{"id":"a3cd9e4d-51b7-4596-8a27-0e97d48913ee","arxiv_id":"2608.11522","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Seesaw Majoron models imply parameter-free correlations among Higgs, muon decay, and neutrino observables that can identify the neutrino mass mechanism.","lead":"This paper builds effective field theories for the three standard Seesaw mechanisms plus a spontaneously broken lepton number symmetry whose Goldstone boson is the Majoron. The low-energy models predict testable relations between Higgs decays, lepton flavor violation, and the lepton-number breaking scale, offering a way to identify the origin of neutrino masses even if the heavy states are never produced.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Tree-level matching is the load-bearing assumption: one-loop effects can populate the absent operators that carry the identifying power.","rationale":"The reader's weakest_assumption isolates the same load-bearing point: the EFT construction and all claims of predictive correlation rest on tree-level matching. The paper itself acknowledges in Sec. 5 that one loop would generate the absent operators, which directly affects the identification power claimed in Table 5 and in the phenomenological analysis. The operator-by-operator agreement of the two matching orders is a genuine internal consistency check and strengthens the tree-level result, but it does not control loop corrections or operator running. I therefore agree with the reader's conditional verdict: the central idea is substantial and well presented, but the tree-level truncation should be made explicit as a leading-order caveat, and the abstract's universal phrasing should be read with the Type I/III restrictions of Sec. 4 in mind. No stronger concern, such as an internal inconsistency or a sign error in the central relations, was identified.","tokens_in":56622,"tokens_out":15249,"duration_ms":187036,"concrete_test":"Compute the one-loop matching correction to the Type II JSMEFT at the scale MΔ, keeping the derivative Majoron coupling of Eq. (2.49) and the triplet Yukawa YΔ, and extract the dimension-7 Wilson coefficient of Q_JHL defined in Eq. (3.7). If this coefficient is nonzero at one loop, the absence of Q_JHL in Table 5 is a tree-level artifact and the Type I/III-vs-Type-II discriminator weakens. In the same calculation, report the one-loop shifts of C_H□ and C_JH to test whether Eq. (4.2) survives beyond leading order.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central discriminators—Q_JHL absent in Type II, J→γγ absent in Types I and II, and the parameter-free locks C_JHL = C_U/(2vφ) and Eq. (4.5)—are all derived at tree level. Section 5 explicitly concedes that 'going to one loop would generate the operators that are absent here.' This is not a cosmetic caveat: the strongest_claim is that a single vev fixes every Majoron coupling and therefore observables form a testable web of relations. That claim requires either that the zero entries remain zero or that loop-generated entries are negligible. In Type II, for example, Q_JHL is absent at tree level because the scalar triplet propagator has no γ5 structure, but at one loop a fermion triangle with the derivative Majoron coupling of Eq. (2.49) can produce the same dimension-7 operator; its coefficient will be nonzero unless a symmetry forbids it, and no such symmetry is identified. Likewise, one-loop corrections to C_H□ and C_JH from heavy HNL loops need not preserve Eq. (4.2), so the Higgs-invisible-width relation and the derived vφ bound are leading-order statements. The paper does not quantify the size of these corrections or include running between M_N, mρ, and the weak scale. For a framework whose central selling point is falsifiability through correlations, the uncontrolled tree-level truncation is the least secure condition for the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper constructs effective field theories for Type I, II, and III seesaw models extended by a complex scalar whose global U(1) charge is identified with lepton number, so that spontaneous symmetry breaking produces a Majoron. For each model the authors integrate out the radial mode and the seesaw mediator in both possible orders, obtaining seven intermediate EFTs and three low-energy JSMEFT Lagrangians, and they report agreement operator by operator. The main physics claim is that a single vacuum expectation value vφ fixes the mediator mass, the radial-mode mass and couplings, and every Majoron coupling, so that observables are predicted as correlations rather than as individual rates. The paper derives parameter-free relations such as Γ(h→JJ) = (1−κV)m_h³/(32πvφ²), a lepton-sector lock C_{JHL} = C_U/(2vφ), and a J→γγ coupling in Type III only, and uses these to translate bounds on the invisible Higgs width and on µ→eJ into independent lower bounds vφ ≳ O(1–10) TeV. It also argues that neutrinoless double beta decay with Majoron emission has no sensitivity in any of these models.","tokens_in":56881,"tokens_out":4100,"duration_ms":51710,"significance":"If the tree-level results are representative, this is a valuable systematic contribution: it provides a unified operator dictionary for Majoron seesaw models, a nontrivial cross-check of matching order independence, compact resummations such as Eqs. (2.25) and (2.64), and falsifiable correlations that go beyond generic ALP/EFT analyses. The negative statement about 0νββ with Majoron emission is a useful reallocation of experimental attention, and the two independent lower bounds on vφ from Higgs and muon data are concrete and testable. The paper is also unusually candid about its own limitations, which makes the assessment easier. The main significance, however, is conditional: the identifying power rests on the pattern of present and absent operators at tree level, and the manuscript explicitly concedes that one-loop effects generate the absent operators, so the central falsifiability claim needs either a loop-level control or a substantial reframing.","major_comments":[{"comment":"The central discriminators are based on operator absences and coefficient equalities that are derived at tree level, yet §5 concedes that 'going to one loop would generate the operators that are absent here.' In particular, Q_{JHL} is absent in Type II at tree level, J→γγ is absent in Types I and II, and the locks C_{JHL}=C_U/(2vφ) (Eq. (3.3)/(3.6)) and Γ(h→JJ)=(1−κV)m_h³/(32πvφ²) (Eq. (4.5)) are tree-level statements. Because no estimate is given of the size of the one-loop coefficients or of the running between M_N, m_ρ, and the weak scale, the claim that the framework is falsifiable through the pattern of presences and absences is not yet supported. The authors should either perform or estimate the one-loop matching, or explicitly restrict all falsifiability claims to a leading-order regime and explain why the missing entries remain numerically negligible there.","section":"§5 and Tab. 5"},{"comment":"The abstract and introduction claim that a single vev fixes the mediator mass in all three seesaw realizations, but this is not true for the Type II bare-mass regime: in §2.3.3, M_Δ=µ_3 with µ_3 > v_φ, and the triplet mass is explicitly independent of lepton-number breaking. The body of the paper is careful in places (e.g., §4 refers to 'the β_2 part of M_Δ²'), but the unqualified abstract statement overgeneralizes and, more importantly, the 'relations among observables' claim for Type II in that regime has a different parameter dependence. The wording should be corrected so that the central correlation claims are stated only where the single-scale logic actually applies.","section":"Abstract, §1, and §2.3.3"},{"comment":"The paper asserts that it provides the 'complete set of effective operators up to dimension 7' and uses Tab. 5 as the basis for discriminating between seesaw types, but no proof or independent enumeration of the JSMEFT operator basis is given. Reference to existing νSMEFT bases is partial, and no Hilbert-series or equivalent completeness argument appears. Since the absence of an operator is load-bearing for the identification power, completeness of the basis is not a cosmetic issue. The authors should either provide a completeness argument or explicitly state that their list is complete only with respect to the assumed operator set and then assess how an omitted operator would affect the discriminators.","section":"§1, §3.4"}],"minor_comments":[{"comment":"References [172] and [173] are incomplete: they lack collaboration names and arXiv identifiers or publication details, which will make them difficult to locate.","section":"References [172, 173]"},{"comment":"The reduction of the Type III unitarity operator to the ratio C_Hl^(1):C_Hl^(3)=3:1 plus Q_eH is stated without derivation; a short appendix entry or an explicit Fierz identity chain would improve verifiability.","section":"§3.4, Eq. (3.12)"},{"comment":"The numerical lower bound v_φ > 6.3 TeV uses the current upper bound on BR_inv rather than a measurement of a non-zero width; the sentence should clarify that this is an exclusion bound on the parameter combination, not a determination of v_φ.","section":"§4.2.1, Eq. (4.6)"}],"recommendation":"major_revision","confidential_remarks":"The paper is technically rich and the two-matching-order construction is a genuine strength. My main reservation is that the paper's most prominent claims—falsifiability through operator patterns and the numerical window v_φ ∼ 1–10 TeV—are tied to tree-level matching, and the authors themselves flag in §5 that one-loop effects populate the absent operators. This is addressable in revision by adding loop-level estimates or by carefully restricting the claims, so I do not recommend rejection. I would also gently note that several references to the authors' own prior work are interwoven with the novelty claims; this is not inappropriate, but the new results would stand out more if the distinction were sharpened."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is a careful and mostly new EFT construction. They match Type I, II and III seesaws plus a U(1)_L complex scalar in both integration orders, obtain seven intermediate EFTs, and verify that the two orders agree operator by operator. The dimension-7 operator sets—including O_JNN^7 and the radial-mode dressings—are new as far as I can tell, and the parameter-free locks like C_JHL = C_U/(2v_phi) and Eq. (4.5) are genuine results. Second, the main caveat is real and it is the tree-level matching: Section 5 concedes that one loop would generate operators that are absent here. For a framework whose selling point is the pattern of presences and absences, that is the load-bearing seam, not a footnote.\n\nWhat the paper does well: the two-order matching is a nontrivial consistency check; the Type III J->gamma gamma discriminator from anomaly coefficients is clean; the observation that 0nu beta beta J is dead by nine orders of magnitude is a useful redirect. The numerical coincidence that invisible Higgs width and mu->eJ both point at v_phi ~ 1-10 TeV is striking and survives the caveats at order-of-magnitude level.\n\nWhere it is soft, in proportion. The tree-level truncation is not cosmetic. A one-loop triangle in Type II can produce Q_JHL from the derivative Majoron coupling of Eq. (2.49), and no symmetry is identified that forbids it. The Higgs-width relation Eq. (4.5) is also leading-order: running between M_N, m_rho, and the weak scale is not included. For a first systematic paper this is acceptable, but the abstract overreaches when it says 'these models predict relations' without saying 'at tree level.' Also, Eqs. (4.2)/(4.5) apply to Type I and III only; the Type II bosonic sector has extra triplet contributions, and the abstract's blanket claim should be narrowed.\n\nThe math looks consistent—coefficients reduce properly to the Warsaw basis, and the missing nuSMEFT dimension-7 operator is identified fairly. The citation pattern is standard seesaw/axion literature, with proper credit to earlier operator classifications. Data inputs are standard PDG/TWIST bounds; no circularity.\n\nWho this is for: BSM phenomenologists working on axion/majoron couplings and seesaw EFTs. It deserves a serious referee. My recommendation: send to review, with the request that the authors either compute or bound the one-loop corrections to the key absent operators, or explicitly frame the identification claims as leading-order statements.","headline":"Systematic Majoron–seesaw EFT with real new operator content and a genuinely interesting web of tree-level relations; the tree-level matching is honest, but the paper’s identifying power leans on operator absences that one loop can populate.","tokens_in":791,"tokens_out":1915,"would_cite":true,"duration_ms":46517,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-16T00:37:21.118402+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}