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REVIEW 3 major objections 5 minor 1 cited by

Dark matter, this paper claims, is a Dirac sterile neutrino whose observed abundance is set by the CP-violating parameter of an out-of-equilibrium decay.

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2026-08-02 21:17 UTC pith:E74TTZKQ

load-bearing objection The central claim doesn't survive contact with the paper's own equations: only the asymmetry is tracked and the symmetric N+Nbar population is dropped, overproducing DM by ~1/ε. the 3 major comments →

arxiv 2602.20570 v2 pith:E74TTZKQ submitted 2026-02-24 hep-ph

Sterile Neutrino as an Asymmetric Dark Matter

S. Peyman Zakeri This is my paper
classification hep-ph
keywords dark mattersterile neutrinoasymmetric freeze-inCP violationrelic abundanceDirac dark matterscalar mediatorLyman-alpha bounds
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Dark matter, this paper proposes, is a Dirac sterile neutrino — a neutrino-like fermion that feels only a new hidden-sector force, not the weak interaction — produced by a mechanism called asymmetric freeze-in. A feebly coupled scalar mediator decays out of equilibrium into neutrino–antineutrino pairs, and a CP-violating phase makes the decay slightly favor neutrinos, so what survives to the present day is almost entirely matter. The paper derives a closed-form expression for the resulting asymmetry and shows the observed relic abundance (Ω_DM h² ≈ 0.12) can be reproduced across a correlated range of the sterile neutrino mass and decay parameters, without the dark sector ever reaching thermal equilibrium with the standard model. Because each decay emits the neutrino at a fixed momentum, the dark matter is born with a colder-than-thermal spectrum, which the paper argues keeps it consistent with Lyman-α structure-formation bounds. The payoff: the dark matter density becomes a prediction of one CP-violating parameter rather than a tuned input.

Core claim

The paper claims dark matter's relic abundance is set by one out-of-equilibrium decay: the scalar mediator φ decays into a sterile neutrino N and an auxiliary fermion χ, with a CP-violating asymmetry ε that favors N over N̄. Solving the Boltzmann equation for n_− = n_N − n_N̄ gives Y_−^∞ ∝ (M_Pl/g_*^{3/2})(ε Γ_φ/m_φ²), so the observed Ω_DM h² = 2.75×10^8 (m_N/GeV)Y_− fixes a correlation between the sterile neutrino mass and the decay parameters. The mediator never thermalizes, so production is purely freeze-in; two-body kinematics give a non-thermal spectrum peaked at p ≈ m_φ/2 with ⟨p/T⟩ < 3.15 — colder than a Fermi–Dirac spectrum and consistent with Lyman-α bounds. Relic-density, Higgs-inv

What carries the argument

The mechanism is asymmetric freeze-in driven by the CP-violating decay of the scalar mediator φ: the parameter ε, defined as [Γ(φ → χ̄ N) − Γ(φ → χ N̄)]/Γ_φ, converts the out-of-equilibrium decay into a net particle–antiparticle asymmetry in the sterile sector. The carrying identity is the closed-form yield Y_−^∞ = (90/(1.66 π^4)) (M_Pl/g_*^{3/2}) (ε Γ_φ/m_φ²), derived by integrating the source term ε Γ_φ n_eq^φ over the freeze-in epoch; combined with Ω_DM h² = 2.75×10^8 (m_N/GeV)Y_−, it turns the relic abundance into a relation among m_N, m_φ, Γ_φ, and ε. The conserved dark U(1) charge of the Dirac neutrino N is what makes the asymmetry survive to today.

Load-bearing premise

The load-bearing premise is that the symmetric N + N̄ population created by the same decays contributes nothing to the relic density, since only the net asymmetry n_N − n_N̄ is tracked and no mechanism is specified to remove the symmetric part, which is larger by roughly 1/ε.

What would settle it

Evolve n_N and n_N̄ separately from the same decay source Γ_φ n_eq^φ at the paper's benchmark ε = 5×10^-6: with no annihilation or dilution, the total yield exceeds the asymmetric yield of Eq. (13) by about 1/ε, so the predicted Ω_DM h² would overshoot the observed 0.12 by roughly 2×10^5 — a calculation that would settle whether the asymmetric-only Boltzmann equation is complete.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The observed dark matter density becomes a measurement of CP violation in the dark sector: the abundance is set by the combination m_N Γ_φ ε / m_φ², and if ε were zero the mechanism would produce no dark matter at all.
  • Dark matter is born cold: the two-body decay deposits sterile neutrinos at a fixed momentum p ≈ m_φ/2, giving ⟨p/T⟩ < 3.15, so the scenario relaxes rather than strains the Lyman-α bounds (m_N ≳ 5 keV).
  • The small couplings required for out-of-equilibrium production keep the Higgs invisible branching ratio below the current bound (BR_inv < 0.11) and push the decay above the BBN scale, giving ΔN_eff ≈ 0 — the scenario clears all currently imposed constraints simultaneously.
  • Correct relic density forces a correlated scaling, m_N ∝ m_φ²/(ε Γ_φ), producing diagonal viable bands in the (m_N, μ) and (m_N, ε) planes rather than a single tuned point, which makes the parameter space predictive and testable.

Where Pith is reading between the lines

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

  • Editorial inference: the paper tracks only the net asymmetry n_N − n_N̄ (its Eq. 5) and gives no equation for the total sterile population before the relic-density formula Eq. (15); since the full decay source is Γ_φ n_eq^φ, the symmetric yield is Y_−/ε, roughly 2×10^5 times larger at the benchmark ε = 5×10^-6. If no annihilation or dilution removes that symmetric component, the predicted density
  • Editorial inference: the sharply peaked production momentum is a spectral fingerprint — future high-resolution Lyman-α or 21-cm measurements of the small-scale matter power spectrum could in principle distinguish this cold non-thermal distribution from a thermal warm dark matter one, since the effective WDM mass mapping depends on the ⟨p/T⟩ ratio.
  • Editorial inference: the Higgs-portal coupling λ_φH is simultaneously the knob that keeps the mediator out of equilibrium and the observable probed by invisible Higgs searches; an improved bound on BR_inv below ~0.11 would translate directly into a constraint on the allowed (m_N, ε) correlation, giving collider physics a concrete handle on this dark matter framework.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes a minimal asymmetric freeze-in (AFI) model in which a Dirac sterile neutrino N carrying a conserved U(1)_DM charge is produced by the out-of-equilibrium decay of a real scalar mediator φ, with a CP-violating parameter ε generating a particle-antiparticle asymmetry. The central calculation tracks only the asymmetric number density n_- = n_N - n_Nbar through Eq. (5), obtains an analytic freeze-in yield Y_- in Eq. (13), and then equates the present DM density to m_N Y_- via Eq. (15). The author claims that the observed relic abundance ΩDMh^2 ≃ 0.12 can be reproduced without thermal equilibrium, and uses this to identify viable parameter regions in the (m_N, μ) and (m_N, ε) planes while imposing Lyman-α, Higgs invisible decay, and BBN constraints.

Significance. If the calculation were correct, the model would provide a simple and analytically transparent realization of asymmetric sterile-neutrino DM via freeze-in, with the useful feature that the non-thermal momentum distribution is colder than a Fermi-Dirac spectrum. The analytic evaluation of the freeze-in integral and the compilation of experimental constraints are strengths. However, the central relic-density claim is invalid as written: the Boltzmann treatment follows only the asymmetry, and the much larger symmetric N+Nbar population produced by the same decays is omitted. This flaw is load-bearing, not a presentation issue, and it removes the paper's main conclusion.

major comments (3)
  1. [Sec. III.A, Eqs. (5), (13), (15)] Eq. (5) evolves only n_- = n_N - n_Nbar, with source ε Γφ n_eq^φ. The same decays φ → N χ and φ → Nbar χbar produce the total N+Nbar number density with source Γφ n_eq^φ, so the total symmetric-plus-asymmetric yield is Y_tot = Y_-/ε. No annihilation term appears in Eq. (1) or in the Boltzmann treatment, and no prior mechanism is cited to remove the symmetric component. The compact expression for Y_- in Eq. (13) therefore undercounts the DM density by a factor 1/ε. For the benchmark ε = 5×10^-6 quoted in Sec. IV.E, this is a factor ~2×10^5, meaning the model overcloses the Universe by orders of magnitude even before considering the m_N scaling in Eq. (15). The statement that 'the observed relic abundance can be naturally reproduced' is unsupported by the equations presented. Adding a N Nbar → χ χbar annihilation term would not help in the shown freeze-in regime because the tiny abundances
  2. [Sec. IV.E, Figs. 5 and 6] The 'viable parameter space' is constructed by imposing ΩDMh^2 ≃ 0.12 on the relation m_N Y_- ∝ m_N μ^2 ε, with m_N, μ, ε, m_φ and λ_φH treated as free. This defines a contour, not a prediction. The claim that the model 'naturally reproduces' the relic abundance is therefore a parameter fit, and the diagonal bands in Figs. 5 and 6 are the direct algebraic consequence of Eq. (30) combined with Eq. (31). Moreover, once the symmetric yield is included as required by Eq. (5), these bands would shift by 1/ε and the model would no longer match the observed density in the displayed parameter region.
  3. [Sec. II, Eq. (3)] The CP-violating parameter ε is introduced as a free input and is never calculated. With only one sterile neutrino N, one auxiliary fermion χ, and a single Yukawa-type coupling μ in Eq. (1), there is no defined loop-level interference that can generate a non-vanishing CP asymmetry; at minimum the model needs additional fields or couplings to provide the required phases and cut diagrams. This is not necessarily fatal, but it undercuts the paper's claim that the framework is 'minimal and predictive' and should be addressed explicitly if a revised version is considered.
minor comments (5)
  1. [Secs. II, III.B, IV.E] The symbol μ is introduced in Eq. (1) as a Yukawa coupling, but the text repeatedly calls it an 'effective chemical potential.' There is no chemical potential in the Boltzmann equations. This terminology should be corrected throughout.
  2. [Figs. 1-4] The plots lack explicit axis label details and numerical scales in the text description. Fig. 4 in particular would benefit from showing the specific parameter values and the horizontal band quantitatively, since it is used to claim a mass range for DM.
  3. [Sec. IV.C, Eq. (23), Figs. 5-6] The Lyman-α constraint is stated as m_N ≳ 5 keV, but the rigorous bound applies to the effective WDM mass m_eff^WDM defined in Eq. (23). Since ⟨p/T⟩ < 3.15, m_eff^WDM > m_N, so the vertical dashed lines in Figs. 5 and 6 should be drawn on m_eff, not directly on m_N, unless the mapping is explicitly justified.
  4. [Sec. III.B, Eq. (17)] Eq. (17) is a schematic delta-function spectrum. A robust freeze-in treatment should integrate over the production temperatures and the parent momentum distribution; the estimate ⟨p/T⟩ ∼ O(1) in Eq. (18) is too crude to support a quantitative Lyman-α consistency claim without further details.
  5. [Sec. II, Eq. (1)] The auxiliary fermion χ is assumed to decay 'efficiently into lighter hidden-sector states,' but no such lighter states or decay operators appear in Eq. (1). This is an additional model-building assumption that should be specified or removed.

Circularity Check

1 steps flagged

Relic-density 'prediction' is the asymmetry yield by construction: Eqs. (4)-(5) evolve only n_N−n_N̄, while the total N+N̄ source is 1/ε times larger; Eq. (15) then equates Ω to Y−, omitting the symmetric population.

specific steps
  1. self definitional [Sec. III.A, Eqs. (4), (5), and (15)]
    "Y− ≡Y N −Y ¯N = nN −n ¯N s ,(4) ... The evolution of the asymmetric number density n− =n N −n ¯N is then described by the Boltzmann equation dn− dt + 3Hn− =εΓ ϕ neq ϕ .(5) ... the present-day DM relic density is related to the asymmetry yield by [4, 5] ΩDMh2 = 2.75×10 8 (m N /GeV) Y ∞ − .(15)"

    The Boltzmann equation evolves only the difference n− = n_N − n_N̄ with source ε Γϕ n_eq^ϕ. The same decays produce N and N̄ with total source Γϕ n_eq^ϕ, so the total N+N̄ yield is Y−/ε (≈2×10^5 times Y− for ε=5×10^-6 in Sec. IV.E). No annihilation or depletion term for the symmetric population appears in the Lagrangian or Boltzmann treatment; the dark charge is conserved. By inserting Y− into Eq. (15), the paper's 'relic abundance' is, by construction, the asymmetry yield rather than the physical sterile-neutrino density, so the claimed match to ΩDMh2≃0.12 is an artifact of the definition, not a derived prediction.

full rationale

The derivation of Y− from ε Γϕ n_eq^ϕ is a standard freeze-in integral and is not itself circular: it follows from the assumed Lagrangian and CP-violating decay. The phenomenological constraints (Higgs invisible width, Lyman-α, BBN) are independent external bounds, and the parameter-space plots correctly show that imposing ΩDMh2=0.12 selects a surface in (m_N, μ, ε) rather than a parameter-free prediction; that feature is a fit, but not a circular reduction. The circular/definitional step is the identification of the computed asymmetry Y− with the total DM abundance in Eq. (15). Since the decays producing the asymmetry also produce the symmetric population at rate Γϕ n_eq^ϕ, and no depletion operator is introduced or solved, the physical N+N̄ yield is Y−/ε. For the displayed benchmark ε=5×10^-6 this is ~2×10^5 times larger, so the claimed 'naturally reproduced' relic density is not derived from the model; it is obtained only by defining DM as the asymmetry. The non-thermal momentum and Lyman-α discussion remains independent, but the central abundance claim is partially circular.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 3 invented entities

The model introduces three new fields and a new global symmetry, with ε and several mass/coupling parameters chosen by hand. The central 'prediction' of the relic abundance is a re-arrangement of the freeze-in formula with the observed Ω used to fix parameter combinations.

free parameters (6)
  • m_N = not fixed; >5 keV from Lyman-α
    Sterile neutrino mass, free parameter tuned to match relic density and constraints.
  • m_φ = benchmarks 300 GeV
    Mediator mass; chosen by hand, no prediction.
  • m_χ = unspecified
    Auxiliary fermion mass; enters phase space but not constrained.
  • μ = ~10^-6 [units unclear]
    Coupling/chemical potential; fitted to reproduce ΩDMh^2≈0.12; dimensionally ambiguous (Γ = |μ|^2/(8π m_φ) implies [μ]=mass).
  • λ_φH = 10^-8 in plots
    Higgs portal coupling; chosen small to keep freeze-in; unconstrained in shown region.
  • ε = ~10^-6 in plots
    CP-asymmetry parameter inserted by hand; no loop calculation provided; fitted to relic density.
axioms (5)
  • domain assumption The parent scalar φ has equilibrium number density n_eq^φ at the SM temperature
    Eq. (8) uses equilibrium φ density, but §II states φ never equilibrates with the visible sector. The actual φ abundance would be set by freeze-in via λ_φH and is not computed.
  • ad hoc to paper The symmetric N+Nbar component does not contribute to DM density
    Eq. (15) takes Ω∝m_N Y_-; the same decays produce a symmetric population with yield Y_sym ≈ Y_-/ε, which would dominate the relic density unless annihilated. No annihilation operator or Boltzmann equation for the total number density is provided.
  • ad hoc to paper χ decays efficiently into lighter hidden-sector states
    §II assumes χ decays away, but no such lighter states or couplings are specified.
  • domain assumption The Dirac mass m_N \bar{N}N is generated by a Higgs-type mechanism
    Introduction claims mass generated via Higgs mechanism, but §II contains an explicit mass term and no dark Higgs is introduced.
  • domain assumption g_* is constant over the integration range
    Eqs. (12)-(13) pull g_*^{-3/2} out of the integral, ignoring its temperature dependence across the production epoch.
invented entities (3)
  • Gauge-singlet Dirac sterile neutrino N with conserved U(1)_DM charge no independent evidence
    purpose: Dark matter candidate carrying a global charge to support asymmetry
    No new experimental signature is derived; the U(1)_DM symmetry is postulated.
  • Real scalar mediator φ no independent evidence
    purpose: Out-of-equilibrium parent decaying to N+χ with CP violation
    No production or decay signature is quantified beyond the tiny Higgs portal coupling.
  • Auxiliary singlet fermion χ no independent evidence
    purpose: Partner in φ decay; assumed to decay away
    No decay mechanism or final states are given; it is introduced solely to enable the two-body decay.

pith-pipeline@v1.3.0-alltime-deepseek · 9485 in / 19375 out tokens · 171780 ms · 2026-08-02T21:17:43.414202+00:00 · methodology

0 comments
read the original abstract

We propose a minimal and predictive framework for asymmetric sterile neutrino dark matter (DM) produced via freeze-in. The standard model (SM) is extended by a gauge-singlet Dirac sterile neutrino carrying a conserved dark charge, a real scalar mediator, and an auxiliary singlet fermion. DM is generated through the out-of-equilibrium decay of the mediator, which simultaneously produces a particle{antiparticle asymmetry in the sterile sector controlled by a CP-violating parameter. We show that the observed relic abundance can be naturally reproduced without thermal equilibration with the SM plasma. The resulting non-thermal momentum distribution is colder than a thermal Fermi{Dirac spectrum, ensuring consistency with structure formation constraints. Combining relic density, Lyman-{\alpha}, Higgs invisible decay, and big bang nucleosynthesis (BBN) bounds, we identify correlated and predictive regions of the parameter space characterized by non-trivial relations among the sterile neutrino mass and the decay parameters. This scenario provides a self-consistent realization of Dirac asymmetric sterile neutrino DM within an asymmetric freeze-in (AFI) framework, offering a constrained and testable alternative to conventional production mechanisms.

Figures

Figures reproduced from arXiv: 2602.20570 by S. Peyman Zakeri.

Figure 1
Figure 1. Figure 1: FIG. 1: Evolution of the asymmetric sterile neutrino abundance [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Evolution of the asymmetric sterile neutrino abundance [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Evolution of the sterile neutrino yield [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Relic density Ω [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Viable parameter space in the ( [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Viable parameter space in the ( [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗

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