{"id":"f593811b-0f05-4200-a72c-086b5f5a1dd6","arxiv_id":"2501.11529","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"In the majoron+triplet model, scatterings of neutrinos with the new particles can suppress the leptogenesis efficiency by up to a factor of about six, making a full coupled Boltzmann treatment necessary.","lead":"This paper studies how the presence of a new fermion triplet and the majoron boson changes the way the universe's matter-antimatter asymmetry can be generated from neutrino decays. It finds that for many parameter choices, one must track the abundances of all the new particles together rather than just the neutrinos, because particle scatterings can suppress or delay the asymmetry generation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The IA/IA boundary in case Bz is defined by an arbitrary criterion (z_N^eq = 1) and may not robustly separate initial-condition-dependent regimes, undercutting the headline factor-of-six claim.","rationale":"The reader focused on the pre-z_I initial-condition assumption, which is a valid caveat about unknown cosmology. However, that is an external assumption and not the most load-bearing weak point for the internal claim. The paper's own text reveals that the IA/IA boundary is defined by an explicitly acknowledged arbitrary convention. This convention directly sets the region where initial abundances are said to matter, which is central to the claimed dependence on coupled Boltzmann equations in case Bz. The abstract's emphasis on 'large parts of parameter space' and the factor-of-six misestimation is anchored in this region. If changing the boundary criterion changes the conclusion, the central claim is not robust. This is a concrete, checkable issue that can be settled by re-running the numerically stated criterion. It does not require rejecting the paper, but it means the headline claim should be presented with a caveat about this boundary sensitivity. Therefore the reader's CONDITIONAL verdict remains appropriate, without escalating to REJECT.","tokens_in":53258,"tokens_out":1538,"duration_ms":20238,"concrete_test":"Recompute the case Bz results with the IA boundary defined by z_N^eq = 2 instead of z_N^eq = 1, and trace how the boundary curve (\\tilde{m}_{IA}, g_N^{IA}) and the region where |\\eta_z^B/\\eta_t^B| significantly deviates from 1 change. If the IA region shrinks or grows substantially (e.g., by more than ~30% in area) or if the qualitative statement that the simplified treatment misestimates the efficiency by up to a factor of ~6 changes, then the paper's central claim is not robust to the arbitrary definition of the IA/IA boundary.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that coupled Boltzmann equations are essential in large parts of parameter space relies heavily on the case Bz analysis, where the efficiency can change sign and depends on initial abundances (Sec. 4.4.3). The paper defines the IA (initial-abundance sensitive) / IA (initial-abundance insensitive) boundary in Sec. 4.4.3.1 via Eq. (4.28): z_N^eq(\\tilde{m}_{IA}, g_N^{IA}) = 1, where z_N^eq is the value of z_N at which Y_{N B}^z first reaches thermal abundance. The text explicitly states: \"There is no fundamental reason to explicitly choose z_N^eq(...) = 1\" and that the choice \"is irrelevant as long as it is close to 1\" (Sec. 4.4.3.1). This is a load-bearing assumption because the existence and location of the IA region, including the negative-efficiency triangular region in Fig. 4.2, is what distinguishes case Bz from case Bt and drives the conclusion that initial abundances can matter. If a different but equally reasonable criterion (e.g., z_N^eq = 2 or a threshold on |\\eta_z^B/\\eta_t^B|) were used, the size of the IA region could shift, potentially altering which parts of the g_N-\\tilde{m} plane are deemed initial-condition-dependent. The claim that the efficiency is strongly affected by coupled dynamics and that simplified treatments misestimate it by up to a factor ~6 may therefore be sensitive to this arbitrary partition of parameter space, rather than being a robust feature of the dynamics.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies leptogenesis in a singlet-majoron model extended by a Z2-odd right-handed SU(2)L triplet fermion. It derives the full set of coupled Boltzmann equations for the heavy neutrino N, the CP-even scalar σ, the majoron J, and the triplet T, including on-shell subtraction of σ-mediated scatterings. The equations are solved numerically for four parameter cases (full dynamics with gT=1 or gT=10^-7, and a simplified scenario where σ, J, T are pinned to equilibrium), with either thermal or vanishing initial abundances at the spontaneous-symmetry-breaking scale. The central finding is that the simplified neutrino-only treatment can misestimate the final efficiency by up to about a factor of six in parts of the scanned (gN, m-tilde) plane, and that initial abundances of the new fields matter only in a restricted 'IA' region of the small-gT scenario. The paper also derives the modified sphaleron conversion relation in this model, computes the CP violation required to match the observed baryon asymmetry, and discusses dark-matter constraints on the majoron and triplet.","tokens_in":53563,"tokens_out":8112,"duration_ms":91157,"significance":"If the numerical results are sound, the paper provides a concrete, fairly comprehensive demonstration that in a well-motivated majoron+triplet extension of type-I seesaw, the non-equilibrium dynamics of σ, J, and T can substantially change the efficiency of leptogenesis relative to the usual one-species treatment. The Boltzmann equations are written out explicitly, the on-shell subtraction is discussed, and several analytic approximations (e.g., Eqs. (4.15) and (4.25)) give physical insight that goes beyond a black-box numerical scan. The paper also quantifies the change in the sphaleron conversion factor and connects the analysis to dark-matter and baryon-asymmetry constraints. The author is explicit about the main assumptions (neglect of λmix, flavor effects, pre-existing asymmetries) and about the origin of the sphaleron relation [25]. Overall, this is a useful contribution to leptogenesis model-building, provided the normalization and robustness issues identified below are resolved.","major_comments":[{"comment":"The efficiency normalization Y_N^0 is defined as Y_N(z→∞) in Eq. (3.8). For a decaying heavy neutrino, the asymptotic abundance is negligible and is not the standard normalization in leptogenesis, where Y_N^0 is normally the ultra-relativistic equilibrium abundance (or the initial abundance at z→0). Taken literally, the source term in Eq. (3.9) proportional to 1/Y_N^0 would be singular in a physically irrelevant limit. Since all reported absolute values of η in Figs. 4.1, 4.2, and the derived CP-violation requirements in Sec. 6 depend on this normalization, the definition must be corrected (e.g., to Y_N^eq(z→0) or Y_N(z_I)) and the numerical implementation must be checked to use a consistent constant normalization. If the intended quantity is indeed Y_N^eq(z→∞) in some limiting sense, that limit should be stated precisely.","section":"Sec. 3.2, Eqs. (3.8)–(3.9)"},{"comment":"The IA/IA boundary is defined by the explicit criterion z_N^eq(m-tilde^IA, g_N^IA)=1, and the text admits that there is no fundamental reason for this choice, arguing that the exact value is irrelevant because the thermalization transition is rapid. Since this boundary determines the location and extent of the region in which initial abundances are claimed to be relevant (including the negative-efficiency triangle in Fig. 4.2 and the discussion in Sec. 4.4.3.2), the paper should substantiate the claimed insensitivity with a concrete robustness check. For example, show how the IA/IA boundary and the |η_z^B/η_t^B| contours change when the criterion is varied to z_N^eq=2 and z_N^eq=0.5. This would also make clear whether the boundary is best thought of as a sharp transition or as a convenient contour.","section":"Sec. 4.4.3.1, Eq. (4.28), and Fig. 4.19"}],"minor_comments":[{"comment":"The two regimes labeled 'WO' and 'WO' (with and without washout) are typographically indistinguishable in the typeset text and figure labels; the overline or other diacritic is lost. Please use distinct unambiguous labels, e.g., 'WO' and 'no-WO', and define them in the caption.","section":"Sec. 4.2.3 and Figs. 4.12, 4.16"},{"comment":"The text says the efficiency is split into an 'IA (initial abundance) regime' and an 'IA regime' where initial abundances have no effect; both labels appear identical in the plain text. This makes the central dichotomy hard to follow. Please introduce distinct names (e.g., 'IA-sensitive' and 'IA-insensitive') and use them consistently.","section":"Sec. 4.1 and Fig. 4.4"},{"comment":"The notation (g_N^IA, m-tilde^IA) suggests a single point, but Eq. (4.28) defines a one-dimensional curve in the (g_N, m-tilde) plane. Please clarify that the pair denotes the boundary curve (e.g., by writing z_N^eq(m-tilde, g_N)=1 for the boundary) and that g_N^IA and m-tilde^IA refer to representative values along it, as used in Fig. 4.20.","section":"Sec. 4.4.3.1, Eq. (4.28)"},{"comment":"The factors 3×76/679 and 28/79 are correct only if the initial hypercharge and charge constraints are imposed as in [25]; the sign conventions for Y_L and Y_{B-L} should be stated explicitly so that the 'apart from the different signs' remark is unambiguous. A one-sentence derivation of the factor 3 would help the reader.","section":"Sec. 6.1, Eq. (6.10)"},{"comment":"The abstract states that solving the coupled Boltzmann equations is essential 'for large parts of the considered parameter space,' but Fig. 4.3 shows that the ratio η_hat/η is close to unity over a sizable fraction of the scanned plane, with the largest deviations (factor ~6) concentrated near g_N~0.7 and small m-tilde. Consider softening the wording or adding a quantitative statement about the region where the difference exceeds, say, a factor of two.","section":"Abstract and Sec. 4.1"},{"comment":"The manuscript contains numerous typographical and grammatical errors (e.g., 'condtions', 'seperate', 'dicuss', 'substraction', 'squablack' in App. A.3, 'inital', 'indentical'). A careful proofreading pass is needed before publication.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The referee's concern about the Y_N^0 definition is the most consequential issue; if it is a typo and the numerical code uses the standard relativistic equilibrium normalization, then the paper's quantitative results are unaffected, but the manuscript as written is inconsistent in a load-bearing equation. The IA/IA robustness request is secondary but directly addresses the skeptic's worry about the arbitrary boundary. The paper's central claim about coupled Boltzmann equations is supported by cases A and Bt as well as Bz, so it does not stand or fall on the exact IA boundary. I would encourage the editor to ask for the robustness check as part of the revision, since it is cheap to perform and would materially strengthen the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Punchline: the paper delivers what it advertises. It is the first coupled Boltzmann treatment of leptogenesis in the majoron+triplet model, and the central claim — that freezing σ, J, T at thermal equilibrium can misestimate the efficiency by up to a factor of about six — is supported by the numerics and by a physically sensible mechanism (scatterings suppress decays until z_S, and the ρ-term keeps neutrinos displaced from equilibrium). The factor-of-six number comes from the A and B_t cases, where initial abundances are irrelevant. The stress-test worry about the arbitrary IA/IA boundary therefore does not land on the headline claim; that boundary only labels where initial conditions matter in case B_z, and the negative-efficiency triangle there is a directly computed result, not an artifact of the criterion.\n\nWhat is good: the four-case scan is systematic; the on-shell subtraction for σ exchange is shown explicitly in App. A.4; the semi-analytic reductions in Sec. 4.2.3 make the numerics legible; the dark-matter and baryon-asymmetry sections are honest about what is excluded (case A, cold majoron DM) and what needs help (the DI bound is exceeded by an order of magnitude; resonances or weaker hierarchy could fix it). The sphaleron relation Y_B = (76/679)Y_{B+3L} is taken from the author's own published work and is cited; that is normal practice.\n\nSoft spots, in order of severity:\n\n1. The normalization Y_N^0 ≡ Y_N(z → ∞) in Eq. (3.8) is non-standard and, taken literally, ill-defined when N decays away. The strong-washout efficiencies match VL, so a different normalization was presumably used in practice. This must be clarified before the absolute η values and the required-ε numbers in Sec. 6 can be trusted; the ratios between cases likely survive.\n\n2. The B_z results assume thermal or vanishing abundances at z_I and no pre-existing asymmetry. Fine for the main comparison, structurally limiting for the initial-condition-dependence claim. The paper states it openly.\n\n3. Reproducibility: no code or data, and the appendix has garbled spots (Eq. A.34, 'squablack'). A determined reader can reconstruct, but it costs real time.\n\n4. Typos everywhere ('seperates', 'condtions', a caption comparing B to B where A is meant). Cosmetic, but they fuel referee frustration.\n\nWho this is for: leptogenesis model-builders, especially those extending seesaw models with scalars or triplets. It deserves a serious referee — conditional acceptance after the normalization question is addressed, not a desk reject.","headline":"First coupled-Boltzmann treatment of leptogenesis in the majoron+triplet model; the factor-of-six claim holds up, but the Y_N^0 normalization is sloppy and must be fixed before absolute numbers are trusted.","tokens_in":54111,"tokens_out":9390,"would_cite":true,"duration_ms":100962,"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":"Leptogenesis in the majoron+triplet model is controlled by the coupled out-of-equilibrium evolution of the neutrino, the scalar, the majoron, and the triplet, and neutrino-only Boltzmann equations can misestimate the efficiency by up to a…","keywords":["leptogenesis","majoron","triplet fermion","coupled Boltzmann equations","lepton asymmetry","baryon asymmetry","dark matter","seesaw mechanism"],"falsifier":"Re-run the numerical solution of the Boltzmann equations at $g_N \\approx 0.7$ and $\\tilde m \\approx 10^{-3}$ eV with $\\delta_\\sigma=\\delta_J=\\delta_T\\equiv 1$, keeping all scattering terms in $\\gamma_S$; the paper predicts this simplified efficiency is roughly six times smaller than the full coupled result, so agreement within a few percent would refute the central claim. Independently, at $g_N = 0.1$ and $\\tilde m = 5\\times 10^{-5}$ eV with all initial abundances zero, the paper predicts a negative final efficiency in case $B_z$; a positive sign there would also falsify it.","tokens_in":53010,"feed_emoji":"⚛️","tokens_out":13939,"duration_ms":132725,"temperature":0.7,"pith_summary":"The paper sets out to show that leptogenesis in the majoron+triplet model cannot be reduced to a single Boltzmann equation for the heavy neutrinos. The model adds a CP-even scalar $\\sigma$, the majoron $J$ (a Goldstone boson from broken lepton number), and a fermion triplet $T$ under the weak gauge group; all three scatter with neutrinos and can themselves leave thermal equilibrium. The final lepton asymmetry is therefore shaped by the coupled evolution of all four species. Solving only the neutrino equation, with the other species held in equilibrium, underestimates the efficiency by up to a factor of about six in the scanned parameter space. If correct, this means simplified one-species treatments can misjudge whether this class of seesaw extensions produces the observed baryon asymmetry.","feed_headline":"Leptogenesis efficiency swings sixfold when all new particles evolve","feed_subtitle":"Ignoring the majoron, scalar, and triplet's out-of-equilibrium evolution can misestimate the asymmetry up to sixfold.","key_machinery":"The load-bearing element is the coupled system of Boltzmann equations (3.12)–(3.15) for the abundances $Y_N$, $Y_T$, $Y_\\sigma$, and $Y_J$, together with the efficiency equation (3.9). The summed scattering rate $\\gamma_S$ collects the processes that change the neutrino abundance, and the $\\rho$ term encodes how deviations of $\\sigma$, $J$, and $T$ from thermal equilibrium feed back into neutrino production. The named diagnostic is the efficiency factor $\\eta$, defined through $Y_L = \\varepsilon Y_N^0 \\eta$, whose final value $\\eta(z_N\\to\\infty)$ is the quantity compared across scenarios. Cases $\\hat{A}$ and $\\hat{B}$ impose $\\delta_T=\\delta_\\sigma=\\delta_J=1$, reducing the system to a single neutrino equation; cases A and B solve the full system for $g_T=1$ and $g_T=10^{-7}$, respectively. The contrast between these two levels of treatment is what exposes the sixfold effect.","core_discovery":"The central claim is that the new particles in the majoron+triplet model do not merely rescale the vanilla leptogenesis efficiency; they change how the heavy neutrino $N$ is populated and depleted. Scattering processes involving $\\sigma$, $J$, and $T$ keep $N$ near thermal equilibrium early on and push its decays to later times, and in the simplified treatment with $\\delta_T=\\delta_\\sigma=\\delta_J=1$ this suppresses the efficiency. In the full coupled system the deviations of $\\sigma$, $J$, and $T$ from equilibrium feed back into the neutrino abundance, producing a larger efficiency in cases A and B. The author further finds that the initial abundances of the new fields are irrelevant in most of parameter space but matter in a narrow region of small $g_N$ and small effective neutrino mass with vanishing initial abundances, where the final efficiency can be negative. The paper also derives a modified sphaleron conversion relation for the model and uses dark matter bounds to exclude the large-triplet-coupling case, leaving only the small-coupling case B as cosmologically viable.","pith_inferences":["The sixfold sensitivity to spectator dynamics probably extends beyond this specific model: any leptogenesis setup in which additional fields scatter strongly with heavy neutrinos should be checked with the full coupled system, not just the neutrino equation.","Including flavour effects or resonant CP enhancement, which the paper leaves out, could move the boundary of the negative-efficiency region; computing the same cases in a flavour-basis Boltzmann treatment would test how robust the initial-abundance dependence is.","The paper's division of parameter space by $z_N^{\\mathrm{eq}} = 1$ could serve as a practical diagnostic for when initial abundances matter in other multi-species leptogenesis models."],"forward_implications":["For large parts of the $g_N$\\u2013$\\tilde m$ plane, efficiencies from neutrino-only Boltzmann equations are not reliable; quantitative leptogenesis predictions in this model require the coupled system.","In the strong-washout limit, $\\tilde m\\to 10^{-1}$ eV, inverse neutrino decays dominate and the efficiencies converge to the vanilla-leptogenesis values, so the simplification is safe there.","In the small $g_N$ and small $\\tilde m$ region with zero initial abundances, the sign of the final lepton asymmetry is not fixed: the model permits a negative efficiency, which would translate into the wrong sign of the baryon asymmetry.","Dark matter bounds force the triplet Yukawa coupling below about $2.9\\times 10^{-7}$, excluding the large-coupling case A and leaving case B, where the triplet barely affects the efficiency, as the viable version.","The triplet changes the sphaleron conversion from $Y_B = (28/79)Y_{B-L}$ to $Y_B = (76/679)Y_{B+3L}$; the numerical factor is similar, but the conserved combination is different."],"supporting_citations":[{"why":"Supplies the vanilla-leptogenesis Boltzmann equations, efficiency parameterization, and washout behaviour that the majoron+triplet results are compared against.","marker":"[39]"},{"why":"Provides the reaction-density formalism $sHz\\,dY/dz$ used to write all coupled Boltzmann equations.","marker":"[42]"},{"why":"Supplies the gauge-interaction rates that keep the triplet thermal, a central input distinguishing case A from case B.","marker":"[33]"},{"why":"Gives the $[SU(2)_L]^2\\times U(1)_{L'}$ anomaly factor and the sphaleron conversion relation used to turn the lepton asymmetry into a baryon asymmetry.","marker":"[25]"},{"why":"Davidson–Ibarra bound used to determine whether the CP violation required to match the observed baryon asymmetry is achievable.","marker":"[29]"},{"why":"Defines the efficiency factor $\\eta$ in $Y_L = \\varepsilon Y_N^0 \\eta$, the quantity whose evolution is computed throughout.","marker":"[31]"},{"why":"Defines the effective neutrino mass $\\tilde m$, the central parameter scanned in all cases.","marker":"[26]"}],"fun_headline_variants":["Coupled evolution of new particles reshapes leptogenesis","Ignoring new particles skews leptogenesis by sixfold","Coupled Boltzmann equations crucial for leptogenesis","New fields force coupled evolution for accurate leptogenesis","Majoron-triplet leptogenesis hinges on coupled equations"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that at the symmetry-breaking scale the new fields start either exactly thermal or exactly absent, with zero pre-existing lepton asymmetry; if the earlier universe left different abundances or an asymmetry, the final efficiency, especially its sign in the small-parameter region, could change.","fun_headline_variants_meta":{"raw":{"variants":["Coupled evolution of new particles reshapes leptogenesis","Ignoring new particles skews leptogenesis by sixfold","Coupled Boltzmann equations crucial for leptogenesis","New fields force coupled evolution for accurate leptogenesis","Majoron-triplet leptogenesis hinges on coupled equations"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000487,"raw_usage":{"total_tokens":2348,"prompt_tokens":843,"completion_tokens":1505,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":459,"completion_tokens_details":{"reasoning_tokens":1441}},"tokens_in":459,"tokens_out":1505,"duration_ms":11036,"temperature":1.0,"reasoning_tokens":1441,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T18:09:42.530798+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the numerical solution of the Boltzmann equations at $g_N \\approx 0.7$ and $\\tilde m \\approx 10^{-3}$ eV with $\\delta_\\sigma=\\delta_J=\\delta_T\\equiv 1$, keeping all scattering terms in $\\gamma_S$; the paper predicts this simplified efficiency is roughly six times smaller than the full coupled result, so agreement within a few percent would refute the central claim. Independently, at $g_N = 0.1$ and $\\tilde m = 5\\times 10^{-5}$ eV with all initial abundances zero, the paper predicts a negative final efficiency in case $B_z$; a positive sign there would also falsify it.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the effective neutrino mass $\\tilde m$, the central parameter scanned in all cases."},{"cited_title":"Medeiros V arzielas, I","cited_arxiv_id":null,"evidence_quote":"Supplies the vanilla-leptogenesis Boltzmann equations, efficiency parameterization, and washout behaviour that the majoron+triplet results are compared against."},{"cited_title":"In: New J","cited_arxiv_id":null,"evidence_quote":"Supplies the gauge-interaction rates that keep the triplet thermal, a central input distinguishing case A from case B."},{"cited_title":"In: Phys","cited_arxiv_id":null,"evidence_quote":"Gives the $[SU(2)_L]^2\\times U(1)_{L'}$ anomaly factor and the sphaleron conversion relation used to turn the lepton asymmetry into a baryon asymmetry."}],"review_version":1}