arxiv: 2602.20237 · v2 · submitted 2026-02-23 · ✦ hep-ph · astro-ph.CO· hep-ex

Recognition: 2 theorem links

· Lean Theorem

Linking Leptogenesis and Asymmetric Dark Matter: A Testable Framework for Neutrino Mass and the Matter-Antimatter Asymmetry

Henry G. F. McKenna , Juri Smirnov , Martin Gorbahn

Authors on Pith no claims yet

Pith reviewed 2026-05-15 19:47 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-ex

keywords leptogenesisasymmetric dark matterbaryon asymmetryneutrino massseesaw mechanismdirect detectionCP violationMajorana neutrino

0 comments

The pith

Heavy Majorana neutrino decay generates both the observed baryon asymmetry and asymmetric dark matter abundance at TeV scales.

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

The paper examines a minimal extension of leptogenesis in which the decay of one heavy Majorana neutrino produces the cosmic matter-antimatter imbalance and the dark matter density at the same time. Complex Yukawa couplings supply the needed CP violation that creates asymmetries in both the Standard Model leptons and a dark sector. In the co-genesis regime a hierarchical pattern of couplings boosts the asymmetry while keeping the seesaw scale near 2 TeV and reproducing the light neutrino masses. This leads to concrete predictions for the spin-independent scattering cross section of dark matter particles heavier than 10 GeV that existing direct-detection experiments can already test. The framework therefore turns asymmetric leptogenesis into a benchmark model whose signals can be searched for in current and near-future detectors.

Core claim

In the co-genesis scenario the hierarchical coupling structure allows enhanced CP violation while supporting a low-scale seesaw mechanism at order O(2) TeV. This setup links light neutrino masses directly to the Majorana mass term and yields spin-independent cross sections for dark matter heavier than 10 GeV that can be tested in current direct detection experiments, while also motivating searches inside the neutrino fog for lighter masses.

What carries the argument

The co-genesis regime with its hierarchical Yukawa couplings, which simultaneously supplies large CP violation, controls washout, and transfers asymmetry to the dark sector through decays and 2-to-2 scatterings.

If this is right

Spin-independent cross sections for dark matter above 10 GeV fall within reach of existing direct detection experiments.
Lighter dark matter masses motivate dedicated searches inside the neutrino fog region.
Lepton-number violation becomes possible at experimentally accessible TeV energies.
Light neutrino masses are directly tied to the same Majorana mass term that drives the asymmetries.

Where Pith is reading between the lines

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

Observation of the predicted cross sections would tie three major cosmic puzzles to a single particle and scale.
Collider experiments could target production of the heavy Majorana neutrino at comparable energies.
The model supplies a concrete target for interpreting future null results in direct detection as bounds on leptogenesis parameters.

Load-bearing premise

A hierarchical coupling structure can produce enough CP violation, keep washout under control, and match the observed neutrino mass scale at roughly 2 TeV without extra tuning or conflict with existing bounds.

What would settle it

Direct detection experiments reporting no spin-independent events at the cross sections predicted for dark matter masses above 10 GeV, or precision measurements of neutrino masses that cannot be reproduced by a Majorana scale near 2 TeV.

Figures

Figures reproduced from arXiv: 2602.20237 by Henry G. F. McKenna, Juri Smirnov, Martin Gorbahn.

**Figure 1.** Figure 1: FIG. 1. Schematic illustration of the two asymmetry-generation mechanisms studied in this work: (left) the wash-in scenario, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. Departure of the heavy-neutrino abundance from [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Effect of increasing the scalar mass ratio [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Contours of the minimum RHN mass [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Dependence of the dark matter mass [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Predicted spin-independent dark-matter–nucleon [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Feynman diagrams for Higgs-mediated dark matter scattering relevant to direct detection: (left) the effective inter [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Evolution of the lepton and dark asymmetries as a [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

read the original abstract

We investigate a minimal extension of the Leptogenesis framework that simultaneously explains the observed baryon asymmetry and dark matter (DM) abundance through the decay of a heavy Majorana neutrino. In this scenario, CP violation arises from complex Yukawa couplings, enabling the generation of asymmetries in both the Standard Model (SM) and DM sectors. We explore two regimes: (i) wash-in, where an initial dark asymmetry is transferred to SM leptons by $2 \leftrightarrow 2$ scattering processes; and (ii) co-genesis, featuring a hierarchical coupling structure that allows enhanced CP violation while supporting a low-scale seesaw mechanism at order $\mathcal{O}(2)$ TeV. This setup not only links light neutrino masses to the Majorana mass term but also suggests that lepton-number violation may occur at experimentally accessible energy scales. In the co-genesis scenario, we show spin-independent cross sections for DM heavier than 10 GeV that can be tested in current direct detection experiments and motivate the exploration of cross sections inside the neutrino fog for lighter DM masses, establishing asymmetric leptogenesis as a predictive benchmark framework for direct-detection experiments and identifying a new hierarchical-coupling regime enabling TeV-scale leptogenesis.

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.

Desk Editor's Note private letter to a colleague

The co-genesis regime with hierarchical Yukawas gives concrete DM direct-detection targets at TeV scales, but the abstract leaves the Boltzmann dynamics unshown so the washout suppression claim stays unverified.

read the letter

Hi, the paper's main new piece is a co-genesis regime in which a single heavy Majorana neutrino decay at O(2) TeV produces both the observed baryon asymmetry and an asymmetric dark matter component. The authors use a hierarchical structure on the complex Yukawa couplings to boost CP violation while keeping the effective washout small enough and still fitting the light neutrino mass scale through the type-I seesaw. They also sketch a wash-in regime in which an initial DM asymmetry is transferred to SM leptons via 2-to-2 scatterings. This is presented as a minimal extension that turns the model into a predictive benchmark for experiment. What the work does cleanly is to extract spin-independent DM-nucleon cross sections that current direct-detection runs can already test for masses above 10 GeV, with a note that lighter masses would sit inside the neutrino fog. That link to existing and near-term data is the most useful output. The soft spot is exactly the one flagged in the stress-test note. The hierarchical ansatz is asserted to deliver sufficient epsilon while suppressing K below 1 at 2 TeV, but the abstract shows no explicit Yukawa matrix, no solved Boltzmann trajectories, and no scan or error estimate. In the standard treatment, enlarging the imaginary parts enough for the observed eta_B usually drives at least one diagonal entry of Y dagger Y large enough that washout erases the asymmetry. Without the explicit solutions it is impossible to tell whether the hierarchy actually evades that tension or simply assumes it away. The rest of the setup follows standard leptogenesis plus asymmetric DM logic, so there are no obvious internal contradictions once the central assumption is granted. This is for people who build and test low-scale leptogenesis and asymmetric DM models. A reader who wants concrete experimental targets rather than another high-scale scenario will find the direct-detection benchmarks worth looking at. The framework is coherent enough and the claims are specific enough that it deserves a serious referee who can ask for the missing trajectories and parameter scans in the first round.

Referee Report

1 major / 1 minor

Summary. The paper proposes a minimal extension of leptogenesis in which the out-of-equilibrium decay of a heavy Majorana neutrino simultaneously generates the observed baryon asymmetry and an asymmetric dark matter abundance. It examines two regimes—wash-in, where an initial dark-sector asymmetry is transferred to SM leptons via 2↔2 scattering, and co-genesis, which employs a hierarchical Yukawa structure to enhance CP violation while permitting a type-I seesaw at O(2) TeV—thereby linking light neutrino masses to the Majorana mass scale and predicting spin-independent DM-nucleon cross sections testable by current direct-detection experiments for m_DM > 10 GeV.

Significance. If the co-genesis mechanism can be shown to operate without additional tuning, the framework would furnish a predictive, testable connection among neutrino masses, leptogenesis, and asymmetric dark matter, supplying concrete benchmarks for direct-detection searches (including the neutrino fog) and identifying a new hierarchical-coupling regime for TeV-scale leptogenesis.

major comments (1)

[co-genesis scenario] Co-genesis scenario: the claim that a hierarchical Yukawa ansatz simultaneously yields sufficient CP asymmetry (ε_1 ~ 10^{-6}–10^{-7}), suppresses washout (K ≪ 1), and reproduces m_ν ≈ 0.05 eV at M_N ~ 2 TeV is load-bearing yet unsupported by explicit demonstration. The standard expressions ε_1 ≈ (3/16π)(M_1/M_j) Im[(Y†Y)_{1j}^2]/(Y†Y)_{11} and Γ ~ (Y†Y)M_1/(8π) imply that the imaginary parts needed for η_B ≈ 6×10^{-10} typically drive at least one diagonal entry of Y†Y large enough that K > 10, erasing the asymmetry. The manuscript must supply the explicit Yukawa matrix, the solved Boltzmann trajectories, and a parameter scan confirming viability without extra flavor suppression or resonance.

minor comments (1)

The abstract states specific spin-independent cross sections for m_DM > 10 GeV and motivates exploration inside the neutrino fog, but the derivation of these values, including any dependence on the DM–lepton coupling and the resulting relic density, should be shown explicitly with error estimates.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We agree that the co-genesis scenario requires explicit verification to support its viability and will revise the manuscript accordingly.

read point-by-point responses

Referee: Co-genesis scenario: the claim that a hierarchical Yukawa ansatz simultaneously yields sufficient CP asymmetry (ε_1 ~ 10^{-6}–10^{-7}), suppresses washout (K ≪ 1), and reproduces m_ν ≈ 0.05 eV at M_N ~ 2 TeV is load-bearing yet unsupported by explicit demonstration. The standard expressions ε_1 ≈ (3/16π)(M_1/M_j) Im[(Y†Y)_{1j}^2]/(Y†Y)_{11} and Γ ~ (Y†Y)M_1/(8π) imply that the imaginary parts needed for η_B ≈ 6×10^{-10} typically drive at least one diagonal entry of Y†Y large enough that K > 10, erasing the asymmetry. The manuscript must supply the explicit Yukawa matrix, the solved Boltzmann trajectories, and a parameter scan confirming viability without extra flavor suppression or resonance.

Authors: We agree that an explicit demonstration is essential. In the revised manuscript we will include a concrete hierarchical Yukawa matrix realizing ε_1 ∼ 10^{-6}–10^{-7} with K ≪ 1, numerical solutions of the Boltzmann equations showing the time evolution of the lepton and DM asymmetries, and a parameter scan over the relevant couplings and mass ratios that simultaneously reproduces η_B ≈ 6×10^{-10}, m_ν ≈ 0.05 eV, and the observed DM abundance at M_N ∼ 2 TeV without additional flavor suppression or resonance. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation chain is self-contained with independent parameter choices

full rationale

The abstract outlines a minimal leptogenesis extension with co-genesis via hierarchical Yukawa couplings to simultaneously address baryon asymmetry, DM abundance, and neutrino masses at O(2) TeV. No equations, Boltzmann solutions, or self-citations are exhibited that reduce any 'prediction' (such as DM cross sections) to a direct fit or redefinition of the input asymmetries. The hierarchical structure is presented as an ansatz enabling the regime, but the resulting cross-section claims follow from solving the model dynamics rather than tautological re-expression of fitted values. The framework remains externally falsifiable via direct detection and does not rely on load-bearing self-citations or self-definitional loops.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

Model rests on standard leptogenesis assumptions plus new hierarchical coupling structure and DM asymmetry transfer; free parameters include the Majorana mass scale and complex Yukawa couplings adjusted to observations.

free parameters (2)

Majorana neutrino mass
Set to O(2) TeV to realize low-scale seesaw while matching neutrino masses and asymmetries.
Complex Yukawa couplings
Phases and magnitudes chosen to generate required CP violation and asymmetry transfer.

axioms (2)

domain assumption Standard Model extended by heavy Majorana neutrinos
Core assumption of leptogenesis framework invoked throughout.
standard math CP violation generated by complex phases in Yukawa couplings
Standard mechanism for leptogenesis asymmetry generation.

invented entities (1)

Asymmetric dark matter component generated by neutrino decay no independent evidence
purpose: Links DM abundance directly to leptogenesis process
New postulated link between DM and lepton sectors with no independent evidence outside the model.

pith-pipeline@v0.9.0 · 5530 in / 1481 out tokens · 29772 ms · 2026-05-15T19:47:56.220726+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

hierarchical coupling structure that allows enhanced CP violation while supporting a low-scale seesaw mechanism at order O(2) TeV... |λ2| ≫ |y2| > |λ1| ∼ |y1|
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Boltzmann equations... dY_ΔL/dz1 = Γ_N1/H1 ε_L ... − Γ_N2/H1 Br_L2 Br_χ2 I_T+,2 ...

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Reference graph

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