{"id":"16eee539-3f4b-40f4-abc5-2056ca220299","arxiv_id":"2610.20729","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A symmetry-based model generates the baryon asymmetry through Higgs decays involving a GeV-scale quasi-Dirac neutrino, which is accessible to upcoming experiments.","lead":"This paper shows that the observed matter-antimatter asymmetry could arise from Higgs bosons decaying in the early universe, producing a GeV-mass right-handed neutrino. The same neutrino could be detected at future experiments like SHiP and FCC-ee, offering a rare testable connection between baryogenesis and particle physics.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"No significant objection identified","rationale":"The paper's argument is logically consistent and built upon cited results. The parameter space is adequately explored, and the assumptions are clearly stated and justified. I see no reason to alter the reader's verdict of ACCEPT. The suggested concrete test is a prudent check of one approximation but not expected to change the outcome given the small x regime probed.","tokens_in":20201,"tokens_out":3794,"duration_ms":37619,"concrete_test":"Recompute the baryon asymmetry for the benchmark point of Fig. 3 using the full temperature-dependent γ(x) from Ref. [29] instead of the constant γ≈50 approximation, and verify that the final Y_B remains within the observed range (∼8.75×10^{-11}).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper presents a well-motivated model and provides a clear analysis. The central claim that Higgs-decay leptogenesis can produce the observed baryon asymmetry with GeV-scale quasi-Dirac neutrinos is supported by the calculations and parameter scans. No critical assumptions or approximations appear to invalidate the argument. The weakest assumption identified by the reader (c1=c2=1) is a model-building choice that is reasonable and acknowledged. I find no unaddressed vulnerability that would undermine the main conclusion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"The paper presents a model for low-scale leptogenesis in which a GeV-scale quasi-Dirac neutrino (two nearly degenerate right-handed neutrinos) generates the observed baryon asymmetry through thermal Higgs decays.  The model is based on a type-I seesaw with a spontaneously broken global lepton number and a discrete Z2 symmetry, so that the tiny RHN mass splitting required for resonant CP enhancement arises naturally from higher-dimensional operators.  Finite-temperature effects enable the decay H → L N before sphaleron freeze-out, and the CP asymmetry comes from the interplay between the vacuum splitting and thermal corrections.  The authors solve the relevant Boltzmann equations, show that the observed baryon asymmetry can be obtained for RHN masses 0.1–10 GeV, map the viable parameter space onto active-sterile mixing, and demonstrate that a substantial part of that space is within reach of future experiments such as SHiP, MATHUSLA and FCC-ee.  They also briefly discuss gravitational-wave signals from the annihilation of domain walls that arise from the same symmetry-breaking sector.","tokens_in":20417,"tokens_out":4282,"duration_ms":42173,"significance":"If the central claim holds, this work offers a complete, symmetry-motivated framework for testable low-scale leptogenesis.  The natural generation of the tiny mass splitting distinguishes it from ad-hoc resonant leptogenesis models, and the sub-electroweak RHN masses make the scenario directly accessible to upcoming searches for heavy neutral leptons.  The connection to gravitational-wave signatures provides an additional observational handle.  Given the experimental relevance of the GeV mass window, a demonstrated mechanism that simultaneously explains the baryon asymmetry and is within reach of SHiP etc. would constitute a significant advance.","major_comments":[{"comment":"If the formula is intended for readers to reproduce the calculation, this inconsistency needs to be corrected or explicitly explained.","section":"III, Eq. (19)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The approximation γ(x) ≃ 50 for x ≪ 1 is taken from Ref. [29].  For completeness, a brief note on the range of x for which this approximation is valid (e.g., x < 0.1) would be helpful, especially since the scan extends to M_N = 10 GeV (x ≈ 0.076 at T_sph).","section":"III, after Eq. (19)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The vertical axes of Figs. 5 and 6 are labelled as baryon asymmetry YB, but the horizontal black dashed line is described as the 'correct YB to obtain the observed BAU'.  Consider adding a label or legend entry that gives the numerical value (8.75×10^{-11}) to make the plots self-contained.","section":"V, Figs. 5 and 6","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The caption states that the red dashed line indicates ΔM_T(x_sph), but the text later refers to it as '∼2.57×10^{-12} GeV'.  It would be helpful to confirm that this value is indeed the thermal contribution and not the total splitting, and to note whether this value is typical across the parameter scan or specific to the benchmark.","section":"V, Fig. 4","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The definition of active-sterile mixing uses (m_{Dαi})^2 with dimensions of mass^2.  To avoid confusion, a brief comment that this is in the convention where the RHN seesaw formula gives |θ_{αi}|^2 = (m_{Dαi})^2 / M_N^2 would be useful.","section":"VI, Eq. (27)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The peak frequency and amplitude formulas depend on the surface tension σ ∼ √(λ_ϕ) v_ϕ^3.  The value of λ_ϕ is set to 1 for illustration; a note on how varying λ_ϕ would affect the GW signals would be welcome.","section":"VIII, Eq. (31)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abbreviation 'BAU' is introduced in the abstract but not explicitly defined again in the main text until later sections.  Please define it at first use.","section":"General","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Several footnotes contain important technical details (e.g., footnote 2 on the CP symmetry enforced by equal coefficients, footnote 5 on the absence of additional phase).  Consider moving the most essential of these into the main text or a dedicated paragraph, as footnotes are easily overlooked.","section":"General","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"minor_revision","confidential_remarks":"The paper is well-motivated and the calculations appear sound.  The main concern is the apparent discrepancy in Eq. (19), which I expect the authors can clarify or correct easily.  Once that is resolved, the manuscript is suitable for publication.  The paper does an excellent job of connecting the leptogenesis mechanism to concrete experimental prospects, and the inclusion of gravitational-wave signals adds interest without diluting the core result.  I recommend minor revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"This paper does what it says: it extends the authors' earlier symmetry-based framework for resonant leptogenesis down to the GeV scale, where the only viable channel is Higgs-decay leptogenesis. The main result—that the observed baryon asymmetry can be generated for 0.1–10 GeV quasi-Dirac neutrinos—is backed by Boltzmann-equation solutions and parameter scans. The model-building is clean: the tiny mass splitting needed for resonant enhancement arises naturally from higher-dimensional operators, not by hand. The connection to future HNL searches (SHiP, MATHUSLA, FCC-ee) is explicit and gives the paper a clear experimental hook. The brief discussion of gravitational waves from domain-wall annihilation is speculative (it depends on a large effective cutoff) but honest about that.\n\nThe soft spots are real but not load-bearing. The CP asymmetry formula (Eq. 14) and the thermal factor γ(x)≈50 are taken from Hambye & Teresi without re-derivation. That is standard for a phenomenological paper, but a reviewer may ask whether γ≈50 holds uniformly across the scanned parameter range. The equality c1=c2=1 is a model-building choice that enforces a CP symmetry; the authors note it, and any deviation would alter the mass splitting and the CP asymmetry. The GW signals depend on parameters (Λ_eff, β) that are essentially free. None of this invalidates the central argument, but a good referee will probe the robustness of the approximations.\n\nFor a specialist in low-scale leptogenesis or heavy neutral lepton phenomenology, this paper is a useful, coherent piece of work. It doesn't open up a new subfield, but it solidifies a promising one. I would accept it for peer review; it deserves a serious referee and likely publication after minor clarifications.","headline":"Solid, well-motivated extension of their earlier model to the GeV scale; the central claim that Higgs-decay leptogenesis can produce the observed baryon asymmetry is supported by the analysis, though it relies on a few approximations taken from the literature.","tokens_in":20906,"tokens_out":1593,"would_cite":false,"duration_ms":16115,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["12.60.-i","14.60.St","98.80.Cq","04.30.-w","04.30.Tv"],"model":"deepseek/deepseek-v4-flash","headline":"Observed baryon asymmetry explained by GeV-scale quasi-Dirac neutrinos in Higgs decays.","keywords":["baryogenesis","leptogenesis","right-handed neutrinos","quasi-Dirac neutrino","seesaw mechanism","Higgs decay","gravitational waves","domain walls"],"falsifier":"A non-detection of heavy neutral leptons at SHiP or FCC-ee within the predicted parameter region (MN 0.1–10 GeV, |θe|² between about 10⁻⁹ and 10⁻⁷) would cast doubt on the scenario, as would the failure to observe any stochastic gravitational-wave background from domain-wall annihilation at LISA or ET in the correlated frequency range. More directly, if the baryon asymmetry were measured to be incompatible with the predictions from the Higgs-decay CP asymmetry formula for the allowed symmetry-breaking parameters, the model would be disproved.","tokens_in":21714,"feed_emoji":"⚛️","tokens_out":4554,"duration_ms":41020,"temperature":0.7,"pith_summary":"This paper claims that the observed matter–antimatter asymmetry of the Universe can be generated by Higgs-boson decays into GeV-mass quasi-Dirac neutrinos—two nearly degenerate right-handed neutrinos that form a Dirac pair with a tiny mass splitting. The splitting arises naturally from a symmetry-breaking framework involving spontaneously broken global lepton number and a discrete Z2 symmetry, avoiding ad hoc assumptions. The mechanism works in the narrow temperature window between electroweak symmetry breaking and sphaleron freeze-out, using a CP asymmetry that is purely thermal in origin. The predicted active–sterile neutrino mixing falls within the reach of experiments like SHiP and FCC-ee, and the same symmetry-breaking sector produces gravitational waves from domain-wall annihilation, offering an independent test.","feed_headline":"Baryon asymmetry from Higgs decays of GeV-scale neutrinos","feed_subtitle":"A symmetry-based model naturally yields the tiny mass splitting for resonant leptogenesis, testable at SHiP and FCC-ee.","key_machinery":"The central objects are two quasi-degenerate right-handed neutrinos N1, N2 that constitute a quasi-Dirac fermion with mass MN ~ 0.1–10 GeV and a vacuum mass splitting ∆M0 = 2vφ²/Λ, where vφ is the vev of a scalar field that spontaneously breaks global U(1)L and Λ is the cutoff of dimension-five operators. The tiny ∆M0 is naturally generated by explicit symmetry-breaking operators and is essential for resonant enhancement of the CP asymmetry in the decay H → L N. Finite-temperature corrections add a thermal component ∆MT(x) to the splitting, and the total ∆M(x) = ∆M0 + ∆MT(x) governs the resonance condition. The CP asymmetry formula (Eq. 14) depends on the interplay of vacuum and thermal terms, while the decay width and thermal factor γ(x) ≈ 50 (for x ≪ 1) determine the efficiency. All parameters are connected to neutrino oscillation data via a specific parametrization of the Dirac mass matrix.","core_discovery":"The authors show that in a type-I seesaw model with spontaneously broken global lepton number (U(1)L) and a discrete Z2 symmetry, two right-handed neutrinos form an almost exact Dirac fermion with a tiny mass splitting generated by higher-dimensional operators. This quasi-Dirac neutrino, with mass 0.1–10 GeV, can produce the correct baryon asymmetry through out-of-equilibrium Higgs decays (H → L N) in the early Universe. The CP asymmetry arises solely from finite-temperature effects, because the required absorptive part in the loop diagram is absent at zero temperature. Successful leptogenesis occurs for vacuum mass splittings where the total splitting is dominated either by vacuum or thermal contributions, and the observed asymmetry can be reproduced for different Majorana phases. The viable parameter space for active–sterile mixing overlaps significantly with the projected sensitivities of SHiP, MATHUSLA, and FCC-ee.","pith_inferences":["The naturalness of the tiny mass splitting in this model suggests that successful leptogenesis could be tightly tied to the scale of global-symmetry breaking, potentially linking it to other beyond-Standard-Model phenomena such as axion physics or neutrino mass generation.","If future experiments like SHiP or FCC-ee observe a heavy neutral lepton in the predicted mass-mixing region, it would constitute strong evidence for the Higgs-decay leptogenesis scenario; a non-observation would push the required mass splitting to even smaller values, potentially requiring new physics to explain the degeneracy.","The model's connection to gravitational waves offers a unique multi-messenger probe: observing a stochastic GW background from domain walls at LISA would correlate with the baryogenesis mechanism, providing a cross-check independent of collider searches.","The tension between viable leptogenesis and Majoron dark matter hints that if a cosmologically stable Majoron were discovered, it would disfavor the parameter space where Higgs-decay leptogenesis alone explains the baryon asymmetry, possibly requiring additional ingredients."],"forward_implications":["If correct, the model predicts that heavy neutral leptons with masses 0.1–10 GeV and active–sterile mixing |θe|² in the range 10⁻⁹ to 10⁻⁷ should be detectable at SHiP, MATHUSLA, and FCC-ee.","The same symmetry-breaking sector that generates the neutrino mass splitting also produces domain walls that annihilate, emitting a stochastic gravitational-wave background detectable by LISA, ET, or DECIGO for suitable parameter choices.","The Majoron arising from U(1)L breaking cannot constitute stable dark matter in the parameter region of successful leptogenesis, but it can affect the effective number of relativistic species Neff, providing a distinct cosmological signature.","The Higgs-decay leptogenesis mechanism dominates over the ARS oscillation mechanism in the regime T_osc < T_sph, which corresponds to the smallest vacuum mass splittings, marking a clear parameter-space distinction."],"supporting_citations":[{"why":"Establishes the symmetry-based framework (U(1)L and Z2) that naturally produces the quasi-degenerate RHN spectrum and small mass splitting.","marker":"[27]"},{"why":"Proposes the Higgs-decay leptogenesis mechanism and derives the CP asymmetry formula used in this work.","marker":"[29]"},{"why":"Provides further details on Higgs-decay leptogenesis, including thermal effects and the Boltzmann equations.","marker":"[30]"},{"why":"Justifies the assumption of identical coefficients for Φ and Φ* in the higher-dimensional operators to enforce the CP symmetry Φ → Φ*.","marker":"[45]"},{"why":"Supplies the sphaleron freeze-out temperature (Tsph ≃ 131.7 GeV) that defines the relevant temperature window for baryon asymmetry conversion.","marker":"[28]"},{"why":"Provides the computation of thermal loop contributions and the temperature-dependent decay width, essential for the thermal CP asymmetry.","marker":"[52]"},{"why":"Describes gravitational-wave production from domain-wall annihilation, used to connect the symmetry-breaking sector to observable GW signals.","marker":"[31]"}],"fun_headline_variants":["GeV-scale quasi-Dirac neutrinos from Higgs decays explain baryon asymmetry","Thermal Higgs decays of quasi-Dirac neutrinos generate matter asymmetry","Finite-temperature CP violation in GeV-scale neutrino decays","Leptogenesis via quasi-Dirac neutrinos testable at SHiP and FCC-ee","Baryogenesis from nearly-Dirac neutrinos in the early Universe"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The model assumes equal coefficients c1 = c2 = 1 for the two dimension-five operators in Eq. (3), which enforces a CP symmetry under the transformation Φ → Φ*; any deviation would alter the mass splitting and introduce additional CP-violating phases, potentially invalidating the resonant enhancement and the predicted baryon asymmetry.","fun_headline_variants_meta":{"raw":{"variants":["GeV-scale quasi-Dirac neutrinos from Higgs decays explain baryon asymmetry","Thermal Higgs decays of quasi-Dirac neutrinos generate matter asymmetry","Finite-temperature CP violation in GeV-scale neutrino decays","Leptogenesis via quasi-Dirac neutrinos testable at SHiP and FCC-ee","Baryogenesis from nearly-Dirac neutrinos in the early Universe"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.000195,"raw_usage":{"cost":0.00019512948,"is_byok":false,"cost_details":{"upstream_inference_cost":0.00019512948,"upstream_inference_prompt_cost":4.260312e-05,"upstream_inference_completions_cost":0.00015252636},"total_tokens":2645,"prompt_tokens":948,"completion_tokens":1697,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":0,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":1596}},"tokens_in":948,"tokens_out":1697,"cost_source":"openrouter_usage","duration_ms":15457,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":1596,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-16T18:03:11.863706+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"A non-detection of heavy neutral leptons at SHiP or FCC-ee within the predicted parameter region (MN 0.1–10 GeV, |θe|² between about 10⁻⁹ and 10⁻⁷) would cast doubt on the scenario, as would the failure to observe any stochastic gravitational-wave background from domain-wall annihilation at LISA or ET in the correlated frequency range. More directly, if the baryon asymmetry were measured to be incompatible with the predictions from the Higgs-decay CP asymmetry formula for the allowed symmetry-breaking parameters, the model would be disproved.","supporting_citations":[{"cited_title":"Leptogenesis with Majoron Dark Matter","cited_arxiv_id":"2412.14121","evidence_quote":"Establishes the symmetry-based framework (U(1)L and Z2) that naturally produces the quasi-degenerate RHN spectrum and small mass splitting."},{"cited_title":"Higgs doublet decay as the origin of the baryon asymmetry","cited_arxiv_id":"1606.00017","evidence_quote":"Proposes the Higgs-decay leptogenesis mechanism and derives the CP asymmetry formula used in this work."},{"cited_title":"Baryogenesis from L-violating Higgs-doublet decay in the density-matrix formalism","cited_arxiv_id":"1705.00016","evidence_quote":"Provides further details on Higgs-decay leptogenesis, including thermal effects and the Boltzmann equations."},{"cited_title":"A cancellation mechanism for dark matter-nucleon interaction","cited_arxiv_id":"1708.02253","evidence_quote":"Justifies the assumption of identical coefficients for Φ and Φ* in the higher-dimensional operators to enforce the CP symmetry Φ → Φ*."},{"cited_title":"The Sphaleron Rate in the Minimal Standard Model","cited_arxiv_id":"1404.3565","evidence_quote":"Supplies the sphaleron freeze-out temperature (Tsph ≃ 131.7 GeV) that defines the relevant temperature window for baryon asymmetry conversion."},{"cited_title":"Systematic approach to thermal leptogenesis","cited_arxiv_id":"1211.2140","evidence_quote":"Provides the computation of thermal loop contributions and the temperature-dependent decay width, essential for the thermal CP asymmetry."},{"cited_title":"A review of gravitational waves from cosmic domain walls","cited_arxiv_id":"1703.02576","evidence_quote":"Describes gravitational-wave production from domain-wall annihilation, used to connect the symmetry-breaking sector to observable GW signals."}],"review_version":1}