{"id":"e2678286-3f21-4a30-96cc-f4b76cc6d557","arxiv_id":"1909.01552","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"Only texture two zero Majorana mass matrix cases B2 and B4 remain viable at 2σ under the updated Planck sum-of-masses bound, favoring normal ordering, θ23 > 45°, and δ near 270°.","lead":"This paper checks five popular patterns for the neutrino mass matrix against the newest data on neutrino masses and oscillations. Only two patterns survive, and both point to normal mass ordering, an upper atmospheric octant, and maximal CP violation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The analytic Σ(θ23) formulas in Eqs. 14 and 17 use the solar mass splitting δm² where the atmospheric splitting Δm₃₁² is required; the quoted Σ_min values and the B1/B3/C exclusion claims therefore do not follow from the stated equations.","rationale":"The reader's weakest_assumption identifies the leading-order-in-s13 expansions as fragile because they diverge at θ23 = 45°. That is a real concern, but the more concrete and decisive problem is that the paper uses the wrong mass-squared difference in those expansions: Eqs. (13) and (16) place δm² (solar splitting) in a denominator that must be the atmospheric splitting to give m3 the correct scale. This is not a subtle next-order correction; it is a leading-order error that makes the analytic formulas numerically incompatible with the quoted Σ_min values. The inconsistency is internal to the manuscript: Eq. (9) explicitly labels δm² as solar, and Eq. (19) for case C switches to Δm², so the reader cannot infer that a different convention was intended. Because the paper's exclusion of B1/B3/C rests directly on these formulas, and because no code or data are provided to reproduce the underlying scan, the central claim is not supported by the derivation as written. The verdict should remain CONDITIONAL rather than being upgraded to ACCEPT or downgraded to REJECT: the conclusion may survive a corrected calculation, but the current version needs a corrected and reproducible derivation before it can be relied upon.","tokens_in":10659,"tokens_out":6171,"duration_ms":57986,"concrete_test":"Independently re-derive Σ(θ23) for B1 and B2 from the two-zero conditions M_ab = 0 using the exact parameterization of Eq. (7), keeping m1, m2, m3 and all CP phases, and impose δm² = m2²−m1² and Δm₃₁² = m3²−m1² for NO. Then evaluate Σ over the 2σ ranges of Table 1 with the atmospheric splitting Δm₃₁² in place of δm² in Eqs. (13) and (16). If the recomputed Σ_min for B1/B3 drops below 0.17 eV for any allowed θ23, the paper's exclusion of these cases fails; if it stays above, the conclusion is restored but only after the corrected derivation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central exclusion of B1, B3 and C (and the claimed survival of B2/B4 only for NO) is derived in Section 3 from approximate expressions for Σ(θ23). Eq. (9) defines δm² as the solar mass-squared difference and sets m3 = sqrt(δm²/(β²−α²)). In leading order in s13, Eqs. (12)–(13) give m1 ≃ m2 ≃ m3 tan²θ23 and m3 ≃ sqrt(δm²/(1 − tan⁴θ23)). But for θ23 > 45°, tan⁴θ23 > 1 and the denominator is negative; for the allowed NO range the formula is not even real-valued over most of the 2σ interval. More fundamentally, when m1 ≃ m2 at leading order, the solar splitting δm² = m2²−m1² is a next-order effect; the leading-order m3 must be fixed by the atmospheric splitting Δm₃₁² = m3²−m1². Using δm² in Eq. (13) and Eq. (16) is a dimensional mismatch: for θ23 = 47.7° it gives m3 ~ 0.015 eV (with δm² = 7.55×10⁻⁵ eV²), whereas the atmospheric scale gives m3 ~ 0.087 eV. Eq. (17) similarly cannot produce the quoted Σ_min ≃ 0.154 eV from the stated inputs. Since the analytic formulas are the explicit justification for the Σ_min values, and the numerical scan is not provided, the exclusion claims are not presently supported by the equations as written.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper re-examines five viable two-zero texture Majorana neutrino mass matrices (B1-B4 and C) using updated oscillation parameters, the Planck bound on the sum of neutrino masses (Sigma < 0.17 eV at 95% CL), and the KamLAND-Zen bound on neutrinoless double beta decay. The author claims that only B2 and B4 remain viable for normal mass ordering at 2 sigma CL, while B1, B3, and C are excluded for both orderings. The viable cases are reported to prefer the upper octant of theta23, a Dirac phase delta near 270 degrees, a quasi-degenerate spectrum, and |Mee| close to the KamLAND-Zen limit. The paper combines approximate analytical formulas for Sigma(theta23) with correlation plots to support these conclusions.","tokens_in":10955,"tokens_out":9702,"duration_ms":94129,"significance":"If the conclusions were correct, the paper would provide a sharp experimental discrimination among texture-two-zero neutrino mass matrices, which is useful for model building. The author also connects the texture analysis to cosmology and neutrinoless double beta decay, which are timely topics. However, the central quantitative support is not reproducible: the key formulas use the solar mass-squared difference where the atmospheric scale is required, the quoted minima are not obtainable from the stated equations, and the numerical scan is not documented. These issues affect the main viability claims, so the significance cannot be assessed without a corrected and reproducible analysis.","major_comments":[{"comment":"The notation delta m^2 is defined in Eq. (9) as the solar mass-squared difference, but the leading-order relations m1 ~ m2 in Eqs. (12) and (15) imply that the solar splitting is a next-order effect. The mass scale that fixes m3 at leading order is the atmospheric splitting |Delta m31^2|, not delta m^2. Consequently, evaluating Eq. (17) with delta m^2 = 7.55e-5 eV^2 and theta23 = 49.8 degrees gives Sigma of order 0.03 eV for B2 NO, not the quoted Sigma_min ~ 0.154 eV. The text therefore does not demonstrate the claimed exclusions and survivals from the equations as written. In addition, Eq. (13) is not real-valued for theta23 > 45 degrees, which is the region the text associates with inverted ordering, so a separate treatment for IO is needed.","section":"Section 3, Eqs. (9), (13), (16), (14), (17)"},{"comment":"Even if delta m^2 were replaced by |Delta m31^2|, the quoted minima do not match a direct evaluation over the stated 2 sigma ranges. For B2 NO, the 2 sigma upper end is theta23 = 49.8 degrees; using |Delta m31^2| = 2.50e-3 eV^2 in Eq. (17) gives Sigma ~ 0.17 eV, not 0.154 eV. Since the expression diverges as theta23 approaches 45 degrees and the allowed range extends close to the singularity, the leading-order approximation is not controlled, and the paper provides no estimate of the neglected next-order s13 corrections. The claimed survival of B2 and B4 under the Planck bound is therefore not established.","section":"Section 3, Eqs. (14), (17) and Table 1"},{"comment":"The author states that input parameters are scanned within their 3 sigma ranges, but the scanning procedure is not specified: there is no description of the number of points, the parameter sampling, the acceptance criteria, or the treatment of the texture-zero conditions. No code or data are provided. Since the analytic formulas above are used as the explicit justification for the exclusions, and the numerical plots cannot be independently reproduced, the central claims in Table 2 are not verifiable from the manuscript.","section":"Section 3, computational scan"},{"comment":"The relation |Mee| ~ (Sigma/3) tan^2 theta23 does not follow from Eq. (11) combined with the leading-order mass relations for B2 and B4 in Eq. (15). Using m1 = m2 = m3 cot^2 theta23 gives |Mee|/Sigma ~ cot^2 theta23/(1 + 2 cot^2 theta23) in the leading order, which differs from the quoted expression by a factor of order tan^2 theta23. The derived bound |Mee| < 0.0684 eV is therefore not supported by the stated equations.","section":"Section 3, Eq. (18)"}],"minor_comments":[{"comment":"There are numerous typographical errors, including 'superkomiokande' for Super-Kamiokande, '2700' and '450' for 270 degrees and 45 degrees, and stray brackets such as 'Table 1]' and 'Fig.[1, 2' in Section 3.","section":"Throughout"},{"comment":"The captions state that the solid line indicates Planck's limit Sigma = 0.23 eV, but the abstract and Section 1 state the current limit is Sigma < 0.17 eV and that 0.23 eV is the older comparison value; the captions should be corrected for clarity.","section":"Figure captions, Figs. 1 and 2"},{"comment":"The formula for case C in the inverted ordering case contains an undefined notation c_delta and t2(23), and the expression is not derived or explained; the reader cannot verify the quoted Sigma_min ~ 0.174 eV from the stated equation.","section":"Section 3, Eq. (20)"},{"comment":"Reference [15] is the 2016 Planck paper, but the abstract describes it as the latest Planck data; the authors should update the reference to the relevant 2018 Planck release or clarify the date.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The central viability claims may be correct after a proper treatment of the mass-squared differences, but as written the analytic core is dimensionally inconsistent and the numerical scan is undocumented. The authors should be asked to rerun the analysis with the atmospheric mass-squared difference in the leading-order mass formulas, provide the scan details or code, and check whether B2 and B4 still survive the Planck bound at 2 sigma. If the corrected calculation reverses the survival of B2/B4, the main conclusion will need substantial revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague —\n\nThis is a modest but legitimate update of a known framework. The new claim is that with Planck's Σ < 0.17 eV and updated global oscillation fits, only B2 and B4 survive at 2σ for normal ordering, while B1, B3, and C are ruled out. If true, that is useful for model builders. The paper also connects the surviving cases to δ ≈ 270°, upper octant of θ23, and |Mee| near the KamLAND-Zen limit.\n\nThe author cites the prior work honestly: Meloni et al. and Zhou are acknowledged, and the analytic forms are explicitly taken from the earlier texture-zero literature. What is new is the updated exclusion statement and the sharper allowed θ23 range. The qualitative conclusion is plausible and consistent with earlier analyses; the stress-test note identifies a real problem, not a manufactured one.\n\nThat problem is dimensional. Eq. (9) defines δm² as the solar mass-squared difference and uses it to fix m3. But in the leading-order limit m1 ≈ m2, the solar splitting is a next-order effect; the object that fixes m3 is the atmospheric splitting Δm31². As written, Eqs. (13)–(14) even turn imaginary for θ23 > 45°, and Eqs. (16)–(17) give m3 ≈ 0.015 eV instead of order 0.09 eV at the best fit. The quoted Σ_min values therefore do not follow from the displayed formulas. It is possible the text meant Δm² in those equations, but that is not what it says, and the reader cannot verify the numbers without guessing.\n\nA second soft spot: the leading-order expansions diverge at θ23 = 45°, and the paper uses them to quote minima over 2σ ranges that include both sides of 45°. That is a misuse of an expansion that is singular in the middle of the range. Third, no scan code or data table is provided; the data-availability statement points to the figures, which are not enough to reproduce the scan.\n\nNone of this means the conclusion is wrong. The correlation plots and the earlier literature both suggest B2 and B4 are favored. But the analytic support as printed is not reproducible, and the exclusion of B1, B3, and C rests partly on those formulas. If the author corrects the mass-splitting identification and provides the scan details, the paper could be a useful reference. As it stands, I would not cite it without redoing the numerics myself.\n\nFor a reader who wants the current status of texture two zeros with the post-2018 Planck bound, this is worth a reading-group slot, but it needs a serious referee and likely major revision before the claims are reliable.","headline":"A plausible update of texture-two-zero neutrino mass matrices under the 2018 Planck bound, but the printed analytic formulas do not reproduce the quoted Σ minima and need correction before the exclusion claim is usable.","tokens_in":11523,"tokens_out":2981,"would_cite":false,"duration_ms":32762,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["14.60.Pq"],"model":"deepseek-v4-flash","headline":"Two neutrino mass matrices survive Planck's 0.17 eV limit","keywords":["neutrino mass matrices","texture two zero","Majorana neutrinos","neutrino mass ordering","atmospheric mixing angle octant","Dirac CP phase","neutrinoless double beta decay","sum of neutrino masses"],"falsifier":"Run the same $2\\sigma$ scan using the exact texture-two-zero reconstruction of the mass matrix instead of the approximate formulas (14), (17), (19), and (20), and read off the minimum $\\Sigma$ for B1, B3, and C. If any of those minima falls below $0.17$ eV, the paper's central exclusion fails; if all three stay above $0.17$ eV, the shortlist of B2 and B4 survives.","tokens_in":10382,"feed_emoji":"⚛️","tokens_out":11264,"duration_ms":86711,"temperature":0.7,"pith_summary":"This paper re-tests the five remaining “texture two zero” patterns of the neutrino Majorana mass matrix against the current experimental map: Planck's bound $\\Sigma<0.17$ eV on the sum of neutrino masses, the updated $2\\sigma$ range of the atmospheric angle $\\theta_{23}$, and the KamLAND-Zen limit on neutrinoless double $\\beta$ decay. It claims that only two patterns, B2 and B4, survive, and only for normal mass ordering; B1, B3, and C are excluded at $2\\sigma$ for both orderings. The survivors force a quasi-degenerate spectrum, $\\theta_{23}>45^\\circ$, a Dirac CP phase near $270^\\circ$, and an effective Majorana mass $|M_{ee}|$ close to the KamLAND-Zen sensitivity. This matters because texture two zero matrices are a minimal, symmetry-motivated ansatz for neutrino flavor, so a shortlist of two concrete patterns can be decisively tested by upcoming long-baseline, cosmological, and double-$\\beta$ experiments.","feed_headline":"Two neutrino mass matrices survive Planck's 0.17 eV limit","feed_subtitle":"Three of five two-zero patterns are ruled out at 2σ; survivors demand quasi-degenerate masses and δ ≈ 270°.","key_machinery":"The central object is the texture two zero Majorana mass matrix in the flavor basis: a $3\\times3$ symmetric matrix with two independent zero entries, classified into cases B1–B4 and C. The load-bearing identity is the reconstruction of the mass ratios $\\alpha=m_1/m_3$, $\\beta=m_2/m_3$ from the two vanishing entries together with the mixing angles, and the formula $\\Sigma=\\sqrt{\\delta m^2/(\\beta^2-\\alpha^2)}\\,(\\alpha+\\beta+1)$ that turns the texture conditions into a definite prediction of $\\Sigma$ as a function of $\\theta_{23}$. The argument then compares those $\\Sigma(\\theta_{23})$ curves with the Planck bound and the $2\\sigma$ $\\theta_{23}$ window, using the leading-order-in-$s_{13}$ approximations to locate the minima analytically.","core_discovery":"Starting from the five two-zero forms of the flavor-basis Majorana mass matrix allowed at $3\\sigma$, the paper uses the texture conditions to write the neutrino masses as $m_3=\\sqrt{\\delta m^2/(\\beta^2-\\alpha^2)}$, $m_2=m_3\\beta$, $m_1=m_3\\alpha$, with $\\alpha,\\beta$ fixed by the mixing angles, and hence expresses $\\Sigma=m_1+m_2+m_3$ as a function of $\\theta_{23}$. Over the $2\\sigma$ inputs, the leading-order-in-$s_{13}$ formulas give $\\Sigma_{\\min}\\simeq 0.24$ eV for B1 and B3 (both orderings), which exceeds the Planck limit; for B2 and B4 they give $\\Sigma_{\\min}\\simeq 0.154$ eV for normal ordering, inside the limit; for case C the inverted-ordering formula gives $\\Sigma_{\\min}\\simeq 0.174$ eV, marginally above $0.17$ eV. The conclusion is that B2 and B4 are the only viable texture two zero cases, both requiring normal ordering, upper octant $\\theta_{23}$, $\\delta$ in a narrow band around $270^\\circ$, and $|M_{ee}|$ in the range $0.0389$–$0.0422$ eV or above, near the KamLAND-Zen bound. The paper also shows that Majorana phases $\\rho$ and $\\sigma$ vanish as $\\delta$ approaches $270^\\circ$, and that distinguishing B2 from B4 at low energies will require sub-degree precision on $\\delta$.","pith_inferences":["If the surviving textures are correct, the neutrino sector has no room for maximal $\\theta_{23}$: the singular behavior of the mass formulas at $45^\\circ$ means any future hint of maximal atmospheric mixing would kill all five cases at once.","The B2/B4 shortlist creates a sharp target for cosmology: the same models predict $\\Sigma$ above $0.141$–$0.151$ eV, so a future cosmological limit pushing below about $0.14$ eV would eliminate them without any oscillation data.","Because the exclusion of case C rests on $\\Sigma_{\\min}\\simeq 0.174$ eV versus $0.17$ eV, a small correction by higher-order terms in $s_{13}$ or a slightly looser cosmological bound could reverse that judgment; the $2\\sigma$ margin is not large.","The vanishing of Majorana phases near $\\delta\\simeq 270^\\circ$ suggests that, if these textures are realized, the dominant CP violation in the lepton sector is Dirac-like, with negligible extra phases in neutrinoless double beta decay."],"forward_implications":["Only the B2 and B4 textures remain viable at $2\\sigma$, and only for normal mass ordering; both force $\\theta_{23}>45^\\circ$, $\\delta\\simeq 270^\\circ$, and a quasi-degenerate spectrum.","B1, B3, and C are excluded for both orderings under $\\Sigma<0.17$ eV; the older $0.23$ eV limit would have kept them alive.","For B2 and B4, $|M_{ee}|$ is bounded below by $0.0389$–$0.0422$ eV, placing the textures within reach of next-generation neutrinoless double beta decay searches and near the KamLAND-Zen $90\\%$ limit.","The lightest neutrino mass is constrained to $m_1\\lesssim 0.06$ eV for the viable cases, sharpening the quasi-degenerate prediction.","Measuring the Dirac phase $\\delta$ with accuracy better than about $1^\\circ$ near $270^\\circ$ would discriminate between B2 and B4."],"supporting_citations":[{"why":"Supplies the Planck bound on the sum of neutrino masses (0.17 eV at 95% CL) that rules out three of the five cases.","marker":"[15]"},{"why":"Supplies the KamLAND-Zen limit on the effective Majorana mass used to test the viable cases and to bound the lightest neutrino mass.","marker":"[16]"},{"why":"Provides the updated global-fit oscillation parameters, including the atmospheric-angle and mass-splitting ranges used in the numerical scans.","marker":"[9]"},{"why":"Defines the texture two zero classification and the leading-order mass formulas in terms of the atmospheric angle.","marker":"[23]"},{"why":"Supplies the mass-ratio construction and the expression for the sum of neutrino masses used in the analysis.","marker":"[24]"},{"why":"Previous analysis of the same five cases at 1 sigma with the weaker limit; serves as the baseline this paper updates.","marker":"[25]"},{"why":"The older Planck limit, used as a comparison to show which exclusions are new.","marker":"[32]"}],"fun_headline_variants":["Planck data trims texture two zero to two survivors","Two zero textures: only B2 and B4 pass Planck sum limit","Planck limit halves texture two zero neutrino matrices","Planck kills three of five two-zero neutrino textures","Neutrino mass textures: only B2 and B4 dodge Planck bound"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The exclusion of cases B1, B3, and C relies on leading-order-in-$s_{13}$ approximations for $\\Sigma$ as a function of $\\theta_{23}$; these formulas diverge as $\\theta_{23}$ approaches $45^\\circ$, so if the neglected higher-order terms are not negligible at the quoted $2\\sigma$ minima, the minimum $\\Sigma$ values — and hence which cases are ruled out — could change.","fun_headline_variants_meta":{"raw":{"variants":["Planck data trims texture two zero to two survivors","Two zero textures: only B2 and B4 pass Planck sum limit","Planck limit halves texture two zero neutrino matrices","Planck kills three of five two-zero neutrino textures","Neutrino mass textures: only B2 and B4 dodge Planck bound"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001327,"raw_usage":{"total_tokens":5502,"prompt_tokens":1148,"completion_tokens":4354,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":764,"completion_tokens_details":{"reasoning_tokens":4268}},"tokens_in":764,"tokens_out":4354,"duration_ms":28672,"temperature":1.0,"reasoning_tokens":4268,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T05:14:29.556553+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same $2\\sigma$ scan using the exact texture-two-zero reconstruction of the mass matrix instead of the approximate formulas (14), (17), (19), and (20), and read off the minimum $\\Sigma$ for B1, B3, and C. If any of those minima falls below $0.17$ eV, the paper's central exclusion fails; if all three stay above $0.17$ eV, the shortlist of B2 and B4 survives.","supporting_citations":[],"review_version":1}