Sarkar and X. Zhang, Weakly interacting dark matter and baryogenesis, Phys. Rev. D 83 (2011) 055008 [ 1009.2690]

arXiv 2011

[7] [6]

Falkowski, J.T

A. Falkowski, J.T. Ruderman and T. Volansky, Asymmetric dark matter from leptogenesis , Journal of High Energy Physics 2011 (2011) 106 [ 1101.4936]

arXiv 2011

[8] [7]

Asymmetric Inelastic Inert Doublet Dark Matter from Triplet Scalar Leptogenesis

C. Arina and N. Sahu, Asymmetric inelastic inert doublet dark matter from triplet scalar leptogenesis, Nuclear Physics B 854 (2012) 666 [ 1108.3967]

work page Pith review arXiv 2012