{"id":"a221ae4c-bf43-4de3-a8e2-0b2e26811ddd","arxiv_id":"2608.07623","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"An A4 modular left-right symmetric model can write down all seven allowed two-zero neutrino textures, but only classes B1, B2 and C pass the paper's oscillation, baryogenesis and 0νββ checks.","lead":"A particle physics model building paper uses A4 modular symmetry inside a left-right symmetric framework to write down all seven known 'two-zero' neutrino mass matrix patterns, then checks which patterns fit oscillation data and can generate the universe's matter-antimatter asymmetry and a testable neutrinoless double beta decay signal. It is a systematic construction rather than a new symmetry principle.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Charged-lepton sector is never constructed; if the same A4 assignments generate Y_l, the physical Mnu is U_e^T Mnu U_e and the two-zero textures and oscillation fits are not established.","rationale":"The reader correctly flags that higher-order corrections could fill the texture zeros, but the more immediate tree-level issue is the absence of the charged-lepton sector. Since L_L and L_R^c carry nontrivial A4 representations and the same bidoublet mediates charged-lepton and Dirac-neutrino masses, the charged-lepton mass matrix cannot simply be assumed diagonal. If it is non-diagonal, the Mnu matrices in Section III are not the matrices that diagonalize the physical neutrino sector, and all seven texture claims and the NuFit comparisons lose their current basis. This concern is more load-bearing than the ones identified by the reader because it affects every class before any discussion of corrections or scan documentation. I do not assert that the model is wrong; a specific A4 contraction or field redefinition might render Y_l diagonal, but the manuscript must show it. The proposed derivation and numerical transformation is a concrete way to settle the issue. On that basis, CONDITIONAL is the appropriate verdict: the central construction is testable, but the current text does not yet establish the central claim.","tokens_in":18000,"tokens_out":7406,"duration_ms":76756,"concrete_test":"Construct the charged-lepton Yukawa superpotential for the kY=4 assignment using the same A4 contractions as Eq. (3.2); compute the charged-lepton mass matrix M_l, and for representative modular parameter tau and vev ratios compute its diagonalizing matrix U_e. Transform Eq. (3.8) to Mnu_phys = U_e^T Mnu U_e and check whether the (1,2) and (3,3) entries remain zero. If they become nonzero at order one, the claimed B2 texture is not the physical texture; repeat for one kY=8 class and the kY=10 class to test whether any texture survives.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The most load-bearing gap is the missing charged-lepton mass matrix. The paper compares the light neutrino mass matrices of Eqs. (3.8)-(3.33) directly with NuFit oscillation data, which is only legitimate if the charged leptons are already mass eigenstates. No such basis choice is stated or derived. In this LRSM, the charged leptons and Dirac neutrinos couple through the same bidoublet and the same A4 assignments (Tables III-VIII), so the charged-lepton Yukawa matrix has the same non-diagonal zero pattern as the Dirac neutrino mass matrix, e.g. Eq. (3.3) for kY=4. Diagonalizing it gives a nontrivial U_e, and the physical light neutrino mass matrix becomes U_e^T Mnu U_e. A two-zero texture is not invariant under this transformation: zero entries generically fill in. Therefore the claimed realization of the seven classes, and the oscillation-parameter plots based only on Mnu, are not established. This is an internal-completeness gap at tree level, not merely a question of higher-order operators: the texture is defined in an unspecified flavor basis.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript constructs an A4 (Gamma3) modular-symmetric left-right symmetric model without flavon fields, assigns modular weights 4, 8 and 10 to the lepton sector, and claims to realize, one by one, the seven phenomenologically allowed two-zero textures of the light neutrino mass matrix (classes A1, A2, B1, B2, B3, B4, C). For each texture the paper scans the modular parameter and the VEV ratio, compares the resulting neutrino observables with NuFit-6.0 ranges, and then studies resonant leptogenesis and neutrinoless double beta decay. The central claims are that classes B1, B2 and C reproduce the observed baryon asymmetry and that all seven classes yield effective 0νββ masses compatible with KamLAND-Zen.","tokens_in":18252,"tokens_out":15971,"duration_ms":134515,"significance":"If correct, the framework would be a compact, flavon-free modular LRSM in which a small set of A4 charge and modular-weight assignments determines the entire neutrino mass matrix and yields correlated predictions for the sum of neutrino masses, Dirac CP phase, baryon asymmetry, and 0νββ. The paper has useful strengths: the mass matrices are written out explicitly, all seven two-zero classes are systematically addressed, and the phenomenological section confronts several independent constraints simultaneously. However, the central derivation contains a load-bearing algebraic inconsistency, and the flavor basis in which the textures are defined is never specified. As it stands, the claimed realization of the seven textures and the resulting phenomenological fits are not established.","major_comments":[{"comment":"The light neutrino matrix in Eq. (3.8) does not follow from the preceding matrices by the stated seesaw formula. Writing a = Y_1^4 and b = Y_{1'}^4 in Eqs. (3.3), (3.5) and (3.7), a direct multiplication of M_D M_R^{-1} M_D^T gives (2,2) entry b^2/a and (2,3) entry [a^2b^2 - b^4 + a^4 + ab^3]/[ab(a+b)], whereas Eq. (3.8) has b and a respectively. The matrix in Eq. (3.8) is instead simply proportional to M_L, which would require M_D M_R^{-1} M_D^T ∝ M_L; this proportionality does not hold for the displayed matrices. Since the same computation underlies the other texture matrices in Eqs. (3.15), (3.20), (3.23), (3.26), (3.29) and (3.33), the central claim that all seven two-zero textures are realized is unsupported as written.","section":"Section III, Eq. (3.8)"},{"comment":"The charged-lepton mass matrix is never constructed. In this model the same bidoublet and the same A4 assignments generate the charged-lepton and Dirac neutrino Yukawa couplings, so the charged-lepton mass matrix is generically non-diagonal. The physical light neutrino mass matrix in the mass basis of charged leptons is U_e^T Mν U_e with a non-trivial U_e, and this rotation generically fills two-zero entries. The paper compares Mν directly with NuFit oscillation data in Figs. 1-7 without specifying or deriving such a basis, so the claimed two-zero textures are defined only in an unspecified flavor basis and the oscillation fits are not justified.","section":"Section III, Tables III-VIII and Eqs. (3.3)-(3.33)"},{"comment":"The numerical analysis is not documented in a reproducible way. No chi-square or likelihood function is defined, the scan ranges for the modular parameter τ, the VEV ratio v_L/v_R, and the overall mass scale are not given, and the red 'best-fit' points in the figures are not defined by any stated criterion. The text repeatedly states that data points lie inside the 3σ NuFit ranges, but without a statistical measure and a description of the sampling, the viability claims and the summary in Table IX cannot be verified or reproduced.","section":"Section IV, Figs. 1-11 and Table IX"},{"comment":"The resonant leptogenesis analysis lacks the necessary quantitative ingredients. The heavy right-handed neutrino mass spectrum is never presented, and the degeneracy condition M_i - M_j ~ Γ_i needed for resonant enhancement is asserted rather than demonstrated for the scanned parameters. Moreover, Eq. (4.2) as written is not the standard CP asymmetry formula for quasi-degenerate heavy neutrinos, since the denominator does not have the usual product (Y†Y)_ii (Y†Y)_jj structure, and the efficiency parametrization in Eq. (4.5) is introduced without derivation. Consequently the claim that classes B1, B2 and C reproduce the observed baryon asymmetry is not quantitatively supported.","section":"Section IV.A, Eqs. (4.1)-(4.5)"}],"minor_comments":[{"comment":"The type-I seesaw term is written with a plus sign; the conventional expression is M_I = -M_D M_R^{-1} M_D^T. Please state the sign convention, since it can affect cancellations with the type-II term even when texture zeros are unchanged.","section":"Section II, Eq. (2.4)"},{"comment":"The text says the assignments are 'shown in table V' a second time, but the table in question is Table VI.","section":"Section III.B, after Eq. (3.21)"},{"comment":"The superpotential appears to contain a duplicated term: the same L^c_R2 iσ2 Δ_R L^c_R3 Y_1^6 contribution is written twice inside one parenthesis. Please check whether one of the fields should be L^c_R3 iσ2 Δ_R L^c_R2.","section":"Section III.C, Eq. (3.31)"},{"comment":"The text states that sin^2θ23 data fall in the range 0.5 to 0.6 'radians'; sin^2θ23 is dimensionless, so the unit should be removed.","section":"Section V, bullet on Class B1"},{"comment":"The figures would benefit from explicit axis labels, legends identifying normal versus inverted ordering in every panel, and a statement of how many scan points were used; several panels currently rely on color alone.","section":"Figures 1-11"},{"comment":"Reference [27] realizes two-zero textures with modular A4 symmetry; the present manuscript should state more explicitly what is new relative to that work, beyond embedding the same ideas in the LRSM.","section":"Introduction and Section III"}],"recommendation":"reject","confidential_remarks":"The algebraic check in Section III is not a matter of presentation: the displayed light-neutrino matrices do not follow from the displayed Dirac and Majorana matrices. Combined with the missing charged-lepton sector, this means the paper's central claim would need a full rederivation rather than a local correction. If the authors can correct the matrix computation and add a proper charged-lepton analysis, a substantially revised manuscript could merit re-review."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a coherent modular A4 LRSM exercise. The authors explicitly build MD, MR, ML for modular weights 4, 8, and 10 and show that the type-I plus type-II seesaw combination yields all seven allowed two-zero texture patterns. That algebraic part is real and is the paper's genuine contribution. It is also useful that they connect each texture to resonant leptogenesis and 0νββ, giving the framework experimental targets.\n\nThe load-bearing problem is the charged-lepton sector. In LRSM, the same Dirac Yukawa operator gives mass to charged leptons and neutrinos; the paper never constructs or diagonalizes the charged-lepton mass matrix. It compares the flavor-basis Mν directly with NuFit. But the Dirac matrices in Section III are not diagonal (Eq. (3.3) is a clear example), so the physical light-neutrino mass matrix is U_e^T Mν U_e with a non-trivial U_e. A two-zero texture is not invariant under that rotation; the zeros generically fill in. This is not a higher-order or loop caveat—it is a tree-level basis problem. The stress-test note lands.\n\nSecondary soft spots: the numerical scan is undocumented. There is no chi-square, no scan ranges, no definition of the red \"best-fit\" points. Resonant leptogenesis is asserted via a near-degeneracy and one efficiency formula, with no parameter values or demonstration that ΔM ~ Γ actually holds. The paper's own Table IX shows that several classes fail at least one oscillation parameter, so \"all seven textures\" is true only in the algebraic sense, not as a phenomenological statement.\n\nThe audience is modular-symmetry and LRSM model builders. The paper would be a legitimate contribution if the charged-lepton issue were fixed, for example by choosing assignments that make the charged-lepton Yukawa diagonal or by explicitly including U_e. As written, the texture-realization claim is not established. It deserves a serious referee, not a desk reject, because the construction is explicit and checkable. I would not cite it until the basis problem is resolved.","headline":"The A4 construction is explicit and the seven mass matrices are there, but the paper never diagonalizes the charged leptons, so the physical neutrino texture is not the one being fitted—the central claim is unestablished.","tokens_in":18759,"tokens_out":4281,"would_cite":false,"duration_ms":43769,"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 single flavon-free A4 modular left-right symmetric model can realize all seven experimentally allowed two-zero neutrino mass textures.","keywords":["two-zero texture","left-right symmetric model","A4 modular symmetry","modular forms","neutrino mass matrix","resonant leptogenesis","neutrinoless double beta decay","seesaw mechanism"],"falsifier":"Compute, for each of the seven charge and weight assignments, the lowest modular weight at which an $A_4$-invariant operator contributes to a position that the texture sets to zero; if any such operator enters at a weight that is not suppressed far below the neutrino mass scale set by the non-zero entries, the exact-zero claim fails. On the experimental side, a future neutrinoless double beta decay signal above the largest effective mass the paper predicts for the allowed classes would rule out the framework.","tokens_in":17752,"feed_emoji":"⚛️","tokens_out":12480,"duration_ms":103499,"temperature":0.7,"pith_summary":"This paper argues that the seven two-zero patterns in the light neutrino mass matrix that survive current neutrino oscillation data can all be realized inside a left-right symmetric model whose flavor sector is an A4 (Gamma3) modular symmetry, with no flavon fields. The realization is achieved by assigning modular weights 4, 8 and 10 to the lepton fields so that modular invariance of the superpotential forbids the entries that become the zeros. If the construction holds, neutrino flavor structure is reduced to a small set of symmetry assignments plus a single complex modulus, and the model makes concrete predictions for the sum of neutrino masses, the Dirac CP phase, the baryon asymmetry from resonant leptogenesis, and the effective mass for neutrinoless double beta decay. The paper's central phenomenological claims are that exactly the seven allowed texture classes arise, that classes B1, B2 and C reproduce the observed baryon asymmetry, and that every class stays below the current neutrinoless double beta decay bound.","feed_headline":"Seven neutrino textures from one flavon-free A4 modular model","feed_subtitle":"Weights 4, 8 and 10 fix all allowed two-zero patterns and pass the baryogenesis and 0νββ checks.","key_machinery":"The central machinery is the assignment of $A_4$ ($\\Gamma_3$) modular weights and representations to the three left-handed lepton doublets $L_L$ and right-handed singlets $L_R^c$, with Yukawa couplings promoted to modular forms of weight 4, 8 and 10. The modular forms $Y^{(k)}$ are fixed functions of the modulus $\\tau$, and the rule that the modular weights in every term of the superpotential sum to zero decides which entries of the Dirac mass matrix $M_D$, the right-handed Majorana matrix $M_R$, and the left-handed Majorana matrix $M_L$ are non-zero. Combining type-I and type-II seesaw contributions, $M_\\nu = M_\\nu^{\\mathrm{I}} + M_\\nu^{\\mathrm{II}}$, then produces the two-zero textures, each characterized by exactly two vanishing entries among the six independent elements of the symmetric light neutrino mass matrix.","core_discovery":"Within the generic left-right symmetric model, promoting flavor symmetry to the $A_4$ modular group and choosing modular weights 4, 8 and 10 for the three left-handed lepton doublets and right-handed singlets yields a light neutrino mass matrix $M_\\nu = M_\\nu^{\\mathrm{I}} + M_\\nu^{\\mathrm{II}}$ that takes exactly the seven experimentally allowed two-zero textures. The zeros are not imposed by hand: a superpotential term is present only if the $A_4$ representations combine to a singlet and the modular weights of the fields sum to zero, so the allowed entries of $M_D$, $M_R$ and $M_L$ are fixed by the symmetry. By permuting the $A_4$ charges and modular weights of the lepton fields, the paper obtains classes B2 and B1 from weight 4, classes B4, B3, A2 and A1 from weight 8, and class C from weight 10. With these mass matrices, resonant leptogenesis gives a baryon asymmetry consistent with observation for B1, B2 and C, and the computed total effective Majorana mass for neutrinoless double $\\beta$ decay remains below the current experimental limit for all seven classes.","pith_inferences":["The paper never estimates how higher-order modular-invariant operators, non-minimal Kähler terms, or loop corrections fill the positions set to zero; an extension would compute the lowest modular weight that can populate each zero and translate it into a bound on the modulus $\\tau$.","The same weight-assignment scanning could be applied to other modular groups such as $S_3$, $S_4$ or $A_5$; the seven-texture classification is a property of the two-zero condition, not of $A_4$, so the method is transferable.","The authors take the type-I and type-II seesaw terms to contribute with equal strength; relaxing this assumption would change the relative sizes of the non-zero entries and could alter which textures reproduce the baryon asymmetry, a testable difference for future leptogenesis and $0\\nu\\beta\\beta$ analyses.","The allowed set of seven textures is imported from current global fits; future experiments with sharper oscillation measurements may exclude some textures, which would single out a subset of the modular weight assignments and make the model more predictive."],"forward_implications":["All seven experimentally allowed two-zero textures arise from one flavon-free modular $A_4$ LRSM, so the usual flavon alignment problem is bypassed.","The model yields correlated predictions linking $\\sum m_\\nu$, $\\delta_{\\mathrm{CP}}$, the solar and atmospheric mixing angles, the baryon asymmetry, and the neutrinoless double beta decay effective mass, so measuring any of these sharpens the others.","Resonant leptogenesis works only for classes B1, B2 and C in this framework, so a confirmed baryon asymmetry together with a texture from the other classes would require new ingredients.","Every texture class survives the current neutrinoless double beta decay limit, so future experiments with improved sensitivity can distinguish the predicted total effective mass ranges among classes.","Several classes disfavor or exclude one of the two mass orderings for particular parameters, giving a route to ordering discrimination."],"supporting_citations":[{"why":"Supplies the modular A4 two-zero texture construction whose modular-form multiplets and superpotential structure this paper adapts to the LRSM.","marker":"[27]"},{"why":"Establishes the modular-invariant Yukawa formalism that replaces flavon fields with modular forms.","marker":"[23]"},{"why":"Provides the general modular symmetry framework and the counting of modular forms used to choose weights 4, 8 and 10.","marker":"[24]"},{"why":"Gives the LRSM seesaw decomposition, heavy-neutrino decay rates, and 0νββ formulas used in the phenomenological analysis.","marker":"[22]"},{"why":"Defines the 3σ ranges of the neutrino oscillation parameters against which every texture class is tested.","marker":"[28]"},{"why":"Supplies the cosmological bound on the sum of neutrino masses and the observed baryon asymmetry used in the figures.","marker":"[29]"},{"why":"Provides the experimental upper limit on the neutrinoless double beta decay effective mass that all seven textures must satisfy.","marker":"[54]"},{"why":"Underlies the resonant leptogenesis mechanism used to turn near-degenerate right-handed neutrino decays into the baryon asymmetry.","marker":"[34]"},{"why":"Gives the efficiency-factor formula used to convert CP asymmetries into the baryon asymmetry for classes B1, B2 and C.","marker":"[39]"}],"fun_headline_variants":["Flavon-free A4 modular model yields all seven two-zero neutrino textures","Two-zero textures from A4 modular symmetry without flavons","A4 modular symmetry sets all seven two-zero texture classes","Flavon-free modular A4 generates two-zero textures and passes baryogenesis","Seven two-zero textures from A4 modular weights 4,8,10"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The construction assumes that the superpotential terms written down are the only contributions to the light neutrino mass matrix, so the zero entries are exact; additional interactions or quantum corrections could fill those entries, and the paper does not estimate how large such corrections could be.","fun_headline_variants_meta":{"raw":{"variants":["Flavon-free A4 modular model yields all seven two-zero neutrino textures","Two-zero textures from A4 modular symmetry without flavons","A4 modular symmetry sets all seven two-zero texture classes","Flavon-free modular A4 generates two-zero textures and passes baryogenesis","Seven two-zero textures from A4 modular weights 4,8,10"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00083,"raw_usage":{"total_tokens":3622,"prompt_tokens":937,"completion_tokens":2685,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":553,"completion_tokens_details":{"reasoning_tokens":2592}},"tokens_in":553,"tokens_out":2685,"duration_ms":16005,"temperature":1.0,"reasoning_tokens":2592,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T00:29:50.544983+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute, for each of the seven charge and weight assignments, the lowest modular weight at which an $A_4$-invariant operator contributes to a position that the texture sets to zero; if any such operator enters at a weight that is not suppressed far below the neutrino mass scale set by the non-zero entries, the exact-zero claim fails. On the experimental side, a future neutrinoless double beta decay signal above the largest effective mass the paper predicts for the allowed classes would rule out the framework.","supporting_citations":[{"cited_title":"A modularA 4 symmetry realization of two-zero textures of the Majorana neutrino mass matrix.Nucl","cited_arxiv_id":null,"evidence_quote":"Supplies the modular A4 two-zero texture construction whose modular-form multiplets and superpotential structure this paper adapts to the LRSM."},{"cited_title":"Lepton number violation, lepton flavor violation, and baryogenesis in left-right symmetric model.Phys","cited_arxiv_id":null,"evidence_quote":"Gives the LRSM seesaw decomposition, heavy-neutrino decay rates, and 0νββ formulas used in the phenomenological analysis."},{"cited_title":"Abe et al","cited_arxiv_id":null,"evidence_quote":"Provides the experimental upper limit on the neutrinoless double beta decay effective mass that all seven textures must satisfy."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Underlies the resonant leptogenesis mechanism used to turn near-degenerate right-handed neutrino decays into the baryon asymmetry."},{"cited_title":"New aspects of leptogenesis bounds.Nucl","cited_arxiv_id":null,"evidence_quote":"Gives the efficiency-factor formula used to convert CP asymmetries into the baryon asymmetry for classes B1, B2 and C."}],"review_version":1}