{"id":"57f3a890-8df4-40e8-bff4-492be1f2d428","arxiv_id":"2608.10062","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A texture-zero seesaw model allows large lepton-number violation together with naturally small neutrino masses by protecting the light neutrino with an accidental symmetry.","lead":"This paper constructs a seesaw model where the tiny neutrino mass and the strength of lepton-number violation are controlled by different parameters, breaking the usual tight link. It predicts heavy neutral leptons with measurable mixing at colliders while keeping ordinary neutrinos nearly massless.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The accidental U(1)_acc used for technical naturalness is not a symmetry of the full Lagrangian, so radiative corrections could lift the zero mode and re-introduce M22 into m_nu; the central decoupling is not established beyond tree level.","rationale":"Most load-bearing concern is not the three-flavor extension (deferred but plausibly straightforward), but the absence of a true symmetry protecting the massless mode. The paper's own Supplemental admits U(1)_acc is a symmetry of the mass matrix; however, the transformation mixes fields in different gauge representations, so it is not a symmetry of the full gauge-invariant action. Since U(1)_X does not forbid the Weinberg operator, loop corrections can generate the active-neutrino mass even at mu=0. The size and M22-dependence of such corrections are not computed, so the central assertion that M22 does not feed into m_nu has no all-orders justification. This is a correctness risk, not merely a missing phenomenological extension. The tree-level mass-matrix algebra in Eqs. (7)-(13) is correct as a tree-level statement; the issue is whether the protected zero survives quantum corrections. The reader's weakest assumption identified the three-flavor extension, which I view as secondary; the verdict remains CONDITIONAL but for a different reason.","tokens_in":14594,"tokens_out":37733,"duration_ms":388788,"concrete_test":"Compute the one-loop correction to the N1N1 entry of the heavy-neutrino mass matrix, delta M11, in the renormalizable limit mu1=mu2=0, using the vertices y2 L H N2, lambda phi N1 N2, and the M22 Majorana mass (equivalently, the one-loop coefficient of the Weinberg operator). Then evaluate m_nu_loop = m2^2 delta M11 / M12^2 and compare it with Eq. (13) in the benchmark planes of Figs. 3-4. If m_nu_loop is non-zero, or is not suppressed below about 0.1 eV for the large-M22 trajectories plotted, the tree-level decoupling is not radiatively stable and the model's central claim fails; if it vanishes to all orders (which would require a genuine symmetry), the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (23) defines U(alpha)=exp(i alpha T) with T=|nu><nu|, where |nu>=(M12,-m2,0)/rho is the massless eigenvector of Eq. (21). This transformation mixes nu_L, an SU(2) doublet with U(1)_X charge 0, with N1, an SU(2) singlet with U(1)_X charge 1. It leaves the tree-level mass matrix M0 invariant by construction, but it does not leave the gauge-covariant kinetic terms invariant, and it does not commute with the imposed U(1)_X. Hence U(1)_acc is a symmetry of the mass matrix, not of the Lagrangian, and the Supplemental's claim that this symmetry 'assures the zero neutrino mass technically natural' is unsupported. The Weinberg operator (LH)(LH) is neutral under U(1)_X, so nothing forbids radiative generation of the (1,1) entry of the neutrino mass matrix even when mu1=mu2=0. If this loop-induced mass is nonzero, the exact zero mode is lifted and generically depends on the heavy parameters, including M22. The paper does not compute any loop correction, so Eq. (13) and the conclusion that 'arbitrarily large LNV can coexist with sub-eV neutrino masses' are only established at tree level / leading order in the small texture-lifting parameters.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a seesaw variant, the \"Archimedean seesaw,\" in which a texture-zero mass matrix for one active and two sterile neutrinos has an exact massless eigenstate even when the heavy Majorana sector violates lepton number by a large amount. Small neutrino masses are then generated by small texture-lifting parameters (mu1, mu2), and the paper claims that the heavy Majorana mass M22 that controls LNV does not enter the light-neutrino mass, thereby evading the conventional seesaw relation U^2 M_N ~ m_nu. The authors present a U(1)_X extension intended to justify the texture zeros, give tree-level formulas for the masses and mixings, and map the model onto experimental HNL searches. The tree-level matrix algebra in Eqs. (8)-(13) is correct, but the paper's broader claims of a natural, symmetry-protected mechanism are not established.","tokens_in":14968,"tokens_out":24045,"duration_ms":243713,"significance":"If the core claim were correct, it would open a qualitatively new avenue for low-scale seesaw phenomenology: heavy neutral leptons with sizeable active-sterile mixing and observable LNV could coexist with sub-eV neutrino masses, in contrast to the standard Type-I seesaw relation. The paper also gives a clear EFT interpretation of the texture-lifting, and the phenomenological projections are concrete and useful. However, the significance is currently conditional: the explicit U(1)_X realization is internally inconsistent, the accidental symmetry used for technical naturalness is not a symmetry of the full Lagrangian, and the three-generation extension is not provided. The tree-level one-flavor result is a valid mathematical observation, but it does not by itself support the advertised class of realistic models.","major_comments":[{"comment":"The U(1)_X assignments are internally inconsistent under the standard convention that the charge conjugate N_i^c has charge -q_i. With the stated charges q(L)=0, q(N1)=1, q(N2)=0, q(H)=0, q(phi)=-1, the term lambda phi N_1^c N_2 has total charge -2 and the term beta phi^2 N_1^c N_1 has total charge -2, so neither is invariant; only the alpha term is allowed. This invalidates the claim that Eqs. (15)-(16) are the complete set of U(1)_X-invariant operators. More generally, invariance of the beta operator forces q(phi)=0, which together with invariance of the lambda operator forces q1=q2, and then the renormalizable M11 term is allowed, destroying the texture zero. The advertised symmetry protection of the texture-zero structure is therefore not realized by the explicit model.","section":"TEXTURE ZEROS FROM AN EXTRA U(1)_X SYMMETRY (Eqs. (15)-(16) and charge table)"},{"comment":"The accidental symmetry U(1)_acc is only a symmetry of the tree-level mass matrix M0, not of the full Lagrangian. The transformation U(alpha)=exp(i alpha T) mixes nu_L, an SU(2) doublet with U(1)_X charge 0, with N_1, an SU(2) singlet with U(1)_X charge 1, so it does not commute with the gauge-covariant kinetic terms. Consequently, the statement that this symmetry 'assures the zero neutrino mass technically natural' is unsupported. Since the Weinberg operator (LH)(LH) is neutral under U(1)_X, radiative corrections will generically generate the (1,1) entry of the neutrino mass matrix even when mu1=mu2=0, re-introducing M22 into m_nu. The paper does not compute any loop correction, so Eq. (13) and the central conclusion that 'arbitrarily large LNV can coexist with sub-eV neutrino masses' are established only at tree level.","section":"End Matter, Eqs. (21)-(25) and main text after Eq. (13)"},{"comment":"The proof of the mechanism is carried out for a single active flavor, and the realistic extension to three generations is deferred to a forthcoming paper. The observed neutrino spectrum requires at least two non-zero masses and a specific flavor mixing pattern, and it is not demonstrated that the texture-zero protection survives the required flavor structure. The Supplemental Material's assertion that the mechanism is 'flavor independent' is not backed by a construction. Without an explicit three-generation model, the abstract's claim of a 'class of seesaw models' that realizes sub-eV neutrino masses with sizeable LNV is not supported.","section":"Footnote 1 and the phenomenology section"}],"minor_comments":[{"comment":"The phrase 'without loss of generality' is misleading: the choice m1=0, M11=0 is one particular solution of Eq. (6), not the general solution. The paper is free to adopt this ansatz, but the wording overstates its generality.","section":"Section 'ACCIDENTALLY VANISHING NEUTRINO MASSES', after Eq. (6)"},{"comment":"The sign of m_nu is not fixed; a Majorana mass eigenvalue can be negative, but the paper should refer to |m_nu| when comparing to sub-eV bounds and to experimental constraints.","section":"Eq. (13) and the discussion following it"},{"comment":"The charges of the conjugate fields N_i^c are not listed in the table. Given that the mass terms involve N_i^c, this omission contributes to the inconsistency discussed above and should be clarified.","section":"Charge table in 'TEXTURE ZEROS FROM AN EXTRA U(1)_X SYMMETRY'"},{"comment":"The captions refer to 'colored diagonal lines' and shaded regions, but the actual figures are not included in the manuscript text. The captions should be self-contained enough for a reader to interpret the constraints independently.","section":"Figure captions (Figs. 3 and 4)"}],"recommendation":"reject","confidential_remarks":"The tree-level mechanism is a neat observation, but the paper as written has a load-bearing inconsistency in the U(1)_X model-building and an unaddressed radiative-stability problem. The charge assignments in the table cannot produce the claimed operator set under standard charge conjugation, and the accidental symmetry invoked for technical naturalness is not a symmetry of the Lagrangian. These issues concern the central claims of the paper, not just presentation. If the authors can construct a genuinely consistent symmetry and demonstrate that the zero mode survives quantum corrections, the core idea might become publishable, but the current manuscript does not support its conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nRead the Archimedean seesaw paper. The tree-level mechanism is real: with one active doublet and two singlet fermions, the texture m1 = 0, M11 = 0 gives an exact massless mode for arbitrary M12 and M22, and the lifted mass in Eq. (13) is independent of M22. That is a clean observation, and the explicit U(1)_X construction makes the texture look less ad hoc. The paper is honest that the three-generation extension is deferred.\n\nWhat is actually new is modest but useful. The texture-zero condition is an elementary solution of Eq. (6) and overlaps with known minimal-seesaw texture studies; the paper's own Ref. [24] states an equivalence between massless neutrinos and lepton number conservation in singlet extensions, and the paper does not explain why that theorem does not cover this model. The novel packaging is the two-HNL 'counterweight' picture and the mapping onto constant-M2 trajectories in the |V|^2-M_N plane, which is a helpful way to present HNL search results.\n\nThe soft spot is real and central. The accidental U(1)_acc is constructed as a transformation on the mass matrix, not on the Lagrangian. It rotates nu_L into N1, so it does not respect the electroweak gauge symmetry or the kinetic terms. That means the 'technically natural' claim is not supported. Radiative corrections can generate the M11 entry, and nothing in the paper shows the induced mass remains independent of M22 once loops are included. U(1)_X forbids the renormalizable M11 term, so the protection is not nothing, but the paper needs a loop-level calculation to justify 'arbitrarily large LNV'. This is addressable, but currently it is a gap between what is proven and the headline.\n\nTwo secondary points. Spontaneous breaking of U(1)_X should produce a Goldstone boson unless the symmetry is gauged; the paper does not say which. And the practical claim of sub-eV masses is only established in the one-flavor toy model; the three-flavor extension, with lepton flavor violation and CP phases, could reintroduce M22 into m_nu.\n\nNet: I would send it to a serious referee. The tree algebra is correct, the model is concrete, and the phenomenology section is usable. But the referee report should insist on the radiative analysis and the Goldstone discussion before publication.","headline":"The tree-level cancelation is real and the paper is worth refereeing, but the 'arbitrarily large LNV' claim is only established at tree level because the accidental symmetry is not a symmetry of the Lagrangian.","tokens_in":15471,"tokens_out":4679,"would_cite":false,"duration_ms":55104,"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":"A texture-zero seesaw can cancel the active neutrino mass exactly while lepton-number violation in the heavy sector stays large, and small perturbations make the neutrino mass naturally small without reinstating the usual suppression.","keywords":["neutrino mass","seesaw mechanism","lepton-number violation","heavy neutral leptons","texture zeros","accidental symmetry","Majorana neutrinos","Archimedean seesaw"],"falsifier":"Compute the three-flavor generalization: if any light neutrino mass acquires a term proportional to $M_{22}$, or if the exact massless mode cannot be maintained while fitting oscillation data, the central decoupling claim collapses. An experimental falsifier would be a precise measurement of same-sign dilepton production that returns $|V_{\\ell N}|^2 M_N \\simeq m_\\nu$ in a parameter region where the Archimedean model predicts a much larger value.","tokens_in":14388,"feed_emoji":"⚖️","tokens_out":15837,"duration_ms":145712,"temperature":0.7,"pith_summary":"The paper claims that the familiar seesaw rule, under which observable lepton-number violation is always suppressed by the tiny neutrino mass, is not forced by the seesaw mechanism itself. In a model with one active neutrino and two heavy neutral leptons, a texture-zero (symmetry-enforced vanishing entries) choice for the Yukawa coupling and the heavy Majorana mass matrix leaves one active neutrino exactly massless while the heavy sector still violates lepton number. Small perturbations lift that zero mode and give naturally small neutrino masses that depend on the perturbation parameters $\\mu_1,\\mu_2$, not on the heavy Majorana mass $M_{22}$. Heavy neutral leptons can therefore have sizeable mixing with the active neutrino and produce observable lepton-number-violating signals while light neutrinos stay sub-eV. The paper argues this would give collider searches for lepton-number violation a concrete target across a broad mass range.","feed_headline":"Seesaw texture frees lepton-number violation from tiny neutrino mass","feed_subtitle":"Heavy neutral leptons can keep large mixing and observable lepton-number violation even with sub-eV neutrino masses.","key_machinery":"The mechanism is the texture-zero Archimedean seesaw: a $3\\times3$ neutrino mass matrix whose first two rows are linearly dependent, so that one active eigenstate is exactly massless. The load-bearing object is the accidental $U(1)_{\\rm acc}$ symmetry generated by the projector $T=|\\nu\\rangle\\langle\\nu|$; it leaves the renormalizable mass matrix invariant for all heavy-sector parameters and makes the zero mode exact rather than fine-tuned. Higher-dimensional operators that respect the underlying $U(1)_X$ symmetry but break $U(1)_{\\rm acc}$ provide the leading perturbation $\\Delta M$, and the active neutrino mass is simply $\\langle\\nu|\\Delta M|\\nu\\rangle=\\mathrm{Tr}(T\\Delta M)$, naturally small and independent of $M_{22}$. The paper also gives a lever-arm picture: the relation $m_\\nu V_{\\ell\\nu}^2+M_1 V_{\\ell N_1}^2+M_2 V_{\\ell N_2}^2=0$ is an Archimedean balance condition, with the heavy masses acting as counterweights that allow large active-sterile mixing without a large neutrino mass.","core_discovery":"The central claim is that the light neutrino mass in a seesaw can be made independent of the heavy Majorana mass that controls lepton-number violation. With the texture-zero choice $m_1=0$ and $M_{11}=0$ for $Y=(0,y_2)$ and $M=(M_{ij})$, the $3\\times3$ neutrino mass matrix has an exact zero eigenvalue for arbitrarily large $M_{12}$ and $M_{22}$; the eigenvector $|\\nu\\rangle=(M_{12},-m_2,0)/\\rho$ with $\\rho^2=m_2^2+M_{12}^2$ defines a projector $T=|\\nu\\rangle\\langle\\nu|$, and $U(\\alpha)=e^{i\\alpha T}$ is an accidental $U(1)$ symmetry of the renormalizable mass matrix. Lifting the texture zeros by small perturbations $\\mu_1,\\mu_2$ gives $m_\\nu=-2\\mu_1 m_2 M_{12}/\\rho^2+\\mu_2 m_2^2/\\rho^2=\\mathrm{Tr}(T\\Delta M)$, an expression in which $M_{22}$ does not appear. The induced mass is naturally small because the breaking first appears through higher-dimensional operators suppressed by $\\langle\\phi\\rangle/\\Lambda$, and the two heavy eigenstates need not form a Dirac pair, so heavy-sector lepton-number violation remains unsuppressed.","pith_inferences":["The paper proves the decoupling for a single active flavor; a natural next test is whether a three-flavor texture can protect all three light neutrinos while fitting solar and atmospheric oscillations, a check not carried out here.","Because the neutrino mass is proportional to $\\mu_1,\\mu_2$, generating these parameters radiatively at one loop would make their smallness fully natural without needing a very large $\\Lambda$; the paper does not explore this origin.","An anomaly-free gauging of $U(1)_X$ would introduce a $Z'$ coupled to the singlet sector, giving an additional search channel through heavy neutral lepton pair production that is not discussed in the paper."],"forward_implications":["If the central claim is right, $|V_{\\ell N}|^2 M_N=m_\\nu$ is not a universal seesaw constraint, and heavy neutral lepton searches no longer need to be pre-scaled by the tiny neutrino mass.","The model maps the observable $(M_N,|V_{\\mu N}|^2)$ plane directly onto the heavy-sector scale $M_2$, so current and future exclusions become bounds on $M_2$.","Same-sign dilepton signatures, both vector-boson fusion and resonant Drell-Yan $q\\bar q\\to W\\to \\ell N_i$, become viable discovery channels at the LHC and future colliders for HNL masses from MeV to TeV.","In the limit $M_{22}\\to0$ the two heavy states form an approximate Dirac pair and lepton-number violation is partially cancelled, recovering the inverse seesaw; the new physics is the asymmetric regime where this cancellation is absent."],"supporting_citations":[{"why":"Defines the dimension-five Weinberg operator whose suppression of lepton-number violation by neutrino mass is the lore the paper overturns.","marker":"[1]"},{"why":"Introduces the Type-I seesaw and the heavy right-handed neutrinos that provide the model's starting point.","marker":"[2–5]"},{"why":"Introduces the inverse seesaw, where approximate lepton number suppresses lepton-number violation; the paper contrasts with this and recovers it in the $M_{22}\\to0$ limit.","marker":"[6, 7]"},{"why":"Introduces the linear seesaw, another approximate-lepton-number alternative to which the new mechanism is compared.","marker":"[8, 9]"},{"why":"Supplies the neutrinoless double-beta decay treatment used to estimate lepton-number-violating rates in the model.","marker":"[25–27]"},{"why":"Provides the heavy Majorana neutrino production and decay cross sections used for collider sensitivity estimates.","marker":"[27]"},{"why":"Gives the resonant $W\\to\\ell N$ production channel that yields the same-sign dilepton signature analyzed.","marker":"[39]"}],"fun_headline_variants":["Seesaw texture decouples neutrino mass from lepton-number violation","Large LNV with sub-eV neutrino masses: a seesaw loophole","Texture zeros free lepton-number violation from neutrino mass","Archimedean seesaw: heavy LNV, light neutrinos independent","Neutrino mass and LNV decoupled via texture-zero seesaw"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the realistic three-generation version needed to fit neutrino oscillations keeps the same protective structure, so the heavy mass that controls lepton-number violation stays out of the light neutrino mass formula; the paper shows this only for one active flavor.","fun_headline_variants_meta":{"raw":{"variants":["Seesaw texture decouples neutrino mass from lepton-number violation","Large LNV with sub-eV neutrino masses: a seesaw loophole","Texture zeros free lepton-number violation from neutrino mass","Archimedean seesaw: heavy LNV, light neutrinos independent","Neutrino mass and LNV decoupled via texture-zero seesaw"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000603,"raw_usage":{"total_tokens":2834,"prompt_tokens":987,"completion_tokens":1847,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":603,"completion_tokens_details":{"reasoning_tokens":1753}},"tokens_in":603,"tokens_out":1847,"duration_ms":13983,"temperature":1.0,"reasoning_tokens":1753,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:17:00.351471+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the three-flavor generalization: if any light neutrino mass acquires a term proportional to $M_{22}$, or if the exact massless mode cannot be maintained while fitting oscillation data, the central decoupling claim collapses. An experimental falsifier would be a precise measurement of same-sign dilepton production that returns $|V_{\\ell N}|^2 M_N \\simeq m_\\nu$ in a parameter region where the Archimedean model predicts a much larger value.","supporting_citations":[],"review_version":1}