{"id":"d6b70f62-7b00-47ae-9dd9-d6357d54b6fb","arxiv_id":"2411.15120","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"TeV-scale leptogenesis in the scotogenic model is viable with proper treatment of spectator processes, yielding benchmark points that reproduce the baryon asymmetry and predict observable CLFV rates.","lead":"This preprint studies leptogenesis in the scotogenic model, where neutrino masses are radiative and dark matter is an inert scalar. It shows that with a heavy inert Higgs and the right spectator processes, the lightest sterile neutrino can generate the observed baryon asymmetry at TeV masses.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Boltzmann equation for Y_Δη likely includes an elastic φη→φη term that conserves η number, which if spurious would overestimate spectator damping and inflate Y_B.","rationale":"My stress-test pass identifies a different load-bearing concern than the reader's weakest assumption. The reader flagged the chemical-potential closure relations (6)–(7) because they are not derived and are used to convert the evolved asymmetries into Y_B. That is a legitimate issue of completeness and reproducibility, but the coefficients in (6)–(7) reduce correctly to the standard SM limits when Y_Δη→0, and the author is an expert in this derivation; I do not see a specific reason to doubt them. The more concrete and potentially fatal problem is the presence of γ_{φη→φη} in the Boltzmann equation for Y_Δη. Elastic scattering conserves the η number, so it cannot contribute to the evolution of Y_Δη at first order in the asymmetries; the term as written is formally incorrect. The mechanism of the paper depends on the spectator processes damping Y_Δη; if this term is removed, the remaining ηη→φφ process may still be fast enough (especially for the larger λ5 cases), but for BP1 with λ5∼10^{-5} the ηη→φφ rate is Boltzmann suppressed at late times, so the spurious φη→φη term could be numerically important. This directly affects the central numerical results. The concrete test proposed would settle the issue by simply removing the term and recomputing; it is a minimal, unambiguous check. For this reason I move the verdict to CONDITIONAL: the paper should not be accepted in its current form until the transport equation is corrected or justified, and the benchmark points are re-evaluated.","tokens_in":13793,"tokens_out":35533,"duration_ms":348751,"concrete_test":"Re-derive the collision term for the process φη→φη in the equation for Y_Δη from the underlying Lagrangian, confirming whether the process conserves η number and therefore drops out of dY_Δη/dz at linear order. Then modify the last line of Eq. (5) by deleting the γ_{φη→φη} contribution, while keeping γ_{ηη→φφ}, and re-integrate the BEs for BP1–BP4 with all other parameters unchanged. If any benchmark point then gives Y_B below 8.7×10^{-11}, the demonstrated parameter space shifts and the central claim requires retuning; if Y_B stays within a factor of two, the term was numerically irrelevant.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim rests on the set of BEs (5) and the control of the inert-Higgs asymmetry Y_Δη. In the last line of Eq. (5), the evolution of Y_Δη contains the term −2(γ_{φη→φη} + 2γ_{ηη→φφ})[y_η − y_φ]. The process φη→φη is elastic scattering: it conserves η number exactly (one η in the initial state, one η in the final state). For a number-conserving process, the collision term contributing to dY_Δη/dz vanishes at linear order in the asymmetries because the net number of η particles is unchanged; such a process cannot drive y_η toward y_φ. The bracket [y_η − y_φ] is the correct form for a number-changing process such as ηη↔φφ, where two η convert into two φ, but not for elastic scattering. The paper states that both γ_{φη→φη} and γ_{ηη→φφ} are proportional to λ5^2; however, the λ5 quartic term (η†φ)^2 + h.c. at tree level mediates ηη→φφ and its conjugate, not a number-conserving φη→φη amplitude. Thus the BE as written appears internally inconsistent. If γ_{φη→φη} is erroneously included, the damping of Y_Δη is overestimated, which suppresses the η-number weighted washout terms and can artificially boost the final Y_B. Since the benchmark points are tuned to give Y_B ≃ 8.7×10^{-11}, removing this term could shift the result below the observed value, weakening or invalidating the paper's existence claim. The closure relations (6)–(7), flagged by the reader, are a separate concern; without a derivation they are opaque, but here the issue is a concrete, testable formal error in the transport equation.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":14227,"tokens_out":20925,"duration_ms":221036,"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":[{"comment":"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.","section":"Section II, Eqs. (6)-(7)"},{"comment":"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.","section":"Section II, Eq. (5) and Section III"},{"comment":"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.","section":"Section II, after Eq. (5)"}],"minor_comments":[{"comment":"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.","section":"Fig. 1 caption"},{"comment":"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.","section":"Table I caption"},{"comment":"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}.","section":"Table I caption"}],"recommendation":"major_revision","confidential_remarks":"This is a serious phenomenological study, and the central mechanism is plausible. The main obstacle to acceptance is the lack of a derivation of the closure relations and the lack of explicit reaction densities; I would ask the author to supply these before acceptance. There is no indication of misuse of prior work; the overlap with the author's previous papers is disclosed and the extension is substantial."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Racker has a concrete, useful result: in the scotogenic model, non-resonant leptogenesis is viable with M1 as low as 1.3 TeV for a thermal initial abundance and 2.5 TeV for zero initial abundance, with benchmark points where CLFV rates are within reach of planned experiments. That is new relative to Hugle-Platscher-Schmitz [29], which quoted a ~10 TeV lower bound and did not include the inert Higgs mass effects or flavor structure in the transport equations. The paper's main technical step—tracking the inert Higgs asymmetry YDelta-eta and the spectator processes that erase it—is well motivated, and Fig. 1 makes the mechanism clear: without those processes the final baryon asymmetry drops by an order of magnitude.\n\nThe physics is plausible and the Boltzmann treatment is standard. The real soft spot is the chemical potential closure, Eqs. (6)-(7). These relations are asserted with only a pointer to [36], and they are load-bearing: they connect Y_B, the flavor asymmetries, and YDelta-eta. The paper does not show the derivation or argue that the lowest-temperature regime is valid throughout the TeV-scale leptogenesis epoch. That is a legitimate referee request. I would also like a small scan around the benchmarks to check they are not fine-tuned, and some estimate of the error from Maxwell-Boltzmann statistics and kinetic equilibrium. These are not fatal, but they are worth asking for.\n\nOn the stress-test note: the claimed elastic phi-eta -> phi-eta term is a misreading. The process in Eq. (5) is phi-bar-eta -> phi-eta-bar, which changes eta and phi number by two units each and is related to eta-eta <-> phi-phi by crossing (both from the lambda5 quartic). So the [y_eta - y_phi] structure is correct. The notation is easy to misread; that can be cleaned up.\n\nOverall, this is a solid model-building paper. The central existence claim—TeV-scale leptogenesis without quasi-degenerate neutrinos, with observable CLFV in some corners—survives scrutiny of the analysis, given the closure-relation caveat. I would send it to peer review. The referee should focus on Eqs. (6)-(7); once that is answered, the paper is ready. For anyone working on leptogenesis or the scotogenic model, this will be a useful reference.","headline":"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.","tokens_in":14738,"tokens_out":9673,"would_cite":true,"duration_ms":93187,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper argues that non-resonant leptogenesis in the scotogenic model works at TeV masses for both thermal and zero initial sterile-neutrino abundances.","keywords":["leptogenesis","scotogenic model","radiative neutrino mass","inert Higgs doublet","sterile neutrino decay","spectator processes","charged lepton flavor violation","dark matter"],"falsifier":"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 $Y_B \\simeq 8.7\\times10^{-11}$.","tokens_in":13549,"feed_emoji":"⚛️","tokens_out":18549,"duration_ms":161193,"temperature":0.7,"pith_summary":"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.","feed_headline":"Leptogenesis succeeds at 1.3 TeV in the scotogenic model","feed_subtitle":"Spectator processes suppress washouts, and predicted flavor-violating rates reach upcoming muon experiments.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the measured baryon asymmetry $Y_B \\simeq 8.7\\times10^{-11}$ that the benchmark points must reproduce.","marker":"[1]"},{"why":"Defines the scotogenic model, with radiative neutrino masses, the inert Higgs doublet, and the $Z_2$ dark matter candidate.","marker":"[23]"},{"why":"Earlier study that identified the inert Higgs mass as a washout suppressor with simplified spectator treatment and no neutrino-data fit.","marker":"[28]"},{"why":"Previous scotogenic leptogenesis scan with neutrino data that found a roughly 10 TeV lower bound, which the present benchmark points extend.","marker":"[29]"},{"why":"Gives the complex-orthogonal parametrization used to compute Yukawa couplings from neutrino masses and mixing.","marker":"[30]"},{"why":"The flavor chemical-potential analysis whose lowest-temperature regime is extended to include the inert Higgs doublet in closure relations (6)-(7).","marker":"[36]"},{"why":"Supplies the neutrino mixing angles and mass-squared differences used in the benchmark computations.","marker":"[61]"},{"why":"Provides the reaction-density and Boltzmann-equation framework used to compute rates and integrate the transport equations.","marker":"[65]"},{"why":"Supplies the analytical expressions for the charged lepton flavor violation rates quoted for the benchmark points.","marker":"[73]"},{"why":"Gives the planned experimental sensitivity to $\\mu\\to e$ conversion that makes the BP2 and BP4 parameters testable.","marker":"[71]"}],"fun_headline_variants":["TeV-scale leptogenesis works thanks to spectator processes","Scotogenic leptogenesis drops to 1.3 TeV with spectators","Spectator processes enable TeV leptogenesis in scotogenic model","Leptogenesis at TeV masses: spectator factor unlocks","New benchmarks: scotogenic leptogenesis at 1.3 TeV and beyond"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["TeV-scale leptogenesis works thanks to spectator processes","Scotogenic leptogenesis drops to 1.3 TeV with spectators","Spectator processes enable TeV leptogenesis in scotogenic model","Leptogenesis at TeV masses: spectator factor unlocks","New benchmarks: scotogenic leptogenesis at 1.3 TeV and beyond"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000163,"raw_usage":{"total_tokens":1267,"prompt_tokens":991,"completion_tokens":276,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":607,"completion_tokens_details":{"reasoning_tokens":199}},"tokens_in":607,"tokens_out":276,"duration_ms":3090,"temperature":1.0,"reasoning_tokens":199,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:28:51.967202+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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 $Y_B \\simeq 8.7\\times10^{-11}$.","supporting_citations":[{"cited_title":"Mass bounds for baryogenesis from particle decays and the inert doublet model","cited_arxiv_id":"1308.1840","evidence_quote":"Earlier study that identified the inert Higgs mass as a washout suppressor with simplified spectator treatment and no neutrino-data fit."}],"review_version":1}