Gravitational wave signatures of dark sector portal leptogenesis

Debasish Borah; Devabrat Mahanta; Indrajit Saha

REVIEW 3 major objections 6 minor 1 cited by

Gravitational wave signatures of dark sector portal leptogenesis

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A dark-sector portal allows TeV-scale leptogenesis to produce both the observed baryon asymmetry and a gravitational wave background detectable by LISA.

desk verdict A clean FOPT/GW phenomenology wrapper around a leptogenesis mechanism that, as written, sets its CP asymmetry to zero by choosing Mψ ≈ 10 MN1. read the letter →

arxiv 2504.14671 v1 pith:HRIZ34DD submitted 2025-04-20 hep-ph astro-ph.CO

Debasish Borah , Devabrat Mahanta , Indrajit Saha This is my paper · ORCID

classification hep-phastro-ph.CO

keywords leptogenesisgravitationalwavesfirst-orderelectroweakphasetransitionscoto-seesawZ2darksectorTeVscaleright-handedneutrinoLISA

topics Matter-Antimatter Asymmetry

open problems Matter-Antimatter Asymmetry

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 argues that a single dark sector charged under an unbroken $Z_2$ symmetry can do three jobs at once: provide the CP violation needed for leptogenesis, generate one neutrino mass radiatively, and strengthen the electroweak phase transition into a strongly first-order one. If correct, TeV-scale leptogenesis no longer needs resonant enhancement or a high seesaw scale, and the same physics that creates the matter-antimatter asymmetry would leave a stochastic gravitational wave background that LISA could see. The paper demonstrates benchmark points with a right-handed neutrino near $1$ TeV and dark-sector scalars below $1$ TeV that reproduce the observed baryon-to-photon ratio $\eta_B = 6.1 \times 10^{-10}$, the dark matter relic abundance, and a phase transition with LISA signal-to-noise ratios up to about 50.

What carries the argument

The engine of the model is the one-loop vertex correction to the decay $N_1 \to \ell \Phi$, with the $Z_2$-odd fermion $\psi$ and scalars $\chi$, $\eta$ running in the loop. Its interference with the tree-level amplitude gives the CP asymmetry $\epsilon_1$ quoted in Eq. (3.2), which is proportional to $\mathrm{Im}(y^\dagger_N y_\psi y_1 \mu_1)$ and can be dialed up through the dark portal couplings without changing the neutrino masses. The same $Z_2$-odd scalars couple to the SM Higgs and supply the additional bosonic degrees of freedom that make the electroweak phase transition strongly first order, fixing the nucleation temperature $T_n$, the strength $\alpha_*$, and the inverse duration $\beta/H$ that enter the gravitational wave spectrum.

What would settle it

A direct calculation of the imaginary part of the loop integral in Eq. (3.2) for benchmark masses, such as $M_\psi = 10 M_{N_1}$ and dark scalars around a few hundred GeV, would settle the leptogenesis claim: if the logarithm's branch cut is not crossed, $\epsilon_1 = 0$. On the gravitational wave side, a null stochastic background search by LISA after five years at the predicted peak frequencies would rule out the benchmark phase-transition parameter space.

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Extended reading notes

Core claim

The central claim is that an otherwise minimal extension of the Standard Model, one right-handed neutrino $N_1$ plus a $Z_2$-odd sector containing a fermion $\psi$, a scalar doublet $\eta$, and a real singlet $\chi$, can generate the observed baryon asymmetry through the out-of-equilibrium decay $N_1 \to \ell \Phi$, with the CP asymmetry coming from one-loop vertex interference with the dark sector rather than from self-energy diagrams. Because the new couplings $y_1$ and $\mu_1$ enter the asymmetry independently of the tiny neutrino Yukawa couplings, they can be large enough to make $\epsilon_1$ sizable at $M_{N_1} \sim 1$ TeV. The paper further claims that the same scalar sector turns the electroweak transition first-order, with benchmark values like $\alpha_* = 0.52$ and $\beta/H = 136$ producing gravitational wave spectra within LISA reach, and that light neutrino masses arise from a combination of type-I and one-loop seesaw with a vanishing lightest neutrino mass.

Load-bearing premise

The whole baryon asymmetry rests on the claim that the one-loop vertex diagram has a nonzero imaginary part for the chosen mass pattern, with the heavy dark fermion about ten times heavier than $N_1$ and the $Z_2$-odd scalars lighter than $N_1$; if that imaginary part is absent, $\epsilon_1$ vanishes and the model produces no baryon asymmetry.

Editorial extensions

If this is right

The observed baryon-to-photon ratio $\eta_B = 6.1 \times 10^{-10}$ can be produced with $M_{N_1}$ around $1$ TeV and sub-TeV dark-sector masses, so leptogenesis need not live at the high seesaw scale.
CP violation does not require degenerate right-handed neutrinos; the model explicitly avoids resonant enhancement.
A strong first-order electroweak phase transition and a stochastic gravitational wave background with LISA signal-to-noise ratios up to about 50 emerge from the same parameter space that fits neutrino masses and dark matter.
The lightest active neutrino mass is predicted to vanish, so future neutrinoless double beta decay searches could exclude the normal ordering assumed here.
The sub-TeV scalars give collider signatures such as same-sign dilepton plus missing energy, dijet plus missing energy, trilepton plus missing energy, and monojet events.

Reading between the lines

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

Going beyond the paper: if the mechanism is correct, any mass ordering that closes the s-channel cut in the dark loop should suppress leptogenesis, so combining LISA searches for the phase transition with collider searches for the $Z_2$-odd scalars could jointly decide whether the dark sector is the real CP source.
The perturbative calculation of the phase-transition parameters could shift under non-perturbative corrections; a measured gravitational wave peak would be needed to pin down $\alpha_*$ and $\beta/H$ rather than relying only on benchmark values.
A natural companion calculation would be a first-principles evaluation of the vertex integral with full kinematics; if the branch cut behaves differently from the quoted formula, the leptogenesis conclusion would change directly.

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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

Short version: read this for the FOPT/GW part, but don't trust the BAU numbers until the CP asymmetry is rederived for the actual masses. The stress-test concern lands.

What's new: the package itself. Combining scoto-seesaw neutrino masses with a one-loop vertex contribution from the Z2-odd ψ, η, χ fields to N1 decay, and then using the same dark sector to strengthen the electroweak phase transition, is not in the cited literature. The GW machinery is standard but competently executed: effective potential with daisy resummation, β/H and α* benchmarks, LISA SNRs around 50. The DM relic calculation via micrOMEGAs is reproducible. That part is solid.

The problem is central. Eq. (3.2)'s logarithm only has an absorptive piece when its argument is negative, which requires MN1 > Mψ + mχ or an analogous kinematic cut. With Table 2 fixing Mψ ≈ 10 MN1 and mχ < MN1, the log is real, the bracket is real, and ε1 = 0. The Sec. 3 statement that the Z2-odd scalars are lighter than N1 'such that an imaginary part survives' misses that the other cut particle, ψ, is heavier. The formula is imported from ref. [65], which shares an author, without derivation and without checking the branch-cut condition. So the BAU figures are generated by an out-of-regime formula. This is not a minor technicality; it is the whole leptogenesis mechanism.

The other soft spots are mild. Fitting benchmarks to the observed BAU and DM means the numbers are consistency checks rather than predictions; the authors acknowledge this. The main fix is a direct derivation of ε1 for the adopted hierarchy, or a rerun with Mψ < MN1 so the two-body cut opens, followed by a check of washout processes. Self-citation to [65] is not itself a flaw, but it made the kinematic slip easy to miss.

Who this is for: phenomenological model-builders working on low-scale leptogenesis and GW complements. The paper deserves a serious referee, but this version should not be accepted. I would send it back with a request to either prove ε1 is nonzero in the benchmark region or change the mass hierarchy and redo the leptogenesis and washout analysis. If the hierarchy is adjusted, the GW results likely survive; if not, the claimed link between TeV-scale leptogenesis and LISA disappears.

Referee Report

3 major / 6 minor

Summary. The paper studies an extension of the Standard Model with a right-handed neutrino N1 and a Z2-odd dark sector consisting of a fermion ψ, a scalar doublet η, and a real scalar singlet χ. It claims that the decay of a TeV-scale N1 can produce the observed baryon asymmetry through a one-loop vertex CP asymmetry, that light neutrino masses arise from a scoto-seesaw combination of tree-level and one-loop contributions, that the lightest Z2-odd scalar is a WIMP dark matter candidate, and that the same scalar sector can make the electroweak phase transition strongly first-order with gravitational wave signals detectable by LISA. The manuscript presents benchmark points, Boltzmann-equation results for B−L and dark matter, finite-temperature effective potential computations, and projected LISA signal-to-noise ratios.

Significance. If the leptogenesis mechanism worked, the paper would connect low-scale leptogenesis, dark matter, neutrino mass, and a first-order electroweak phase transition in a single framework with concrete, falsifiable predictions: normal neutrino mass ordering, a vanishing lightest active neutrino mass, LISA SNR values up to about 50, and possible collider and lepton-flavor-violating signatures. The phase transition and gravitational wave parts use standard effective-potential and GW-spectrum machinery, the dark matter computation relies on documented public tools (CalcHEP, micrOMEGAs), and the benchmark selection is transparent. However, the CP asymmetry calculation is the load-bearing element of the paper, and it is not kinematically consistent for the adopted mass hierarchy; this issue must be repaired before the phenomenological claims can be accepted.

major comments (3)

[Section 3, Eq. (3.2)] For the hierarchy adopted in Table 2 (Mψ ≈ 10 M_N1, with mχ < M_N1 and mη < M_N1), the argument of the logarithm in Eq. (3.2) is positive because δ−(1−√σ)^2 > 0 and δ−σ > 0; the bracket is therefore real, and ε1 vanishes identically, since a real loop amplitude cannot interfere with the tree amplitude to produce CP violation. The text in Section 3 says that Z2-odd scalars are chosen lighter than M_N1 'such that an imaginary part survives', but for this vertex diagram the relevant branch cut requires the opposite mass condition, Mψ < M_N1 − mχ. Since Eq. (3.6) and the baryon-asymmetry results in Figs. 2, 5, and 6 are all built on this ε1, the central leptogenesis claim is unsupported as written.
[Section 3, Eq. (3.1)] Equation (3.1) is quoted from ref. [65] without any derivation or analysis of the Cutkosky cuts that would produce the absorptive phase; because ref. [65] shares an author with the present paper, this cannot be treated as an independent check. The authors should provide a derivation of Eq. (3.1), or at least state the iε prescription and the exact kinematic condition under which the logarithm develops an imaginary part, and verify that condition explicitly in the benchmark region, since the whole leptogenesis calculation depends on this formula.
[Section 3 and Table 2] The mass-ordering assumptions used in Section 3 are mutually incompatible: Mψ ≫ M_N1 is adopted so that asymmetries generated by ψ are washed out, but the same ordering closes the only two-body cut (N1 → ψ + χ) that can produce an absorptive phase in the vertex loop. The paper should either adopt the hierarchy Mψ < M_N1 − mχ and re-evaluate the washout and all benchmark points, or identify another source of the imaginary part; the present combination of assumptions yields ε1 = 0.

minor comments (6)

[Section 5 and Fig. 2 caption] The benchmark values are not harmonized between Table 2 and the caption of Fig. 2: BP1 in Table 2 has M_N1 = 1.02 TeV, whereas the Fig. 2 caption uses M_N1 = 1058 GeV and Mψ = 10^4 GeV; please make the benchmark definitions consistent.
[Table 2] Table 2 does not list Mψ even though the mass hierarchy is the decisive input for the CP asymmetry; the footnote 'Mψ∼10M_N1' is too imprecise, and the precise value of Mψ should be given for each benchmark.
[Introduction] The word 'succeess' in the Introduction should be 'success'.
[Section 5] In Section 5, the phrase 'can can give rise' contains a duplicated word; please correct it.
[Appendix A] The thermal-mass line 'm2η2(ϕ,T)=m2η2(ϕ)+Πχ(T)' appears to be a typo; the scalar singlet χ should receive Πχ(T), while the inert doublet components should receive ΠS(T).
[Section 3, Eqs. (3.3)-(3.4)] The Boltzmann equations introduce many thermally averaged cross sections without explicit expressions or definitions; since these determine the efficiency factor κ in Eq. (3.6), the numerical solution is not fully reproducible from the text alone.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the observed baryon asymmetry is used as a selection constraint rather than predicted, and the GW/phase-transition calculation is independently computed from the model potential.

full rationale

The paper's central leptogenesis result is not a prediction in the sense of a fitted parameter being renamed as a prediction. Table 2 explicitly lists 'Benchmark points satisfying the requirements of observed baryon asymmetry and dark matter', and the parameter scans in Figs. 5 and 6 are constructed to be 'consistent with the observed baryon asymmetry' or to show where the resulting YB lies. Thus the observed ηB is an input constraint, not an output forced by construction. The CP asymmetry formula in Eq. (3.1)-(3.2) is attributed to [54,55,65]; although ref. [65] shares co-author Mahanta, it is not the sole support, and the formula is a standard one-loop vertex integral rather than a uniqueness theorem or an ansatz that is adopted without content. The Boltzmann equations and efficiency-factor treatment are standard (Gondolo-Gelmini; Buchmuller et al.). The phase-transition and gravitational-wave sector is self-contained: Veff is constructed from the model's field-dependent and thermal masses (Appendix A), and α*, β/H, vw and the LISA SNR are computed with the standard spectrum formulas in Appendix B, independent of the leptogenesis output. The kinematic concern about whether the absorptive part of the loop integral is open for Mψ ≈ 10 MN1 (with Z2-odd scalars lighter than N1) is a physics-correctness issue about the applicability of the quoted formula, not a circularity: no equation in the paper reduces to an equivalent input by construction, and no fitted quantity is presented as an independent prediction. I therefore find no significant circularity, with only a minor note that the one-loop formula is imported from prior work rather than re-derived here.

Assumptions & free parameters 6 free parameters · 5 assumptions · 4 invented entities

The model introduces four new fields and many couplings; the central claims rest on the imported CP asymmetry formula and on the assumed kinematic regime for its imaginary part, neither of which is derived or independently verified here. The neutrino mass fit uses the Casas-Ibarra parametrization with a free complex angle, and the FOPT/GW computation uses standard finite-temperature potential and GW formulas.

free parameters (6)

y1 = 2e-3 (BP1), 1e-3 (BP2-BP4)
Yukawa coupling between N1, psi, chi; chosen to enhance CP asymmetry and give observed BAU.
mu1 = 161.6i GeV (BP1), 733.5i GeV (BP2), 301.2i GeV (BP3), 461.1i GeV (BP4)
Scalar portal coupling chi Phi^dagger eta; complex phase is the sole CP-violating source; fitted to BAU.
M_psi = ~10 M_N1
Mass of the Z2-odd fermion; set heavier than N1 to let N1-generated asymmetry survive washout.
mu_eta, mu_chi = mu_eta = 450, 938, 660, 524 GeV; mu_chi = 430, 592, 220, 57 GeV (BP1-BP4)
Scalar mass parameters chosen via benchmark selection to satisfy DM and FOPT.
z (Casas-Ibarra angle) = 0.5
Complex orthogonal angle; set to 0.5 so the R matrix does not provide extra CP violation.
Scalar quartic couplings lambda2, lambda3, lambda4, lambda5, lambda7, lambda8, lambda9 = not quoted
Not listed but varied to keep physical scalar masses fixed when mu1 is varied; influence FOPT strength.

assumptions (5)

ad hoc to paper The CP asymmetry formula (3.1) from ref. [65] applies to this model.
The formula is imported from a paper with overlapping authorship; its regime of validity for the adopted mass hierarchy is not demonstrated.
ad hoc to paper The one-loop vertex diagram has a nonzero imaginary part for M_psi > M_N1 with Z2-odd scalars lighter than N1.
The paper asserts this in Section 3, but the s-channel cut N1 -> psi + chi is closed for M_psi > M_N1 - M_chi, making the kinematic function in Eq. (3.2) real.
standard math Casas-Ibarra parametrization correctly encodes neutrino mass and mixing constraints for the combined tree plus loop mass matrix.
This is a standard tool in neutrino phenomenology; assumed valid without re-derivation.
domain assumption Single-step first-order phase transition with only the SM Higgs acquiring a VEV.
The Z2-odd scalars are prevented from VEVs by the unbroken Z2; the analysis considers a one-step transition in the SM Higgs direction.
standard math Standard finite-temperature effective potential and gravitational wave spectral formulas (Caprini et al.) are applicable.
The paper uses conventional resummed thermal potential and LISA parameterization; these are widely accepted.

invented entities (4)

N1 (right-handed neutrino)
purpose: Tree-level seesaw mass generation and source of lepton asymmetry.
Standard seesaw field; no direct experimental evidence yet.
psi (Z2-odd singlet fermion)
purpose: Mediates one-loop contribution to neutrino mass and provides the CP asymmetry vertex.
Introduced for the model; no direct evidence.
eta (Z2-odd scalar doublet)
purpose: Provides radiative neutrino mass, a dark matter candidate, and contributes to the first-order phase transition.
No direct evidence; predicted signals are generic to inert doublet models.
chi (Z2-odd real scalar singlet)
purpose: Provides the CP-violating portal coupling mu1, mixes with eta to form dark matter scalars, and assists the phase transition.
No direct evidence; introduced for the model.

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Cite this review

Pith. "Pith review of Gravitational wave signatures of dark sector portal leptogenesis." pith.science (2026). https://pith.science/paper/HRIZ34DD

@misc{pith2026250414671,
  author       = {Pith},
  title        = {Pith review of: Gravitational wave signatures of dark sector portal leptogenesis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HRIZ34DD}},
  note         = {Machine review of arXiv:2504.14671}
}

abstract

We study the possibility of probing leptogenesis via stochastic gravitational waves (GW) arising from a dark sector assisted first-order electroweak phase transition. The same dark sector, with non-trivial transformation under an unbroken $Z_2$ symmetry is also responsible for providing the only source of CP asymmetry via one-loop interference with the tree level decay of a heavy right-handed neutrino into lepton and Higgs doublets. The new Yukawa and scalar portal couplings enhance the CP asymmetry allowing TeV scale leptogenesis without any resonant enhancement. Light neutrino masses arise from a combination of type-I and one-loop contributions with vanishing lightest neutrino mass. While the new degrees of freedom in sub-TeV range keep the detection prospects at terrestrial experiments promising, the new scalars enhance the strength of the electroweak phase transition keeping the GW signals within reach of near future experiments like LISA.

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Forward citations

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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