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Low-scale leptogenesis in the scotogenic model: spectator processes and benchmark points

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

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Pith's one-line read The paper argues that non-resonant leptogenesis in the scotogenic model works at TeV masses for both thermal and zero initial sterile-neutrino abundances.

desk verdict TeV-scale scotogenic leptogenesis is genuinely new and the spectator treatment is mostly sound; the undefended closure relations are the real soft spot, and the stress-test's elastic-scattering worry is a misreading. read the letter →

arxiv 2411.15120 v1 pith:BHFFGU5H submitted 2024-11-22 hep-ph

J. Racker This is my paper · ORCID
classification hep-ph
keywords leptogenesisscotogenicmodelradiativeneutrinomassinertHiggsdoubletsteriledecayspectatorprocesseschargedleptonflavorviolationdarkmatter
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

The paper tries to establish that the scotogenic model — the Standard Model extended by an inert Higgs doublet, three sterile neutrinos, and a $Z_2$ symmetry that makes the lightest inert scalar the dark matter — can generate the observed baryon asymmetry through TeV-scale leptogenesis, for both thermal and zero initial abundances of the lightest sterile neutrino. The key mechanism is that the inert Higgs mass exponentially suppresses the washout of the lepton asymmetry, provided that spectator processes (reactions that do not generate the asymmetry but redistribute it) keep the asymmetry stored in the inert Higgs field small; earlier work either assumed this suppression without tracking it or neglected the inert Higgs mass entirely. The paper presents four benchmark points, fitted to neutrino oscillation data, that all give $Y_B \simeq 8.7 \times 10^{-11}$, with $M_1$ as low as $1.3$ TeV for a thermal initial abundance and $2.5$ TeV for a zero initial abundance. The reason to care is testability: the successful points with larger imaginary parts of the complex rotation angles have Yukawa couplings large enough for charged lepton flavor violation rates (rare processes such as $\mu\to e\gamma$ and $\mu\to e$ conversion) that current and planned experiments can probe.

What carries the argument

The central object is the inert-Higgs number asymmetry $Y_{\Delta\eta}$, evolved by its own Boltzmann equation in the set (5) and linked to the baryon and lepton-flavor asymmetries by the closure relations (6) and (7). The mechanism works as follows. For $T \lesssim m_\eta$, every washout process that begins with an $\eta$ or $\bar\eta$ carries a Boltzmann suppression; whether that suppression is real depends on $Y_{\Delta\eta}$. When the spectator reactions $\bar\phi\eta\to\phi\bar\eta$ and $\eta\eta\to\phi\phi$ are fast, they enforce $\mu_\eta=\mu_\phi$, making $y_\eta = Y_{\Delta\eta}/Y_\eta^{\mathrm{eq}}$ exponentially small. When they are slow, $Y_{\Delta\eta}$ remains proportional to the lepton asymmetries and the washout terms proportional to $y_\eta$ are not suppressed. Tracking $Y_{\Delta\eta}$ with its own rate equation, instead of assuming $\mu_\eta=\mu_\phi$, is the step that changes the conclusions.

What would settle it

Compute the chemical potentials of all fast-interacting species in the scotogenic model from the full finite-temperature reaction network, without assuming the low-temperature closure relations, and check whether Eqs. (6) and (7) describe $Y_{\Delta\eta}$ and $Y_B$ throughout the epoch; if a complete solution gives order-one different values, rerun the four benchmark points and see whether any still reaches $Y_B \simeq 8.7\times10^{-11}$.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that non-resonant scotogenic leptogenesis can work at TeV masses despite the earlier roughly 10 TeV lower bound of [29]: the washout of the lepton asymmetry is exponentially suppressed once the inert Higgs mass $m_\eta$ is sizable, and this suppression survives because the asymmetry $Y_{\Delta\eta}$ stored in the inert Higgs is depleted by spectator processes. The paper adds a Boltzmann equation for $Y_{\Delta\eta}$, closes the system with flavor-dependent chemical-potential relations, and finds four benchmark points, based on the complex-orthogonal (Casas-Ibarra) parametrization of the Yukawa couplings and on current neutrino mixing data, that all give $Y_B \simeq 8.7 \times 10^{-11}$: $M_1 = 1.3$ TeV with a thermal initial abundance, $M_1 = 3$ TeV with $\mathrm{CR}(\mu-e,\mathrm{Ti}) = 1.3 \times 10^{-19}$, $M_1 = 4$ TeV with $\mathrm{Br}(\mu\to e\gamma) = 5 \times 10^{-13}$, and $M_1 = 2.5$ TeV with zero initial abundance and $\mathrm{CR}(\mu-e,\mathrm{Ti}) = 9.3 \times 10^{-20}$. The same calculation shows that the simplifying assumption $\mu_\eta = \mu_\phi$ overestimates $Y_B$ by a factor of 2 to 3 in part of the parameter space, and that the spectator processes can change $Y_B$ by more than an order of magnitude.

Load-bearing premise

The load-bearing premise is that the chemical-potential closure relations (6) and (7) hold throughout the leptogenesis epoch; these relations are imported by analogy from a low-temperature regime and not derived in the paper, so if they are inaccurate the computed $Y_B$ for every benchmark point changes.

Editorial extensions

If this is right

  • Non-resonant leptogenesis in the scotogenic model is viable with the lightest sterile neutrino at $1.3$ TeV for a thermal initial abundance and at $2.5$ TeV for a zero initial abundance, about an order of magnitude below the previous $10$ TeV scale.
  • The same parameter regions connect cosmology to flavor physics: BP2 gives $\mathrm{CR}(\mu-e,\mathrm{Ti}) = 1.3 \times 10^{-19}$, within reach of planned experiments, and BP3 gives $\mathrm{Br}(\mu\to e\gamma) = 5 \times 10^{-13}$, above the current experimental upper bound.
  • Washout suppression by the inert Higgs mass works only when the spectator processes $\bar\phi\eta\to\phi\bar\eta$ and $\eta\eta\to\phi\phi$ are effective; scaling their rates down by a small factor lowers $Y_B$ by more than one order of magnitude for BP1 and by several orders for BP4.
  • Successful leptogenesis in these benchmark points does not rely on quasi-degenerate sterile neutrinos or resonant enhancement, so it opens a region of parameter space distinct from resonant leptogenesis and leptogenesis via oscillations.
  • The treatment of a massive particle that is different from its antiparticle and carries an asymmetry should transfer to baryogenesis in other Standard Model extensions, as the paper notes.

Reading between the lines

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

  • A density-matrix version of the same transport equations, keeping flavor coherence and finite-temperature corrections, would test whether the four benchmark points survive; the paper's Maxwell-Boltzmann, linearized treatment leaves room for order-one shifts in $Y_B$.
  • The spectator mechanism implies a sharp correlation among CLFV channels: if the baryon asymmetry is set in the BP2 or BP4 region, the same complex rotation angles determine $\mathrm{Br}(\mu\to e\gamma)$, $\mathrm{CR}(\mu-e,\mathrm{Ti})$, and $\mathrm{Br}(\mu\to 3e)$, so a measurement in one channel would predict the others.
  • Deriving the closure relations from the full temperature-dependent network of fast reactions, rather than importing the low-temperature regime of [36], is the most direct way to check robustness; if corrections appear, the viable $z_{23I}$ values could shift.
  • If future $\mu\to e\gamma$ and $\mu\to 3e$ searches stay null while $\mu\to e$ conversion is observed, the ratio structure computed in [73] would become a discriminating signature of the scotogenic model over other radiative neutrino mass models.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. This paper studies non-resonant leptogenesis from the decay of the lightest sterile neutrino N1 in the scotogenic model, adding an inert-Higgs asymmetry Y_Δη and two λ5-induced spectator processes to a set of flavored Boltzmann equations. It argues that these spectator processes control the exponential suppression of washouts for large inert-Higgs masses, and it presents four benchmark points reproducing Y_B ≈ 8.7×10^-11 with M1 as low as 1.3 TeV (thermal initial abundance) or 2.5 TeV (zero initial abundance), with Yukawa couplings of N2,N3 large enough for observable or already-excluded CLFV rates. The paper also quantifies the difference between assuming μη=μφ and solving the full system.

Significance. If the calculation is correct, the paper identifies a new viable region of TeV-scale scotogenic leptogenesis, connecting the BAU to scalar DM and CLFV, and it clarifies a mechanism (spectator-damped inert-Higgs asymmetry) that may apply to other models. The benchmark analysis is concrete and falsifiable, and the paper is explicit about the limits of the approach by showing in Fig. 2 that a common shortcut overestimates Y_B. I also checked the review concern about an elastic φη→φη term: the term in Eq. (5) is actually the number-changing process \barφη→φ\barη, so that specific objection does not apply. The main vulnerability is not this collision term but the unverified chemical-potential closure and the absence of explicit reaction densities.

major comments (3)
  1. [Section II, Eqs. (6)-(7)] The chemical-potential closure relations (6) and (7) are load-bearing: they convert the evolved asymmetries Y_Δα, Y_Δη, and Y_{B-L} into Y_B, and the numerical coefficients are not obvious. The text says only that they follow from an analysis 'similar to the lowest temperature regime described in [36]' and gives no derivation. Because the inert-doublet extension is precisely the new ingredient, this is not a routine citation. Please provide the derivation or an appendix with the chemical-potential equations, and state explicitly why the regime of validity holds over the whole integration range from T ∼ M1 down to the sphaleron freeze-out temperature. Since the benchmark points are tuned to Y_B ≈ 8.7×10^-11, an error in these relations would directly shift the central claim.
  2. [Section II, Eq. (5) and Section III] The reaction densities used in the Boltzmann equations, especially those for the spectator processes \barφη→φ\barη and ηη→φφ, are not given explicitly; the text only states that the cross sections were computed analytically and then integrated numerically. Because the central result depends on the balance between these spectator damping rates and the washout terms (as the λ-scan in Fig. 1 demonstrates), the expressions or a reproducible code should be made available so the reader can verify the claimed Y_B values.
  3. [Section II, after Eq. (5)] The calculation uses Maxwell-Boltzmann statistics, kinetic equilibrium, and neglect of several scattering processes, but no quantitative estimate of the induced error is provided. Given that Fig. 1 shows an exponential sensitivity of Y_B to the spectator rates and that the benchmark points are tuned to the observed value, the existence claim would be substantially strengthened by an estimate of how the standard approximations shift Y_B, for example by comparing the collision terms with a Bose-Einstein/Fermi-Dirac treatment or by varying the neglected scattering rates within a plausible range.
minor comments (3)
  1. [Fig. 1 caption] Please specify that λ multiplies the two spectator rates γ_{\barφη}^{φ\barη} and γ_{ηη}^{φφ} at all temperatures, and state explicitly which curves correspond to the actual benchmark points.
  2. [Table I caption] The caption says 'for all points YB ≃ 8.7×10^-11', but the computed Y_B values are not listed; please add them or point to the figures where they are shown.
  3. [Table I caption] The notation m_η is used both as the potential parameter and as an approximate physical mass; please define m_η clearly (for example, m_η^2 = m_η^2 + λ_3 v^2) and state the relation to m_{ηI}.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: benchmark points are existence proofs selected to match the observed baryon asymmetry, and the spectator/closure treatment is imported from independent standard results, not from the paper's own conclusions.

full rationale

The paper does not derive the baryon asymmetry from the observed value; it integrates the flavor Boltzmann equations (5) for chosen model parameters and checks that Y_B reproduces the measured 8.7e-11. The observed asymmetry acts only as a target for benchmark selection, which is normal model-building practice and not a fitted-input-called-prediction. The CLFV rates are computed outputs of the same Yukawa couplings, and the paper explicitly does not claim them to be independent tests of leptogenesis. The spectator-process treatment is quantified by varying a multiplier λ in Fig. 1 rather than tuned to force Y_B, and the closure relations (6)-(7) are stated to follow from a standard chemical-potential analysis 'similar to' the lowest-temperature regime of Ref. [36]; although Ref. [36] shares an author, it is an independent published derivation of flavor couplings, not an unverified self-citation carrying the conclusion. The central mechanism, exponential washout suppression by the inert-Higgs asymmetry, is presented with a detailed BE treatment and compared with prior qualitative results, but the calculation is self-contained. No equation is shown to reduce to its own input by construction, and no fitted parameter is renamed as a prediction. The possible concern about the φ-bar-η to φ-eta-bar term in Eq. (5) is a physics-consistency question, not a circularity, and the quoted process is number-changing rather than elastic as written in the paper. Overall, the derivation chain is independent of its conclusions.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central calculation uses a standard model framework plus the scotogenic model. The main inputs are the masses and couplings in Table I, several of which are tuned by hand to satisfy the BAU and CLFV constraints. The Boltzmann equation treatment rests on the usual approximations of kinetic equilibrium and Maxwell-Boltzmann statistics, and on an unshown extension of chemical potential relations from [36]. No new entities are introduced.

free parameters (5)
  • m_eta (inert Higgs mass) = 0.6 TeV (BP1), 0.9 TeV (BP2), 1.6 TeV (BP3), 1.75 TeV (BP4)
    Chosen large enough to induce exponential Boltzmann suppression of washouts; this is the central tuning that enables low-scale leptogenesis.
  • z23I (imaginary part of complex rotation angle) = 0 (BP1), 2.5 (BP2), 6 (BP3), 5 (BP4)
    Tuned to large values to enhance the Yukawa couplings of N2 and N3, making CLFV rates observable. It is a free parameter in the Casas-Ibarra parametrization.
  • lambda5 = 1.4e-5 (BP1), 1e-5 (BP2), 1.23e-4 (BP3), 1e-3 (BP4)
    Chosen small to suppress neutrino masses and to control the spectator process rates; its value affects the DM relic density and the washout of the eta asymmetry.
  • M1 (lightest sterile neutrino mass) = 1.3, 3, 4, 2.5 TeV
    Selected to demonstrate TeV-scale leptogenesis; not fitted to data but a free parameter of the model.
  • m1 (lightest active neutrino mass) = 1e-15, 1e-13, 1e-12, 1e-11 eV
    Set effectively to zero in the benchmark points; a free parameter of the neutrino mass matrix.
assumptions (5)
  • domain assumption The universe is radiation-dominated with standard expansion H proportional to T^2/m_Pl during the leptogenesis epoch.
    Invoked in Section II to write the Boltzmann equations in terms of z = M1/T.
  • domain assumption Kinetic equilibrium and Maxwell-Boltzmann statistics hold for all relevant species, and the equations can be linearized in the asymmetries.
    Stated in Section II before Eq. (5); these are standard but uncontrolled approximations.
  • ad hoc to paper The chemical potential closure relations in Eqs. (6)-(7), obtained by extending the low-temperature analysis of [36] to include the inert doublet, are valid.
    The derivation is not shown; the paper says it is 'similar to' [36] and presents only the final relations.
  • domain assumption The two spectator processes phi-bar eta to phi eta-bar and eta eta to phi phi, with rates proportional to lambda5^2, dominate the erasure of the eta asymmetry.
    Used in the last equation of (5); other lepton-number-violating processes involving eta are neglected.
  • ad hoc to paper For BP1-BP3, N1 has a thermal initial abundance produced by unknown higher-scale interactions.
    Explicitly stated in Section III as an assumption for those benchmark points.

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Cite this review

Pith. "Pith review of Low-scale leptogenesis in the scotogenic model: spectator processes and benchmark points." pith.science (2026). https://pith.science/paper/BHFFGU5H

@misc{pith2026241115120,
  author       = {Pith},
  title        = {Pith review of: Low-scale leptogenesis in the scotogenic model: spectator processes and benchmark points},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BHFFGU5H}},
  note         = {Machine review of arXiv:2411.15120}
}
read the original abstract

We study leptogenesis from the decay of the lightest sterile neutrino in the scotogenic model with a scalar dark matter candidate. Our analysis focuses on the possible exponential suppression of washouts for sizable values of the inert Higgs mass and the crucial role of some spectator processes for this to happen. We show that leptogenesis can be successful for TeV-scale masses of the lightest sterile neutrino for both, thermal and zero, initial abundances of the neutrinos. Moreover, leptogenesis is viable for Yukawa couplings of the heavier sterile neutrinos large enough to yield observable charged lepton flavor violation processes in current and planned experiments.

Figures

Figures reproduced from arXiv: 2411.15120 by the authors.

Figure 1
Figure 1. FIG. 1. The baryon asymmetry obtained for BP1 (solid blue [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The baryon asymmetry as a function of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

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