{"id":"59669fd0-52ba-4626-8412-c3ffb98fcd5b","arxiv_id":"2504.14671","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A Z2-odd dark sector with a heavy fermion and two scalars enables TeV-scale leptogenesis and produces LISA-visible gravitational waves from a strong electroweak phase transition.","lead":"This paper proposes a dark sector that boosts the decay of a TeV-scale right-handed neutrino to create the observed matter-antimatter asymmetry, while also making the electroweak phase transition strongly first order and generating gravitational waves within reach of LISA. A generalist might care because it links three hard-to-test puzzles, the origin of matter, dark matter, and cosmic gravitational waves, into one model.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quoted CP asymmetry formula has no absorptive part for Mψ = 10 MN1: the log in Eq. (3.2) is real, so ε1 vanishes and the benchmark baryogenesis is unsupported.","rationale":"The reader identified the right weakest point: the CP asymmetry formula is imported from Ref. [65] without derivation or a check of the branch-cut regime. I agree with that identification. The concern is more specific than the reader's wording suggests: a kinematic function can be real and still represent the imaginary part of a loop integral, as in standard hierarchical leptogenesis. The real question is whether the triangle diagram has any absorptive part for the adopted masses. Here all two-body unitarity cuts are closed: N1 → ψ+χ and N1 → ψ+η require Mψ < MN1, contradicting Mψ ≈ 10 MN1; the χ−η cut has invariant mass m_h^2 and requires mχ+mη < m_h, also false. Consistent with this, the logarithm in Eq. (3.2) has a positive argument for δ ≈ 100, so the quoted bracket is the real part of the loop function and cannot provide the strong phase needed for ε1. The paper's statement that light Z2-odd scalars make an imaginary part survive is not supported by the explicit formula: the branch cut of that log requires (1−√σ)^2 > δ, i.e. MN1 > Mψ + mχ. Since the benchmarks violate this by an order of magnitude, the central leptogenesis claim is internally inconsistent with the quoted expression. The GW and FOPT sections are standard and may be sound, but the paper's headline link between TeV-scale leptogenesis and LISA relies on the nonvanishing of ε1; if that fails, the benchmarks in Table 2 do not satisfy the BAU constraint. No formal verification or independent numerical implementation of Eqs. (3.1)-(3.2) is provided, so this is not a minor presentation issue but the load-bearing core of the paper. The proposed test, computing the Cutkosky discontinuity or re-evaluating ε1 with the correct branch structure, would settle the matter. Until that is done, the correct verdict is REJECT rather than CONDITIONAL, because the current manuscript's central mechanism appears to vanish in its own parameter space.","tokens_in":18932,"tokens_out":28494,"duration_ms":298032,"concrete_test":"Evaluate the Cutkosky discontinuity of the triangle diagram in Fig. 1 at s = MN1^2 for BP1 masses: MN1 = 1.02 TeV, Mψ = 10.2 TeV, mχ ≈ 0.43 TeV, mη ≈ 0.45 TeV, external Higgs mass 125 GeV. If the discontinuity is zero, as expected because the two-body thresholds Mψ+mχ and Mψ+mη exceed MN1 and mχ+mη exceeds m_h, then ε1 = 0 and the baryon asymmetry cannot be produced. An equivalent analytic check: replace the log in Eq. (3.2) by log|argument| + iπ Θ((1−√σ)^2−δ) and recompute ηB for BP1–BP4; if ηB drops to zero, the paper's numerics used the wrong branch.","verdict_should_be":"REJECT","load_bearing_attack":"The central leptogenesis result rests on Eqs. (3.1)-(3.2), an imported formula for ε1. With the adopted hierarchy Mψ ≈ 10 MN1 (Table 2) and Z2-odd scalars lighter than N1, δ = Mψ^2/MN1^2 ≈ 100, σ = mχ^2/MN1^2 < 1, ζ = mη^2/MN1^2 < 1. The logarithm in Eq. (3.2), ln[(δ-(1−√σ)^2)/(δ−σ)], then has a positive argument: δ−(1−√σ)^2 > 0 and δ−σ > 0. Hence the bracket is the real part of the loop integral, not an absorptive part; a real loop amplitude cannot interfere with the tree amplitude to produce CP violation, so ε1 = 0 for these benchmarks. The only s-channel two-body cuts are N1 → ψ+χ and N1 → ψ+η, both kinematically closed since Mψ > MN1; the χ−η cut carries the external Higgs momentum with m_h^2 < (mχ+mη)^2 and is also closed. The paper's statement in Section 3 that light Z2-odd scalars are chosen 'such that an imaginary part survives' is therefore in tension with the explicit formula's branch structure, which requires MN1 > Mψ + mχ (negative log argument) to get an iπ discontinuity. The BAU plots in Fig. 2 are generated with ε1 from this out-of-regime formula.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":19348,"tokens_out":13862,"duration_ms":130761,"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":[{"comment":"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":"Section 3, Eq. (3.2)"},{"comment":"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":"Section 3, Eq. (3.1)"},{"comment":"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.","section":"Section 3 and Table 2"}],"minor_comments":[{"comment":"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.","section":"Section 5 and Fig. 2 caption"},{"comment":"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.","section":"Table 2"},{"comment":"The word 'succeess' in the Introduction should be 'success'.","section":"Introduction"},{"comment":"In Section 5, the phrase 'can can give rise' contains a duplicated word; please correct it.","section":"Section 5"},{"comment":"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":"Appendix A"},{"comment":"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.","section":"Section 3, Eqs. (3.3)-(3.4)"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about the branch structure of Eq. (3.2) is correct and lands on the central claim. I am recommending major revision rather than rejection because the phase transition and dark matter parts are largely independent and could survive a corrected calculation; however, if the leptogenesis calculation cannot be repaired with a nonzero ε1 in the adopted mass regime, the paper would not support its main thesis. Given the overlapping authorship with ref. [65], I would ask the editor to require a self-contained derivation of the CP asymmetry formula in the revised version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nWhat'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.\n\nThe 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.\n\nThe 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.\n\nWho 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.","headline":"A clean FOPT/GW phenomenology wrapper around a leptogenesis mechanism that, as written, sets its CP asymmetry to zero by choosing Mψ ≈ 10 MN1.","tokens_in":19871,"tokens_out":5393,"would_cite":false,"duration_ms":54331,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A dark-sector portal allows TeV-scale leptogenesis to produce both the observed baryon asymmetry and a gravitational wave background detectable by LISA.","keywords":["leptogenesis","gravitational waves","first-order electroweak phase transition","scoto-seesaw","Z2 dark sector","TeV scale","right-handed neutrino","LISA"],"falsifier":"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.","tokens_in":18699,"feed_emoji":"🌊","tokens_out":9205,"duration_ms":79337,"temperature":0.7,"pith_summary":"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.","feed_headline":"TeV-scale leptogenesis leaves a gravitational wave echo for LISA","feed_subtitle":"New dark-sector couplings create the baryon asymmetry and a phase-transition signal LISA could see.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines the leptogenesis mechanism that the model builds on, converting a lepton asymmetry into the observed baryon asymmetry.","marker":"[8]"},{"why":"Provides the Higgs-portal leptogenesis framework and the enhanced CP asymmetry formula that the dark-sector portal generalizes.","marker":"[54, 55]"},{"why":"Supplies the scoto-seesaw mass structure combining type-I and radiative contributions to active neutrino masses.","marker":"[57]"},{"why":"Gives the one-loop radiative neutrino mass formula used for the $Z_2$-odd sector.","marker":"[58, 59]"},{"why":"The Casas-Ibarra parametrization used to fit the Dirac Yukawa couplings to neutrino oscillation data.","marker":"[61]"},{"why":"Provides the scotogenic parametrization and charged lepton flavor violation constraints that shape the allowed dark-sector parameters.","marker":"[62]"},{"why":"The source of the CP asymmetry formula in Eqs. (3.1) and (3.2), including the kinematic structure that must have a nonzero imaginary part.","marker":"[65]"},{"why":"Defines the gravitational wave spectrum parameters $\\alpha_*$ and $\\beta/H$ and the peak-frequency formulas used to produce the predicted LISA signals.","marker":"[95]"},{"why":"The LISA sensitivity curve used to compute the signal-to-noise ratios reported in the paper.","marker":"[111]"}],"fun_headline_variants":["Dark sector CP drives TeV leptogenesis and LISA-visible GWs","One-loop dark CP: TeV leptogenesis with gravitational wave echo","Z2-odd fields: CP source, TeV leptogenesis, and LISA waves","TeV leptogenesis without resonance, plus LISA phase-transition signal","Dark portal leads to TeV leptogenesis and LISA-detectable GWs"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Dark sector CP drives TeV leptogenesis and LISA-visible GWs","One-loop dark CP: TeV leptogenesis with gravitational wave echo","Z2-odd fields: CP source, TeV leptogenesis, and LISA waves","TeV leptogenesis without resonance, plus LISA phase-transition signal","Dark portal leads to TeV leptogenesis and LISA-detectable GWs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000888,"raw_usage":{"total_tokens":3813,"prompt_tokens":910,"completion_tokens":2903,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":526,"completion_tokens_details":{"reasoning_tokens":2801}},"tokens_in":526,"tokens_out":2903,"duration_ms":19872,"temperature":1.0,"reasoning_tokens":2801,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:47:18.511060+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}