{"id":"d4eadf80-4fdd-44cc-a0e0-7450698f8e24","arxiv_id":"2607.06108","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":2,"one_line_summary":"Combined DUNE and Hyper-Kamiokande analysis suppresses hierarchy-CP-non-unitarity degeneracies by a factor of 7 to 16, distinguishing genuine from fake CP violation.","lead":"This paper simulates how non-unitary neutrino mixing (from heavy neutral leptons) could create 'fake' CP-violating signals at DUNE and Hyper-Kamiokande. It finds that combining both experiments' data effectively breaks the degeneracy between genuine and fake CP violation, reducing the allowed parameter space by up to a factor of 16.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"The 'factor of 16' degeneracy reduction is measured relative to Hyper-K alone; relative to DUNE alone the combined result provides no improvement (slightly worse at 3σ), undermining the claim that complementarity drives the result.","rationale":"The reader correctly identified the single-benchmark limitation (only α21 non-zero, single true parameter point), which is a valid concern but secondary. The more load-bearing issue is the misleading framing of the improvement factor. The underlying calculations appear correct — the χ² values, areas, and contour shapes are internally consistent and the paper is transparent in the body text about DUNE providing the dominant constraint. However, the abstract's claim of a 'factor of 16' reduction and the statement that 'neither experiment resolves individually' are inaccurate: DUNE alone resolves the degeneracy quite effectively, and the combined result is essentially DUNE's result with negligible added value from HK on the (δCP, φ21) plane. This is a framing problem rather than a computational error, so the verdict remains CONDITIONAL — the results are conditionally valid but the central claim as stated overstates the role of complementarity. The reader's concerns about unreleased code and the duplicated paragraph in Section 5 further support keeping the verdict conditional. The paper would benefit from: (1) reframing the headline to accurately reflect that DUNE drives the degeneracy resolution, (2) scanning multiple true δCP values to establish robustness of the reduction factors, and (3) releasing the custom probability engine for independent verification.","tokens_in":18477,"tokens_out":4743,"duration_ms":246974,"concrete_test":"Recompute the degeneracy reduction factors relative to DUNE alone at 1σ, 2σ, and 3σ using the existing χ² surfaces. The paper already provides the areas: DUNE 3σ = 0.049π², combined 3σ = 0.059π². Report the ratio combined/DUNE for each confidence level. If the ratios are ≈1.0 (as they appear to be), revise the abstract to state that DUNE alone resolves the degeneracy and the combination provides marginal additional benefit, rather than claiming a 'factor of 16' improvement from complementarity. Additionally, repeat the degeneracy scan at 2–3 alternative true δCP values (e.g., δCP = 0, π/4, π/2) to verify whether the reduction factors are stable across the parameter space.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim states the combined analysis reduces the (δCP, φ21) space 'by a factor of 7 at 1σ and ~16 at 2σ–3σ' and 'substantially suppress[es] the degeneracy that neither experiment resolves individually.' However, the paper's own numbers contradict this framing: (1) at 1σ, the combined area (0.010π²) is described as 'identical to DUNE alone'; (2) at 3σ, the combined area (0.059π²) is actually *larger* than DUNE alone (0.049π²). The 'factor of 16' is the ratio of HK's allowed region to the combined region — it measures how much worse HK is than DUNE, not how much the combination improves over DUNE. DUNE alone strongly rejects the wrong ordering (χ²_min = 485.853) and already constrains the (δCP, φ21) degeneracy effectively. The statement that 'neither experiment resolves individually' is incorrect for DUNE. The complementarity narrative — that the combination exploits 'qualitatively different sensitivity' to break degeneracies — is not supported by the numbers: HK contributes negligible additional constraining power on the (δCP, φ21) plane beyond what DUNE already provides. The paper is transparent about this in the body text (Section 5, discussion of panel c), but the abstract and conclusions frame the result as a synergistic improvement, which the data do not support. A secondary concern: the entire quantitative claim is evaluated at a single true parameter point (δCP = −π/2, φ21 = 0, |α21| = 0.01); the degeneracy structure and reduction factors could differ substantially for other true δCP values, especially near 0 or π where CP sensitivity vanishes.","agreement_with_reader":"partial"},"referee_report":{"model":"glm-5.2","summary":"This paper investigates the impact of non-unitary leptonic mixing on CP violation and mass ordering measurements at future long-baseline experiments (DUNE and Hyper-Kamiokande). Using a custom GLoBES probability engine, the authors evaluate the fake-to-genuine CP asymmetry ratio, CP violation discovery sensitivity, and hierarchy-CP-non-unitarity degeneracies in the (δCP, φ21) parameter space. The authors find that while fake CP violation is a minor effect near the oscillation maximum, it can dominate the genuine signal in specific intermediate energy windows. They also analyze the combined DUNE+Hyper-Kamiokande parameter space, concluding that the combination substantially suppresses degeneracies.","tokens_in":18810,"tokens_out":843,"duration_ms":296040,"significance":"The paper provides a well-structured simulation study using standard GLoBES tools. The quantification of the fake-to-genuine CP asymmetry ratio across different energy windows (Table 1) is a clear and falsifiable result. The identification of specific intermediate energy regions where fake CP violation dominates is a useful phenomenological observation for experimental collaborations. The chi-square formalism and marginalization procedures are standard and correctly applied.","major_comments":[{"comment":"§5, discussion of panel (c) and Abstract/Conclusions: The abstract states that the combined analysis reduces the parameter space 'by a factor of 7 at 1σ and ~16 at 2σ–3σ, substantially suppressing the degeneracy that neither experiment resolves individually.' However, the body text reveals that at 1σ, the combined area (0.010π²) is 'identical to DUNE alone,' and at 3σ, the combined area (0.059π²) is actually larger than DUNE alone (0.049π²). The 'factor of 16' is the ratio of Hyper-K's allowed region to the combined region, measuring how much worse Hyper-K is than DUNE, not how much the combination improves over DUNE. Furthermore, DUNE's χ²_min = 485.853 shows it already strongly rejects the wrong ordering independently. The claim that 'neither experiment resolves individually' is incorrect for DUNE. The abstract and conclusions must be revised to accurately reflect that DUNE alone is提供s","section":null}],"minor_comments":[{"comment":"§2, Eq. (4): The text defines the non-unitary parameter as α_μe = |α_μe|e^{iφ_μe}, but the rest of the manuscript (including the abstract and §5) refers to it as α_21 and φ_21. Please unify the notation for consistency.","section":null},{"comment":"§5, Eq. (20): The text block immediately preceding Eq. (20) is duplicated ('To map these degeneracies quantitatively, we compute...'). Please remove the repetition.","section":null},{"comment":"§4.1: The text mentions 'NuFit 6.0 [55]' but the reference list cites 'NuFit-6.0' as JHEP 12 (2024) 216. Please verify that the citation matches the intended source.","section":null},{"comment":"§7, Figure 5: The text refers to 'dotted curves' for the non-unitarity sensitivities in panel (a), but the caption mentions 'dashed curves.' Please ensure the description matches the figure.","section":null}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern regarding the framing of the 'factor of 16' improvement is well-founded. The paper's own data in §5 clearly shows that DUNE provides the dominant constraint, and the combination does not improve upon DUNE alone at 1σ or 3σ. The abstract and conclusions significantly overstate the synergistic improvement. This is a load-bearing issue for the paper's central narrative and must be corrected before publication can be recommended."},"author_rebuttal":{"model":"glm-5.2","summary":"The referee correctly identifies that the abstract and conclusions overstate the improvement from combining DUNE and Hyper-Kamiokande. The body text shows DUNE alone already strongly rejects the wrong ordering (χ²_min = 485.853), and the combined allowed region at 1σ is identical to DUNE alone while at 3σ it is marginally larger. The 'factor of 7–16' measures improvement over Hyper-K alone, not over DUNE. We will revise the abstract and conclusions to accurately characterize DUNE's individual capability and the true nature of the combined improvement.","responses":[{"response":"The referee is entirely correct on all three points, and we will revise the manuscript accordingly. (1) The phrase 'neither experiment resolves individually' is inaccurate for DUNE. As the body text itself states, DUNE's χ²_min = 485.853 confirms strong rejection of the wrong mass ordering even after marginalization over non-unitary parameters. DUNE does substantially constrain the hierarchy–CP–non-unitarity degeneracy on its own; it does not fully resolve it (the 3σ allowed region remains non-trivial at 0.049π²), but the claim that it fails to resolve the degeneracy is overstated. (2) The 'factor of 7' and 'factor of 16' figures are computed as the ratio of Hyper-Kamiokande's allowed area to the combined area, not as the improvement over DUNE. At 1σ, the combined area (0.010π²) is identical to DUNE's, so the improvement over DUNE is a factor of 1, not 7. At 3σ, the combined area (0.059π²) is actually 1.2× larger than DUNE's alone (0.049π²), meaning the combination does not improve upon DUNE at that confidence level—it slightly worsens the area due to the addition of Hyper-K's poorly constrained φ₂₁ band overlapping DUNE's contour edge, as explained in the body text. (3) The abstract and conclusions will be revised to state that DUNE alone provides strong constraints on the degeneracy through its matter-enhanced oscillations, that the combination with Hyper-Kamiokande provides complementary constraints that are most beneficial at intermediate confidence levels (2σ), and that the factors of 7–16 quantify the improvement relative to Hyper-Kamiokande alone, not relative to DUNE. We will also add an explicit statement that the combined 3σ area is marginally larger than DUNE's alone, with the physical explanation already present in the body text. The conclusions in §6, which","revision_made":"yes","referee_comment":"§5, discussion of panel (c) and Abstract/Conclusions: The abstract states that the combined analysis reduces the parameter space 'by a factor of 7 at 1σ and ~16 at 2σ–3σ, substantially suppressing the degeneracy that neither experiment resolves individually.' However, the body text reveals that at 1σ, the combined area (0.010π²) is 'identical to DUNE alone,' and at 3σ, the combined area (0.059π²) is actually larger than DUNE alone (0.049π²). The 'factor of 16' is the ratio of Hyper-K's allowed region to the combined region, measuring how much worse Hyper-K is than DUNE, not how much the combination improves over DUNE. Furthermore, DUNE's χ²_min = 485.853 shows it already strongly rejects the wrong ordering independently. The claim that 'neither experiment resolves individually' is incorrect for DUNE. The abstract and conclusions must be revised to accurately reflect that DUNE alone is [s"}],"tokens_in":18232,"tokens_out":796,"duration_ms":113889,"standing_objections":[]},"desk_editor":{"model":"glm-5.2","letter":"Short version: the paper does a competent GLoBES simulation of non-unitarity effects at DUNE and Hyper-K, and the fake-to-genuine CP asymmetry ratio in intermediate energy windows is a genuinely useful quantitative result. But the framing of the combined-analysis improvement is misleading, and the stress-test concern about it lands hard on the numbers in the paper itself. The paper deserves a referee, but the abstract and conclusions need correction before publication. Here is my reasoning. What is actually new and well done: the energy-dependent fake-to-genuine CP asymmetry ratio (Table 1) is a clean, useful result. The finding that the fake contribution exceeds the genuine signal at ~130% in the 1.5–1.6 GeV window, while remaining below 5% at oscillation maximum, is a concrete quantitative statement that experiment analysts can use directly. The GLoBES setup, chi-square formalism, and marginalization over |α21|, sin²θ23, and |Δm²31| are standard and correctly applied. The decomposition of A_CP into PMNS, non-unitarity, and matter components is pedagogically clear. The soft spots, in order of importance: First, the 'factor of 16' claim. The stress-test note is correct. The paper's own numbers show that at 1σ the combined area (0.010π²) is identical to DUNE alone, and at 3σ the combined area (0.059π²) is actually larger than DUNE alone (0.049π²). The factor of 16 is the ratio of Hyper-K's allowed region to the combined region — it measures Hyper-K's weakness, not a synergistic improvement. DUNE alone rejects the wrong ordering with χ²_min = 485.853 and already constrains the (δCP, φ21) degeneracy effectively. The abstract's claim that the combination 'substantially suppresses the degeneracy that neither experiment resolves individually' is wrong for DUNE — DUNE resolves it individually. The body text (Section 5, panel c discussion) is transparent about this, but the abstract and conclusions are not. This is a framing problem, not a calculation error, but it is load-bearing for the paper's claimed contribution. Second, the entire quantitative analysis is evaluated at a single true parameter point (δCP = −π/2, φ21 = 0, |α21| = 0.01). The degeneracy structure and reduction factors could look very different for other δCP values, especially near 0 or π where CP sensitivity vanishes. The paper does not discuss this limitation. Third, only α21 is considered non-zero. This is a reasonable starting point but the paper should acknowledge that multiple off-diagonal elements could introduce additional degeneracies. Minor: there is a duplicated paragraph in Section 5 that needs proofreading. Who this is for: neutrino phenomenologists working on DUNE/Hyper-K sensitivity studies. The fake-to-genuine ratio tables and the degeneracy contour plots are useful reference material for that audience. Recommendation: send to a serious referee. The simulation work is sound and the intermediate-energy-window result is worth publishing. But the referee should require the authors to correct the abstract and conclusions to accurately describe what the combination achieves relative to DUNE alone, and to discuss the single-benchmark-point limitation. The paper is a solid contribution with a framing problem, not a broken study.","headline":"The paper's headline 'factor of 16' degeneracy reduction is misleading — it measures how much worse Hyper-K is than DUNE, not how much the combination improves over DUNE. The real result is that DUNE alone already does the heavy lifting.","tokens_in":19339,"tokens_out":810,"would_cite":false,"duration_ms":125409,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["14.60.Pq","14.60.St","13.15.+g"],"model":"glm-5.2","headline":"Combined DUNE and Hyper-K break fake CP violation degeneracy","keywords":["neutrino oscillation","non-unitarity","CP violation","PMNS matrix","DUNE","Hyper-Kamiokande","mass ordering","parameter degeneracy"],"falsifier":"If future DUNE and Hyper-Kamiokande data, analyzed jointly, show that the (δ_CP, φ_21) parameter space remains degenerate at a level inconsistent with the predicted factor-of-7 to ~16 reduction, this would indicate either that the minimal non-unitarity framework is insufficient or that the complementarity between the two baselines does not constrain the degeneracy as strongly as the simulation predicts.","tokens_in":18644,"feed_emoji":"","tokens_out":1252,"duration_ms":116818,"temperature":0.7,"pith_summary":"This paper investigates whether deviations from unitarity in the neutrino mixing matrix — arising from heavy neutral leptons in seesaw models — could produce spurious CP-violating signals at future long-baseline experiments DUNE and Hyper-Kamiokande. The authors decompose the total neutrino-antineutrino CP asymmetry into three components: genuine CP violation from the standard Dirac phase δ_CP, fake CP violation from a non-unitary phase φ_21, and matter-induced asymmetry. They show that the fake contribution can exceed the genuine one in specific intermediate energy windows (reaching ~130% of the genuine signal around 1.5–1.6 GeV at both experiments), meaning an observed CP asymmetry in those bins could be dominated by new physics rather than the standard phase. The central result is that while neither experiment alone can disentangle these effects — Hyper-Kamiokande lacks the matter-effect lever arm to constrain the non-unitary phase, and even DUNE retains residual degeneracy — the two experiments combined reduce the allowed (δ_CP, φ_21) parameter space by a factor of 7 at 1σ and ~16 at 2σ–3σ when tested against the wrong mass ordering. This improvement arises structurally from the complementary baselines (1300 km vs 295 km) and matter-potential regimes, not merely from increased statistics.","feed_headline":"Fake CP violation in neutrino beams meets its match in combined data","feed_subtitle":"Non-unitary mixing can mimic genuine CP violation at DUNE and Hyper-K, but analyzing both experiments together shrinks the ambiguous zone by","key_machinery":"Non-unitary PMNS matrix","core_discovery":"The paper identifies that non-unitary leptonic mixing, parameterized by a single off-diagonal element α_21 = 0.01 e^{iφ_21}, generates CP asymmetries that are indistinguishable from genuine PMNS CP violation in the oscillation-maximum energy region (fake contribution below 5% of genuine signal) but dominate it in specific intermediate energy windows where the genuine asymmetry is locally suppressed (ratio exceeding 120% at ~1.5–1.6 GeV). The key quantitative finding is that the combined DUNE + Hyper-Kamiokande chi-square analysis suppresses the hierarchy–CP–non-unitarity degeneracy — the three-way confusion between mass ordering, δ_CP, and φ_21 — by a factor of 7 (1σ) to ~16 (2σ–3σ) relative","pith_inferences":["The analysis uses a single non-zero off-diagonal parameter α_21; if multiple non-unitary elements (e.g., α_31, α_32) and their phases are simultaneously non-zero, the degeneracy structure could become significantly more complex and the combined DUNE+Hyper-K constraint may weaken.","The energy windows where fake CP violation dominates (~1.5–1.6 GeV) suggest that a targeted spectral analysis — weighting or excluding those bins — could improve the robustness of δ_CP extraction, an optimization strategy the paper motivates but does not fully implement.","The structural complementarity between long and short baselines implies that a third experiment at an intermediate baseline (e.g., ~500–800 km) could provide additional leverage on the non-unitary phase, though the marginal gain may be small given the already strong DUNE+Hyper-K combination."],"forward_implications":["Future CP violation discovery claims from DUNE or Hyper-Kamiokande alone should be interpreted with caution in energy bins around 1.5–1.6 GeV, where fake non-unitarity effects can dominate the asymmetry.","The combined analysis strategy provides a concrete experimental roadmap: DUNE's long-baseline matter effects constrain the non-unitary phase φ_21, while Hyper-Kamiokande's near-vacuum oscillations provide an independent cross-check on δ_CP, and the intersection of their constraints breaks the three-way degeneracy.","If the combined data show a discrepancy between the δ_CP values inferred from the oscillation-maximum region and the intermediate-energy windows, this could serve as a diagnostic for non-unitary mixing at a level below the current α_21 = 0.01 benchmark.","The ~65% degradation in Hyper-Kamiokande's standalone CP-discovery sensitivity under non-unitarity suggests that near-detector constraints on α_21 will be essential for interpreting its results independently."],"fun_headline_variants":["Non-unitary mixing fakes CP violation in intermediate energy windows","DUNE and Hyper-K combined shrink CP–non-unitarity degeneracy by 16x","Fake CP asymmetry exceeds genuine signal at 1.5 GeV in neutrino oscillations","Combined DUNE and Hyper-K data isolate genuine leptonic CP violation","Non-unitary PMNS mixing mimics CP violation near oscillation maximum"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The analysis considers only one non-unitary parameter (α_21) to be non-zero, with a fixed magnitude of 0.01 and a single associated phase. Realistic seesaw models could have multiple non-zero off-diagonal elements and additional phases, introducing degeneracies not captured by this single-parameter benchmark.","fun_headline_variants_meta":{"raw":{"variants":["Non-unitary mixing fakes CP violation in intermediate energy windows","DUNE and Hyper-K combined shrink CP–non-unitarity degeneracy by 16x","Fake CP asymmetry exceeds genuine signal at 1.5 GeV in neutrino oscillations","Combined DUNE and Hyper-K data isolate genuine leptonic CP violation","Non-unitary PMNS mixing mimics CP violation near oscillation maximum"]},"model":"glm-5.2","effort":"high","cost_usd":0.0,"raw_usage":{"total_tokens":855,"prompt_tokens":753,"completion_tokens":102,"prompt_tokens_details":null},"tokens_in":753,"tokens_out":102,"duration_ms":53097,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-08T16:18:10.389784+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"If future DUNE and Hyper-Kamiokande data, analyzed jointly, show that the (δ_CP, φ_21) parameter space remains degenerate at a level inconsistent with the predicted factor-of-7 to ~16 reduction, this would indicate either that the minimal non-unitarity framework is insufficient or that the complementarity between the two baselines does not constrain the degeneracy as strongly as the simulation predicts.","supporting_citations":[],"review_version":1}