{"id":"9cb6b181-ad37-4106-bd8b-ccf65bea3e3b","arxiv_id":"2608.06983","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A resonant leptogenesis framework with degenerate right-handed neutrino masses and a new TBC3 mixing ansatz is shown to fit neutrino data and reproduce the observed baryon asymmetry with m_N1 between 0.13 and 230 TeV.","lead":"This paper proposes a neutrino mass model in which two heavy right-handed neutrinos have nearly equal masses, and it shows how such a setup can produce the observed matter-antimatter asymmetry through resonant leptogenesis. It also introduces a new ansatz for the neutrino mixing matrix and claims a lightest right-handed neutrino mass between 0.13 and 230 TeV.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The BAU calculation rests on a dimensionally ambiguous splitting parameter x_Δ: Eq. (75) defines it as dimensionless, Table III labels it in GeV, and the quoted minima are ~10^6 times larger than the resonance scale in Eq. (64). The headline m_N1 range should be conditional on resolving this.","rationale":"The reader correctly identified the numerical leptogenesis section as the weakest part of the paper, but the specific load-bearing defect is sharper than 'hand-picked ranges': the reported x_Δ,min values are inconsistent, by about six orders of magnitude, with the resonance condition stated in Eq. (64), and the units of x_Δ are ambiguous between Eq. (75) and Table III. If the leptogenesis solutions are in fact valid despite being far from the conventionally resonant regime, the paper must explain why the full resummed formalism still produces sufficient CP asymmetry; if they are not, the central mass range collapses. The concrete test—an independent scan of x_Δ with the same couplings—would settle this unambiguously. I do not see a comparable internal problem in the TBC3 ansatz: its first-order predictions in Eq. (13) are consistent with the NuFIT ranges, the second-order unitarity deviation in Figure 1 is sub-1%, and the χ^2 analysis is standard. The A4 Lagrangian of Sec. V is a coherent construction, although the source of the tiny mass splitting Δ remains unspecified; that is a limitation the authors acknowledge, not an internal inconsistency. The hand-picked bounds 0.1 ≤ y_D1 ≤ 1 and 100 TeV ≤ Λ ≤ 419 TeV are admittedly phenomenological inputs, but they are explicitly stated, and the paper does not claim they are derived from the symmetry. The decisive issue is whether the BAU computation at the four extreme points is correct, which the dimensional/resonance discrepancy calls into question. Therefore the appropriate verdict is CONDITIONAL: accept the model-building framework, but require a corrected or independently reproduced leptogenesis calculation before the headline mass range is taken as established.","tokens_in":24091,"tokens_out":13781,"duration_ms":141205,"concrete_test":"Reproduce the Boltzmann calculation for Set 1 of Table III using the Yukawa matrix from Eq. (63) with the Simple (√2,1; 1,2) alignment, but scan x_Δ over a range that includes both the quoted value 2.45×10^-9 and the conventional resonance value Γ_1/(2m_N1) ≈ 3×10^-15. Compute η_B from Eqs. (66)–(68) and (76) at each x_Δ. If η_B at x_Δ = 2.45×10^-9 is not 6.1×10^-10, or if the true x_Δ,min lies orders of magnitude closer to Γ/(2m), then Table III, Eq. (77), and the resulting m_N1 range in the abstract need correction. Also state explicitly whether x_Δ in Eq. (75) is dimensionless or an energy, and recompute the mass splittings consistently with that definition.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central quantitative claim is that the Simple (√2,1; 1,2) Alignment produces the observed BAU for the four extreme points of (y_D1, Λ), and hence for the m_N1 range 0.13–230 TeV. That claim depends on the mass splittings x_Δ,min reported in Table III. Equation (75) defines m_N2 = m_N1(1 + x_Δ), so x_Δ is a dimensionless relative splitting; however, Table III and Eq. (77) quote x_Δ,min in GeV. Under the dimensionless definition, the Set 1 value x_Δ = 2.45×10^-9 gives a mass splitting m_N2 − m_N1 = 3.2×10^-7 GeV. From Eq. (65) with (Y†Y)_11 ≈ 2.3 y_D1^2/Λ^2 ≈ 1.3×10^-13, the decay width is Γ_1 ≈ 7×10^-13 GeV, so Γ_1/2 ≈ 3.5×10^-13 GeV. The quoted splitting is therefore ~10^6 times the width, not the comparable value required by the paper's own resonant condition in Eq. (64), m_Ni − m_Nj ~ Γ_Ni,j/2. The same factor of ~10^6 holds for all four rows if x_Δ is relative. If x_Δ was instead intended as an absolute mass splitting, Eq. (75) is dimensionally inconsistent, and Set 1 is still far above resonance. Because these splittings are presented as the minima needed to reach η_B = 6.1×10^-10, the numerical leptogenesis result is either operating in the non-resonant tail of the CP asymmetry or contains a normalization/unit error. The derived m_N1 window inherits this problem, since it is populated by exactly those extreme points. This is not an objection to the TBC3 ansatz or the A4 Lagrangian construction, which are internally coherent; it is a specific, checkable defect in the quantitative BAU analysis.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a framework called Resonant Sequential Dominance (RSD), applies it to a Type-I seesaw model with two nearly degenerate right-handed neutrinos, and proposes a new PMNS ansatz (TBC3) that modifies TBM mixing to accommodate the non-zero reactor angle and the JUNO measurement of sin^2(theta_12) < 1/3. Using King's Master Formula and chi^2 analyses, the authors identify a 'Simple (sqrt(2),1; 1,2) Alignment' that fits NuFIT 2025 data within 1 sigma. They construct an A4 x (Z3)^4 x (Z2)^2-symmetric Lagrangian that realizes this alignment, and numerically solve the resonant leptogenesis Boltzmann equations to claim that the observed baryon asymmetry can be produced for m_N1 in [0.13, 230] TeV.","tokens_in":24740,"tokens_out":9110,"duration_ms":78672,"significance":"If the leptogenesis calculation were correct, the paper would be of clear interest: the TBC3 ansatz is a simple alternative to TBM/TM2 that tracks current data, the RSD concept cleanly separates the light-neutrino mass hierarchy from the RH neutrino mass hierarchy, and the explicit A4 model provides a concrete starting point for UV completions. The paper's strengths include a transparent Master Formula treatment, reproducible chi^2 fits via the MPT package, and an explicit symmetry assignment with shaping symmetries. However, the headline quantitative claim (the m_N1 range) is currently not supported because it depends on hand-picked input ranges and on a mass-splitting parameter whose definition and numerical values are inconsistent.","major_comments":[{"comment":"The parameter x_Delta is defined by Eq. (75) as a dimensionless relative splitting, m_N2 = m_N1(1 + x_Delta), but Table III and Eq. (77) quote x_Delta,min in GeV. With the dimensionless reading, the Set 1 value x_Delta,min = 2.45e-9 gives a physical splitting m_N2 - m_N1 = m_N1 x_Delta ~ 3.2e-7 GeV for m_N1 = 0.13 TeV. Using the model's own Yukawa matrix in Eq. (63), one obtains (Y^dag Y)_11 ~ 0.9 y_D1^2/Lambda^2 ~ 5.2e-14 for Set 1, yielding a tree-level width Gamma_1 ~ 2.7e-13 GeV and Gamma_1/2 ~ 1.3e-13 GeV. The quoted splitting is therefore roughly 10^6 times Gamma_1/2, in plain contradiction of the resonant condition Eq. (64). If instead x_Delta is meant to be an absolute mass splitting in GeV, Eq. (75) is dimensionally wrong, and Set 1 still gives a splitting far below Gamma_1/2. The same factor of ~10^6 appears in all four rows under the dimensionless reading. Since x_Delta,min is defined as the minimum splitting needed to reach eta_B = 6.1e-10, the numerical leptogenesis results are not in the resonant regime and thus do not support the claimed resonant enhancement. Please clarify the definition, rerun the calculation with consistent units, and verify that the resonance condition is actually satisfied at the quoted splittings.","section":"Sec. VI.E, Eq. (75), Table III"},{"comment":"The headline range 0.13 TeV <= m_N1 <= 230 TeV is not a derivation from the model but a consequence of the manually chosen intervals y_D1 in [0.1, 1] and Lambda in [100, 419] TeV. The lower bound Lambda_min = 100 TeV is 'conservatively selected' and the upper bound Lambda_max = 419 TeV is fixed by requiring z_crit >= 1 with y_D1 = 0.1. These choices are reasonable but ad hoc, and the abstract's wording 'accounting for the observed baryon asymmetry ... requires the lightest right-handed neutrino mass to lie in the range ...' overstates what has been shown. The correct statement is that within the chosen parameter box the model can reproduce the observed asymmetry. This distinction should be stated prominently in the abstract and conclusions.","section":"Sec. VI.D, Eqs. (73)-(74)"},{"comment":"The mass splitting Delta that breaks the M1 = M2 degeneracy is introduced from unspecified higher-dimensional operators, even though the shaping symmetries in Sec. V are specifically designed to keep the Majorana mass matrix diagonal up to dimension five. The leptogenesis result is therefore conditional on an assumption that is not part of the explicit Lagrangian. The paper acknowledges this in the conclusion, but the leptogenesis section should clearly flag Delta as a model input rather than a prediction, and should discuss how the required size of Delta compares with the scale of the higher-dimensional operators expected in a UV completion.","section":"Sec. VI.B"}],"minor_comments":[{"comment":"The unit label [GeV] on x_Delta,min should be removed if x_Delta is dimensionless, or the definition in Eq. (75) should be changed if an absolute mass splitting is intended. The current inconsistency is confusing and should be fixed in any revision.","section":"Eq. (77) and Table III"},{"comment":"The caption reads x_Delta = 4.36e-6 GeV, while Table III and the text quote 4.31e-6 GeV. Please correct the typo.","section":"Fig. 18 caption"},{"comment":"The sentence stating that 'the values predicted by this set of Dirac neutrino mass matrix elements are all in 1 sigma agreement' is immediately qualified by the marginal theta_23 value. Please rephrase to avoid the apparent contradiction.","section":"Sec. IV.B, text near Eq. (48)"},{"comment":"The acronym TBC3 is never expanded. Even if it follows the naming convention of Ref. [11], please spell it out on first use, or state explicitly that it denotes a particular Tri-Bi-Cabibbo-like ansatz.","section":"Sec. II.C"}],"recommendation":"major_revision","confidential_remarks":"The paper's core model-building content (TBC3 ansatz, RSD framework, and the A4 Lagrangian) is internally coherent and of publishable interest. The main obstacle is the numerical leptogenesis section: the x_Delta unit inconsistency and the resulting violation of the resonance condition undermine the central quantitative claim, and the headline m_N1 range is partly an artifact of chosen input ranges. I recommend major revision rather than rejection because the issues appear fixable: the authors can clarify the definition, rerun the calculation, and reframe the claims as conditional. The paper is within the journal's scope and I do not see concerns about citation patterns or novelty disclosure beyond the self-acknowledged limitations."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe genuinely new pieces here are RSD, TBC3, and the explicit A4 x (Z3)^4 x (Z2)^2 Lagrangian. RSD makes good sense: if you want resonant leptogenesis with sequential dominance, the hierarchy has to move from Majorana masses into the Yukawas, and the paper carries that through carefully. TBC3 is a clean parametrization—setting the solar and atmospheric deviations equal and both proportional to lambda—and it fits current NuFIT data, including JUNO, reasonably well. The Master Formula search and the chi-squared scan are standard but competently done, and the Simple (sqrt 2, 1; 1, 2) alignment is a concrete, useful result. A specialist can re-derive the main steps, and the Lagrangian section is explicit about the shaping symmetries. Credit where due: the framework and ansatz are worth having.\n\nThe soft spots are in the quantitative leptogenesis part. The headline m_N1 window is not a prediction in the strong sense; it follows from choosing y_D1 in [0.1,1] and Lambda in [100,419] TeV. The ranges have motivations (perturbativity, flavon VEVs, sphaleron freeze-out), but they are choices, so \"requires\" in the abstract oversells the result. More importantly, the x_Delta variable is dimensionally ambiguous. Eq. (75) defines m_N2 = m_N1 (1 + x_Delta), so x_Delta is dimensionless, but Table III and Eq. (77) label it in GeV. If x_Delta is relative, then the absolute splitting at the smallest quoted value is several orders of magnitude larger than the decay width, far from the resonance condition in Eq. (64) unless the numerical code is doing something else. If x_Delta is absolute, Eq. (75) is wrong. This is load-bearing because the BAU plots are tuned to x_Delta,min. It may be a units typo in the text; either way, the numerical claim needs a corrected, checked version before the m_N1 range is credible. The paper also admits the small splitting has no UV origin, which is fine for a model-building exercise but should be said more plainly.\n\nOverall: the framework and ansatz deserve serious referee time. The BAU calculation needs fixing, not just polishing.","headline":"A worthwhile model-building paper with a genuinely new PMNS ansatz and RSD framework, but the headline leptogenesis mass range rests on a dimensionally inconsistent splitting parameter that must be fixed before the numerical claim is credible.","tokens_in":25300,"tokens_out":5046,"would_cite":true,"duration_ms":54768,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that the observed baryon asymmetry of the Universe can be produced by resonant leptogenesis in a Type-I seesaw model, with the lightest right-handed neutrino mass fixed to between 0.13 and 230 TeV.","keywords":["Resonant Sequential Dominance","TBC3 mixing ansatz","Type-I seesaw","resonant leptogenesis","baryon asymmetry of the Universe","A4 family symmetry","neutrino mixing","right-handed neutrino mass"],"falsifier":"A collider search that probes the $0.13\\text{--}230$ TeV window and excludes the decay signatures of the Simple ($\\sqrt2,1;1,2$) alignment would settle the central claim by falsifying the BAU mechanism. A precision measurement of $\\theta_{12}$ or $\\theta_{23}$ that moves outside the TBC3 $1\\sigma$ predictions would also undercut the ansatz and the derived Dirac texture.","tokens_in":23798,"feed_emoji":"🌌","tokens_out":9771,"duration_ms":84671,"temperature":0.7,"pith_summary":"This paper tries to show that Sequential Dominance — the idea that each column of the Dirac neutrino mass matrix primarily generates one light neutrino mass — still works when two right-handed neutrinos are nearly degenerate, a variant it calls Resonant Sequential Dominance. It introduces a PMNS matrix ansatz, TBC3, whose deviations from tri-bimaximal mixing are set equal and proportional to the Cabibbo parameter, and shows that a simple Dirac texture reproduces current neutrino oscillation data within $1\\sigma$. It then constructs an $A_4\\times(Z_3)^4\\times(Z_2)^2$-symmetric Lagrangian that realizes this texture and drives resonant leptogenesis. Solving the Boltzmann equations, it finds that matching the observed baryon asymmetry of the Universe requires the lightest right-handed neutrino mass to lie in $0.13\\text{ TeV}\\le m_{N_1}\\le230\\text{ TeV}$.","feed_headline":"0.13-230 TeV heavy neutrino seeds the universe's matter","feed_subtitle":"Resonant leptogenesis in a Type-I seesaw model matches oscillation data and produces the observed baryon asymmetry.","key_machinery":"The load-bearing structures are Resonant Sequential Dominance (RSD), the TBC3 PMNS ansatz, and the Master Formula that relates the Dirac matrix to light-neutrino observables. RSD replaces the conventional hierarchy of right-handed neutrino masses with a Yukawa hierarchy $y_{D1}<y_{D2}$ while keeping $M_1\\approx M_2$, which is what makes resonant leptogenesis available. TBC3 fixes the deviations of the solar and atmospheric angles from tri-bimaximal mixing to be equal, $s=a=-(3\\sqrt3)^{-1}\\lambda$, with the reactor deviation $r=(2/3)\\sqrt2\\,\\lambda$; this equality is what makes the low-energy fit compatible with 'simple' flavon vacuum expectation values. The Master Formula computes the ratios $Z_i$ of Dirac matrix elements and the two physical complex phases from the PMNS matrix, and the resulting Simple ($\\sqrt2,1;1,2$) Alignment supplies the Dirac texture. Resonant leptogenesis then runs through the resummed Yukawa couplings of the resonant formalism and the coupled Boltzmann equations, with the small splitting $\\Delta$ supplied by higher-dimensional operators.","core_discovery":"Within a Type-I seesaw model, the hierarchy of light neutrino masses need not come from the hierarchy of right-handed neutrino masses. In Resonant Sequential Dominance the two lightest right-handed neutrinos are nearly degenerate, $M_1\\approx M_2$, and the sequential dominance of the Dirac columns is enforced purely by Yukawa couplings, $y_{D1}<y_{D2}$, while the third neutrino is ultra-heavy. Using the Master Formula and a $\\chi^2$ fit, the paper identifies a Simple ($\\sqrt2,1;1,2$) Alignment of the Dirac matrix that places all mixing angles, the Dirac phase, and $m_2/m_3$ inside the $1\\sigma$ ranges of current oscillation data. The associated $A_4\\times(Z_3)^4\\times(Z_2)^2$ Lagrangian keeps the Majorana mass matrix diagonal up to dimension five, and a small off-diagonal splitting $\\Delta$ triggers resonant enhancement of CP violation. Numerically solving the coupled Boltzmann equations at the four corners of the allowed $(y_{D1},\\Lambda)$ space yields the observed baryon asymmetry for mass splittings $2.45\\times10^{-9}\\text{ GeV}\\le x_{\\Delta,\\min}\\le4.31\\times10^{-6}\\text{ GeV}$, which corresponds to $0.13\\text{ TeV}\\le m_{N_1}\\le230\\text{ TeV}$.","pith_inferences":["Editorial inference: the $0.13\\text{--}230$ TeV window is not a fundamental prediction; it follows from the adopted ranges $y_{D1}\\in[0.1,1]$ and $\\Lambda\\in[100,419]$ TeV, so a UV completion that fixes either constant could move the window.","The paper leaves the origin of the tiny splitting $\\Delta$ to unspecified higher-dimensional operators; if those operators also mediate lepton-flavor-violating processes, their measured rates could indirectly test RSD.","The TBC3 equality of solar and atmospheric deviations pushes $\\theta_{23}$ to the edge of its $1\\sigma$ range; a future precise value away from the TBC3 prediction would favour relaxing that equality.","Because only normal mass ordering is considered, decisive evidence for inverted ordering would remove the paper's empirical basis."],"forward_implications":["If RSD is correct, the lightest right-handed neutrino can be as light as $0.13$ TeV, putting it within reach of current and future collider searches rather than at the usual $10^9$ GeV seesaw scale.","The TBC3 ansatz offers a parameter-reduced starting point for models that must accommodate a solar angle below $1/3$ together with a nonzero reactor angle.","This setup predicts a required range of mass splittings, $2.45\\times10^{-9}\\text{ GeV}\\le x_{\\Delta,\\min}\\le4.31\\times10^{-6}\\text{ GeV}$; constraining such a tiny splitting would directly test the mechanism.","The explicit $A_4\\times(Z_3)^4\\times(Z_2)^2$ Lagrangian shows that a flavor symmetry can produce the needed texture while keeping the heavy-neutrino mass matrix diagonal up to dimension five."],"supporting_citations":[{"why":"Supplies the Master Formula and the Sequential Dominance texture construction the paper extends to degenerate masses.","marker":"[11]"},{"why":"Supplies the resonant leptogenesis conditions, resummed Yukawa couplings, and Boltzmann equations used for the BAU calculation.","marker":"[41]"},{"why":"Provides the global oscillation data (mixing angles, phases, mass splittings) that the TBC3 ansatz must fit.","marker":"[16]"},{"why":"Provides the precise 2025 solar-angle measurement that motivates replacing TBM and TM2 with TBC3.","marker":"[18]"},{"why":"Sets the sphaleron freeze-out temperature underlying the requirement $z_{\\rm crit}\\ge1$, which fixes the upper bound on $\\Lambda$.","marker":"[47]"},{"why":"Introduces leptogenesis from out-of-equilibrium heavy-neutrino decay and the one-loop function used in the CP-asymmetry calculation.","marker":"[5]"},{"why":"Gives the sphaleron conversion factor $\\eta_B=(28/79)\\eta_L$ used to turn the lepton asymmetry into the baryon asymmetry.","marker":"[48]"}],"fun_headline_variants":["Resonant leptogenesis with degenerate right-handed neutrinos","Degenerate heavy neutrinos explain baryon asymmetry","TBC3 mixing and resonant leptogenesis in Type-I seesaw","Lightest right-handed neutrino 0.13-230 TeV fits baryogenesis","Resonant sequential dominance yields observed matter excess"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The mass window is computed from hand-chosen ranges $0.1\\le y_{D1}\\le1$ and $100\\text{ TeV}\\le\\Lambda\\le419\\text{ TeV}$; unless those ranges are justified by an underlying model, the headline window has no independent standing.","fun_headline_variants_meta":{"raw":{"variants":["Resonant leptogenesis with degenerate right-handed neutrinos","Degenerate heavy neutrinos explain baryon asymmetry","TBC3 mixing and resonant leptogenesis in Type-I seesaw","Lightest right-handed neutrino 0.13-230 TeV fits baryogenesis","Resonant sequential dominance yields observed matter excess"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000797,"raw_usage":{"total_tokens":3531,"prompt_tokens":996,"completion_tokens":2535,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":612,"completion_tokens_details":{"reasoning_tokens":2451}},"tokens_in":612,"tokens_out":2535,"duration_ms":18401,"temperature":1.0,"reasoning_tokens":2451,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T17:09:17.728518+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A collider search that probes the $0.13\\text{--}230$ TeV window and excludes the decay signatures of the Simple ($\\sqrt2,1;1,2$) alignment would settle the central claim by falsifying the BAU mechanism. A precision measurement of $\\theta_{12}$ or $\\theta_{23}$ that moves outside the TBC3 $1\\sigma$ predictions would also undercut the ansatz and the derived Dirac texture.","supporting_citations":[{"cited_title":"King, Physics Letters B659, 244 (2008)","cited_arxiv_id":null,"evidence_quote":"Supplies the resonant leptogenesis conditions, resummed Yukawa couplings, and Boltzmann equations used for the BAU calculation."}],"review_version":2}