{"id":"11b16666-256c-4024-b064-56ec0353521c","arxiv_id":"2603.01031","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Projected GLoBES sensitivities show DUNE constrains the non-unitarity parameters α11 and |α21| better, while P2SO wins on α33 (and marginally α22); non-unitarity also distorts mass-hierarchy, octant, and CP-violation sensitivities.","lead":"This paper simulates how two planned neutrino experiments — DUNE (1300 km) and P2SO (2595 km, Protvino to a denser Super-ORCA detector) — would constrain deviations from unitarity of the neutrino mixing matrix. It finds the two experiments are complementary: DUNE would bound α11 and |α21| more tightly, while P2SO's long baseline and stronger matter effects would better constrain α22 and α33.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"P2SO's α33 sensitivity appears to be an artifact: under the correct non-unitary matter evolution, α33 does not enter the ν_μ→ν_e/ν_μ→ν_μ channels that the simulation analyzes.","rationale":"The reader identified the undocumented P2SO simulation inputs as the weakest assumption, but a more fundamental physics issue is at play. The standard treatment of non-unitary mixing in matter (Ref. [25]) shows that α33, α31, and α32 do not affect the ν_μ→ν_e and ν_μ→ν_μ channels, neither in vacuum nor in matter, because the matter potential in the mass basis depends only on the electron row of the mixing matrix (α11 times the standard electron row). α33 enters only through tau-related amplitudes. The paper's sensitivity curves for α33 (Fig. 1) and its interpretation ('contributes in matter') imply the simulation used a flavor-basis Hamiltonian with N replacing U directly, which introduces a spurious α33 dependence. This would invalidate the headline claim that P2SO improves the current α33 bound and the stated complementarity of DUNE and P2SO. The issue is more load-bearing than the simulation input details because it attacks the physics of the central result, not just its reproducibility. If the authors can demonstrate their GLoBES implementation follows the correct mass-basis formalism or explicitly includes tau appearance, the claim could be salvaged; but the manuscript as written does not provide such evidence and explicitly attributes α33 sensitivity to matter effects in the standard channels, which is inconsistent with the accepted formalism. Therefore the current version should be rejected pending a corrected implementation or a clarified tau-inclusive analysis.","tokens_in":18372,"tokens_out":37615,"duration_ms":327129,"concrete_test":"Recompute the α33 sensitivity for P2SO and DUNE using the correct non-unitary matter evolution (mass-basis H_m = M/(2E) + N† V_f N, amplitude A = N e^{-iH_m L} N†) with only ν_e appearance and ν_μ disappearance samples, as described in Sec. IV. If the χ² curves in Fig. 1 (lower-right panel) become flat (no exclusion), the paper's α33 claim is an artifact. Alternatively, add a τ-appearance sample and check whether the bound survives; that would confirm the mechanism and justify the claim.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's headline P2SO advantage on α33 rests on the claim (Sec. VI.A) that 'α33 does not enter the vacuum oscillation probabilities, but contributes in matter,' referring to the simulated ν_μ→ν_e and ν_μ→ν_μ channels. In the standard non-unitary formalism (Blennow et al. 2017, Ref. [25]), the correct matter evolution is governed by the mass-basis Hamiltonian H_m = M/(2E) + N† V_f N, with oscillation amplitudes A_αβ = (N e^{-i H_m L} N†)_{βα}. For the triangular parametrization with α31=α32=0, N_{e i}=α11 U_{e i}, N_{μ i}=α21 U_{e i}+α22 U_{μ i}, and V_m = |α11|^2 V_CC U_e U_e†. Neither H_m nor the e/μ projections contain α33; hence P_μe and P_μμ are completely independent of α33 in vacuum and in matter. α33 is only accessible through ν_τ appearance (P_μτ/P_eτ). Since the paper's simulation and diagnostics (Figs. 5 and 7) are based on P_μe and P_μμ, and no τ sample is described, the α33 sensitivity in Fig. 1 can only arise from an incorrect matter Hamiltonian (e.g., replacing U by N in the flavor-basis evolution H = U M U† + V, which introduces spurious α33 dependence through the (e,τ)/(μ,τ) entries of N M N†). If so, the claimed P2SO improvement of the α33 bound is an artifact, and the central complementarity claim fails.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript uses GLoBES to simulate the upcoming P2SO and DUNE long-baseline experiments and derives projected constraints on the non-unitarity (NU) parameters α11, α22, α33, and |α21| in the triangular parametrization. It claims that DUNE will give stronger bounds on α11 and |α21|, while P2SO will give stronger bounds on α22 and α33, with DUNE (P2SO) improving the current bound on α11 (α33). It further studies correlations with standard oscillation parameters and quantifies the impact of NU on mass-hierarchy, octant, and CP-violation sensitivities. The methodology is mostly field-standard: Poisson likelihood with pull systematics, NuFIT 6.0 inputs, official DUNE TDR GLoBES files, and published NU probability formulas. The internal diagnostics in Figs. 5 and 7 are careful and valuable. However, the central α33 claim is inconsistent with the standard non-unitary matter evolution, and the P2SO simulation inputs are not quantified. These issues make the main conclusion unsupported as presented.","tokens_in":18588,"tokens_out":25615,"duration_ms":272698,"significance":"If the results were correct, the paper would provide a useful comparison of two complementary long-baseline experiments for NU searches and would quantify how NU distorts standard precision measurements. The authors deserve credit for explicitly investigating the origin of the kinks and dips in their sensitivity curves rather than leaving them unexplained, and for using external global-fit inputs. That said, the headline complementarity claim rests on the α33 sensitivity of P2SO, which appears to be an artifact of an incorrect matter Hamiltonian. Because the abstract and the conclusions rest on this claim, the significance of the paper cannot be assessed as stated; a corrected version could be valuable, but the current central result is not reliable.","major_comments":[{"comment":"The α33 sensitivity is not predicted by the standard non-unitary matter formalism. With the triangular parametrization and α31=α32=0, the matter Hamiltonian in the mass basis is H_m = M/(2E) + N† V_f N = M/(2E) + |α11|² V_CC U_e U_e†, and the amplitudes are (N e^{-iH_m L}N†)_{βα}. For β,α=e,μ, neither N nor H_m contains α33, so P_μe and P_μμ are independent of α33 in vacuum and in matter. The statement that α33 'does not enter the vacuum oscillation probabilities, but contributes in matter' is therefore incorrect for the channels analyzed. No ν_τ appearance sample is described in Secs. IV–V, and the diagnostics in Figs. 5 and 7 use only P_μe/P_μμ. I conclude that the α33 curves in Fig. 1, the α33 rows of Table II, and all α33-dependent sensitivity results are artifacts of the probability engine (apparently replacing U by N in the flavor-basis matter Hamiltonian). The claim that P2SO impr","section":"VI.A, Fig. 1, Table II"},{"comment":"The P2SO projections are not reproducible from the information given. Detector response, energy resolution, efficiencies, background rates, systematic pulls, and matter density profile are not specified; they are only delegated to refs [51,58–61], several of which are co-authored by the present authors. The only quantitative new ingredient is 'Super-ORCA detector 10 times more dense.' Because the P2SO advantage on α22 (and the purported one on α33) depends on these inherited assumptions, the reader cannot judge the robustness of the results. A table listing the simulated channels, signal/background efficiencies, systematic uncertainties, and matter profile should be added.","section":"IV.A, V"},{"comment":"The column labeled 'six dof' is misleading. In the text, α31 and α32 are fixed to zero and only four NU parameters (plus φ21) are varied. Thus the marginalized bounds are four-degree-of-freedom bounds, not six-parameter marginalized bounds. The comparison with the current limits from [36] is therefore not apples-to-apples. Either include α31 and α32 in the marginalization, or rename the column and explicitly justify fixing them.","section":"Table II, Sec. VI"}],"minor_comments":[{"comment":"The symbol 'cos(I_123)' is undefined. It should presumably be cos(δCP + Δm²31 L/(4E)) or an explicitly defined phase.","section":"Eq. (11)"},{"comment":"The column structure of Table II is hard to read. Add explicit column headers in the caption so that the one-dof and six-dof entries for DUNE and P2SO are unambiguous.","section":"Table II"},{"comment":"The dashed curves for the α33 panel, corresponding to θ23 fixed at its true value, are not explained in the caption. The caption should identify all curves.","section":"Fig. 1"},{"comment":"The phrase 'assuming NU does not exist in Nature' is imprecise. The simulations use benchmark true values with αii=1 and αij=0; this is a choice of true parameters, not an assumption about data.","section":"Sec. VI.B"},{"comment":"The paper should state explicitly whether ν_τ charged-current events are included in the GLoBES simulation. If they are not, α33 cannot be constrained by the channels used; if they are, the channel list and efficiencies should be documented.","section":"Secs. IV–V"}],"recommendation":"reject","confidential_remarks":"The main technical issue is the α33 artifact, which invalidates the headline claim. I have no reason to question the authors' intentions, but the dependence of the P2SO simulation on several co-authored references without quantitative details amplifies the reproducibility concern and should be addressed in any resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The first thing you should know: the stress-test note is right, and it is a load-bearing flaw. In the standard non-unitary formalism the paper itself cites (Blennow et al., Ref [25]), α33 does not enter P_μe or P_μμ, not even in matter. With α31=α32=0, the electron row of N is α11 U_e, so the matter Hamiltonian in the mass basis, H_m = M/(2E) + N† V N, becomes M/(2E) + |α11|^2 V_CC U_e† U_e. No α33. The μ and e projections of N also have no α33. So a correct calculation of ν_μ→ν_e and ν_μ→ν_μ gives zero α33 dependence in vacuum and matter. The paper's Sec. VI.A says the opposite ('α33 does not enter vacuum probabilities, but contributes in matter'), which means the simulation is almost certainly evolving with an ad-hoc flavor-basis Hamiltonian like N M N† + V that mixes the τ sector through the kinetic term. That would generate exactly the spurious α33 sensitivity seen in Fig. 1. This is not a minor point: it is the paper's main new result, and it invalidates the complementarity claim.\n\nCredit where due: this is the first NU study for the upgraded P2SO configuration (Super-ORCA, 450 kW beam), and the scans with simultaneous NU parameters plus the |α21|–φ21 and δ_CP–φ21 correlations are new relative to Ref [50]. The internal diagnostics in Figs. 5 and 7 are careful attempts to explain kinks for α11 and α22, and the GLoBES framework with DUNE TDR files and NuFIT 6.0 inputs is standard.\n\nThe other problems are real but smaller. The P2SO detector response, systematics, and matter profile are inherited from self-authored refs [51, 58–61] and never quantified, so the P2SO numbers aren't independently reproducible. 'Six dof' is a misnomer—α31 and α32 are dropped. The abstract compares one-dof projections to six-dof current bounds without flagging the mismatch. And no code or parameter files are provided. None of these is fatal if fixed, but combined with the α33 error they describe a paper that overstates its case.\n\nThe α11 and |α21| comparisons with DUNE probably survive, since those parameters enter the vacuum probabilities. The α22 advantage is marginal (0.002 difference) and may shift under a corrected matter treatment.\n\nI'd send this to a serious referee: the error is subtle and worth catching in writing, and the paper has salvageable content if the authors redo the calculation with the correct evolution and remove the α33 claims. But I would not cite it now, and the reader's report under-weights the central problem.","headline":"The paper's headline claim—P2SO's sensitivity to α33 and its improved bound—is likely an artifact of an incorrect matter Hamiltonian in the GLoBES implementation; the rest is a competent but incremental configuration study.","tokens_in":19342,"tokens_out":12200,"would_cite":false,"duration_ms":120619,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["14.60.Pq","14.60.St"],"model":"deepseek-v4-flash","headline":"Two future long-baseline neutrino experiments would split the job of testing whether the neutrino mixing matrix is truly unitary.","keywords":["neutrino oscillations","non-unitarity","PMNS matrix","P2SO","DUNE","long-baseline experiments","matter effects","CP violation"],"falsifier":"Measure the actual P2SO detector performance (density, efficiency, background rates) and rerun the α33 sensitivity calculation; alternatively, obtain an independent, matter-free measurement of α33 from a short-baseline disappearance channel or a different experimental setup and compare it with the P2SO-projected bound. If the real detector performs noticeably worse than the 10×-ORCA assumption, or if a matter-free α33 measurement disagrees with the P2SO projection, the paper's central complementarity claim would be falsified.","tokens_in":18035,"feed_emoji":"⚛️","tokens_out":4778,"duration_ms":46098,"temperature":0.7,"pith_summary":"This paper asks whether the neutrino mixing matrix is exactly unitary, and how the two next-generation long-baseline experiments—DUNE and P2SO—could find out. Treating non-unitarity (NU) model-independently through a triangular parametrization of the mixing matrix, it finds that DUNE and P2SO probe different NU parameters: DUNE constrains α11 and |α21| more tightly, while P2SO's longer baseline and stronger matter effects give it a superior handle on α22 and especially α33, a parameter that is invisible in vacuum oscillations. The paper also shows that if NU is real, it distorts the apparent sensitivities to mass hierarchy, the θ23 octant, and CP violation, so the flagship measurements of the coming decade could be biased unless NU is included in the fit. A sympathetic reader would care because the two experiments are often treated as interchangeable precision machines; this paper argues they are instead two halves of one measurement.","feed_headline":"DUNE and P2SO would split the hunt for neutrino non-unitarity","feed_subtitle":"Long-baseline matter effects give P2SO a unique handle on α33; DUNE leads on α11 and |α21|.","key_machinery":"The triangular parametrization N = N_NP U, where N_NP is a lower-triangular matrix carrying three real diagonal parameters α11, α22, α33 and complex off-diagonal parameters αij; the paper focuses on α11, α22, α33, and the off-diagonal pair (|α21|, φ21). The analytic oscillation probabilities (Eqs. 7 and 10) show that α11 enters only the νe appearance channel, α22 enters both appearance and disappearance, and α33 enters neither vacuum probability—only matter effects. P2SO's 2595 km baseline and denser detector amplify matter effects, which is the mechanism behind its α33 advantage, while DUNE's larger statistics and beam configuration drive its superior α11 and |α21| bounds.","core_discovery":"The central claim is that DUNE and P2SO have complementary sensitivity to non-unitarity of the leptonic mixing matrix: DUNE gives stronger bounds on the diagonal parameter α11 and the off-diagonal magnitude |α21|, while P2SO gives stronger bounds on α22 and α33, with the α33 advantage driven by P2SO's longer baseline (2595 km) and stronger matter effects. Within current allowed ranges, the paper finds that DUNE can improve the existing lower bound on α11 and P2SO can improve the existing lower bound on α33. It further shows that the presence of NU alters the experiments' ability to determine the mass hierarchy, the octant of θ23, and the CP-violating phase δCP, sometimes increasing and somet","pith_inferences":["A combined fit of DUNE and P2SO with all six NU parameters free would likely sharpen both α11 and α33 bounds beyond either experiment individually, because the two experiments' strongest constraints are nearly orthogonal in parameter space.","Because α33 enters only through matter effects, P2SO's α33 bound carries a direct systematic dependence on the assumed Earth density profile along 2595 km; the paper does not quantify this, so the real-world bound could be looser than quoted.","The 'six dof' scan still omits α31 and α32, so the quoted bounds are not full six-parameter results; reinserting those parameters with current global constraints could shift the allowed regions.","A natural testable extension is to scan over the assumed Super-ORCA detector density (the paper uses 10× ORCA); if the real density or background rejection differs, the relative ordering of DUNE and P2SO on α22 and α33 could change."],"forward_implications":["DUNE should be able to tighten the current bound on α11, while P2SO should tighten the current bound on α33; these are the two concrete improvements the paper claims.","If NU is present at currently allowed levels, mass-hierarchy, octant, and CP-violation sensitivities computed under strict unitarity will be biased—hierarchy sensitivity drops with α11, rises with α22, and octant and CPV sensitivities shift non-monotonically.","The bound on |α21| depends strongly on the phase φ21; marginalizing over φ21 weakens it, and CP-violation measurements must fit δCP and φ21 together rather than fixing the NU phase.","The unusual kink/dip structure in the α33 sensitivity curves is traced to degeneracy with θ23 and to matter effects; removing θ23 or using vacuum would erase those features.","The two experiments are complementary in NU parameter space, so a robust global picture requires combining both rather than relying on either alone."],"fun_headline_variants":["DUNE and P2SO split neutrino non-unitarity sensitivity by parameter","P2SO wins on α22, α33; DUNE on α11, |α21| in non-unitarity hunt","Longer baseline gives P2SO edge in neutrino non-unitarity probes","Complementary strengths: DUNE vs P2SO for non-unitarity","Neutrino non-unitarity: DUNE leads on α11, P2SO on α33"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire P2SO advantage, including the claimed α33 improvement, is computed for a specific assumed detector configuration—Super-ORCA ten times denser than ORCA, 450 kW beam, 4×10^20 POT/year, six-year run—with backgrounds and systematics imported from earlier studies by the same authors and never quantified in this paper; if the real detector's density, efficiency, or background rejection differs, the P2SO curves move and the α33 bound could slip below the current limit.","fun_headline_variants_meta":{"raw":{"variants":["DUNE and P2SO split neutrino non-unitarity sensitivity by parameter","P2SO wins on α22, α33; DUNE on α11, |α21| in non-unitarity hunt","Longer baseline gives P2SO edge in neutrino non-unitarity probes","Complementary strengths: DUNE vs P2SO for non-unitarity","Neutrino non-unitarity: DUNE leads on α11, P2SO on α33"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000398,"raw_usage":{"total_tokens":1946,"prompt_tokens":796,"completion_tokens":1150,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":540,"completion_tokens_details":{"reasoning_tokens":1031}},"tokens_in":540,"tokens_out":1150,"duration_ms":8752,"temperature":1.0,"reasoning_tokens":1031,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T19:47:13.342279+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the actual P2SO detector performance (density, efficiency, background rates) and rerun the α33 sensitivity calculation; alternatively, obtain an independent, matter-free measurement of α33 from a short-baseline disappearance channel or a different experimental setup and compare it with the P2SO-projected bound. If the real detector performs noticeably worse than the 10×-ORCA assumption, or if a matter-free α33 measurement disagrees with the P2SO projection, the paper's central complementarity claim would be falsified.","supporting_citations":[],"review_version":1}