{"id":"1e8d42c9-ee86-4baa-885f-e37ac17e8453","arxiv_id":"2501.16412","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A toy model where neutrino mass ordering flips with redshift reshapes the electron-neutrino part of the diffuse supernova neutrino background in an energy-dependent way, but the effect is below near-future experimental reach.","lead":"This paper asks whether neutrinos whose masses changed over cosmic time would leave a visible mark in the combined neutrino glow from all past supernovae. It finds the glow would change in an energy-dependent way, but current and near-future detectors cannot separate that change from ordinary astrophysical uncertainty.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The DSNB flux calculation uses Pee(z) with no energy dependence, while Eq. (5) and adiabaticity are energy-dependent; the predicted spectral distortion in Fig. 3 is therefore not yet quantitatively established.","rationale":"I read the paper as a deliberately toy-model demonstration that a redshift-dependent mass ordering can leave an energy-dependent imprint on the DSNB. The two ingredients are the redshift-integrated flux formula and the SN survival probability. The numerical method described in Sec. III is the appropriate place to include energy dependence, but the manuscript does not state whether the Schrodinger equation was solved at one energy, averaged over energy, or replaced by adiabatic-limit values. Because Eq. (5) makes the resonance density explicitly E-dependent and adiabaticity depends on E through Δm^2/(2E), the plotted Pee(z) cannot be a complete input to Eq. (3). This is exactly the concern the reader identified. I do not think it invalidates the paper: the central claim is qualitative, the authors flag that the signal is below near-future sensitivity, and no fits or quantitative claims beyond the toy model depend on the exact shape. But the title-level claim 'energy-dependent modification' is not rigorously established unless the calculation is repeated with Pee(E(1+z),z) or the approximation is justified. Hence the CONDITIONAL verdict remains appropriate, with no adjustment.","tokens_in":10595,"tokens_out":7938,"duration_ms":82307,"concrete_test":"Recompute Pee(E,z) with the same presupernova density profile and mass parameterization for a grid of emitted energies E_emit = E_obs(1+z) spanning at least 2, 5, 10, 20, and 40 MeV, for z in 0-2, then integrate Eq. (3) with this Pee(E_emit,z) and compare the resulting flux ratios with the insets of Fig. 3. If any plotted ratio changes by more than ~20% at an energy above 10 MeV, the energy-independent Pee(z) approximation is load-bearing and the paper should explicitly caveat its spectral predictions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (3) evaluates the DSNB integrals with Pee(z) only. The authors state in Sec. III that Pee is obtained by numerically solving Schrodinger equations, but no energy variable is shown or described; Fig. 2 presents a single Pee(z) curve for each ordering. This is the load-bearing gap: the MSW resonance density in Eq. (5) scales as Δm^2/E, and the adiabaticity parameter also depends on E. For a SN at redshift z, the emitted neutrino energy is E(1+z), so the relevant survival probability is Pee(E(1+z), z). At a fixed z, partial adiabaticity will shift the location and width of the transitions between the |Ue3|^2, |Ue2|^2, and |Ue1|^2 plateaus as E changes. Ignoring this energy dependence changes the mixture of primary ν_e and ν_x fluxes contributing to Φ_νe at each observed energy, so the flux ratios in Fig. 3 and the claim of a distinctive energy-dependent distortion rest on an unstated approximation. The qualitative idea may survive, but the quantitative shape is not demonstrated without reporting or averaging Pee(E,z).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes that neutrino masses may have evolved with redshift and studies the imprint of such a dynamical mass spectrum on the diffuse supernova neutrino background (DSNB). After giving the standard DSNB flux formulae, the authors introduce a toy parametrization in which each mass eigenstate transitions from its present-day value to a high-redshift value at a redshift z_i with width B_i. They compute electron-neutrino survival probabilities inside supernovae, both adiabatically and via numerical solution of the Schr\\\"odinger equation, and then evaluate the DSNB electron-neutrino flux for benchmark normal-ordering and inverted-ordering cases. They find energy-dependent modifications of the DSNB spectrum and argue that these modifications are distinguishable from astrophysical uncertainties, while also acknowledging that current experimental and astrophysical uncertainties prevent a definitive detection.","tokens_in":10845,"tokens_out":3394,"duration_ms":36508,"significance":"If established, the idea is timely and interesting: the DSNB could serve as a complementary probe of redshift-dependent neutrino properties, and the claim of a non-normalization energy-dependent signature is a concrete, falsifiable prediction. The paper is honest in presenting a toy model with hand-picked benchmark parameters and does not overclaim a connection to a specific fundamental theory. It also correctly emphasizes that cosmological mass-sum bounds are insensitive to the dynamical history envisaged here. However, the central quantitative claim rests on an energy-averaged or energy-independent survival probability in Eq. (3), and the paper does not yet demonstrate the energy dependence claimed in the abstract and conclusion. The qualitative idea is credible, but the quantitative shape of the predicted distortion is not established as written.","major_comments":[{"comment":"The DSNB flux in Eq. (3) uses a survival probability Pee(z) that depends only on redshift, while the MSW resonance density in Eq. (5) and the adiabaticity of the resonance both depend on neutrino energy. For a supernova at redshift z contributing to the observed energy E, the emitted neutrino energy is E(1+z), so the relevant probability is Pee(E(1+z), z). The manuscript does not state that Pee is energy-independent, nor does it show that the numerical Schr\\\"odinger-equation solutions reported in Sec. III are averaged over energy or evaluated at a representative energy. Without this information, the sharp Pee(z) steps in Fig. 2 and the resulting flux ratios in Fig. 3 are not quantitatively justified.","section":"Eq. (3) and Sec. III"},{"comment":"The antineutrino flux in Eq. (3b) is written with the same Pee(z) as the neutrino flux, but Fig. 2 shows that the antineutrino survival probability differs from the neutrino one. The text elsewhere correctly distinguishes Pee and P_ee (e.g., Eq. (7)), so Eq. (3b) should use P_ee(z), and Eq. (3c) should contain the combination Pee(z)+P_ee(z) rather than Pee(z)+Pee(z). As written, the formalism is internally inconsistent and the numerical results cannot be reproduced.","section":"Eq. (3b) and Eq. (3c)"},{"comment":"The claim that the predicted features are distinguishable from astrophysical uncertainties is supported only by varying the CCSN rate within one orange band. Supernova neutrino spectral uncertainties, black-hole-failed-supernova fractions, and star-formation-rate uncertainties are not propagated. The authors themselves state in Sec. V that current spectral-shape uncertainty makes direct detection beyond reach, which weakens the abstract's statement that the features are distinguishable from significant astrophysical uncertainties. The paper should either soften that claim or present a quantitative comparison against the full set of state-of-the-art DSNB uncertainties.","section":"Sec. IV, Fig. 3"}],"minor_comments":[{"comment":"The summary abstract and the abstract printed at the beginning of the full text differ in the final claim: one says current spectral-shape uncertainty makes detection beyond reach, while the other says the features are distinguishable from astrophysical uncertainties. The authors should harmonize these statements in the published version.","section":"Abstract"},{"comment":"The numerical calculation is described only as solving Schr\\\"odinger-like equations; the initial conditions, the specific supernova density profile used from Ref. [56], and the energy grid or averaging procedure are not specified. Providing these details would also help address the major concern about the energy dependence of Pee.","section":"Sec. III"},{"comment":"The Hubble parameter H(z) is used without specifying the assumed cosmology; a short statement of the cosmological parameters used for the DSNB integration would improve reproducibility.","section":"Sec. II, Eq. (1)"},{"comment":"The text contains a stray paragraph break after 'However,' and uses 'alluring' where 'alluding' is intended. These should be corrected in proof.","section":"Sec. V"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and addresses a timely question. The main concern is not the idea itself, but the missing quantitative treatment of the energy dependence of Pee in the DSNB integral. This is fixable within the manuscript's scope by reporting Pee(E,z) and the averaging procedure. I would encourage the editor to request a revision rather than reject."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take on 2501.16412. The new thing is that they let each mass eigenstate evolve at its own redshift, so the mass ordering can flip in the past, and they compute the resulting DSNB electron-neutrino flux. That is a genuine generalization of de Gouvêa et al. 2022 [42], and the level-crossing logic is sound. The paper is honest about limitations: it says the effect is below near-future sensitivity and that the antineutrino flux (the main detection channel via inverse beta decay) is essentially unchanged, so the near-term experimental relevance is modest.\n\nCredit where due. The toy-model calculation is self-consistent at the adiabatic level, the figures are clear, and the authors do not oversell. They explicitly note that current spectral-shape uncertainties make direct detection impossible with present and near-future experiments. There is no fitting to the DSNB, so no circularity.\n\nThe main soft spot is the one flagged in the stress test: Eq. (3) uses Pee(z) with no energy dependence, but the MSW resonance density in Eq. (5) and adiabaticity both depend on E. The authors say they solve the Schrödinger equations numerically, but they never show or describe Pee as a function of energy. For a SN at redshift z, the emitted neutrino energy is E(1+z), so at fixed observed E the relevant survival probability should be Pee(E(1+z), z). If partial adiabaticity matters, the sharp steps in Fig. 2 would be smoothed and the spectral distortion in Fig. 3 would change shape. The qualitative idea—scrambling the ordering leaves an energy-dependent imprint—probably survives, but the quantitative shape is not yet demonstrated. This is not a fatal flaw, but it is load-bearing for the main claim.\n\nMinor: no code or data are provided, and the numerical procedure is described only vaguely. The benchmark parameters are hand-picked, which is fine for a toy model, but it means the results are illustrative rather than predictive.\n\nOverall: a transparent, honest toy-model study that deserves a serious referee. A referee should ask for a clear statement of Pee(E,z) and ideally the code or a reproducibility section. I would not cite it in my own near-term work, but it is a reasonable paper for a reading group discussion on DSNB probes of new physics.\n\nRecommendation: send to peer review.","headline":"A transparent toy-model extension of de Gouvêa et al. that generalizes to per-eigenstate mass evolution and can scramble the ordering, but the quantitative DSNB distortion relies on an unstated energy dependence in Pee.","tokens_in":11381,"tokens_out":1477,"would_cite":false,"duration_ms":14762,"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":"This paper argues that a redshift-dependent neutrino mass spectrum would imprint an energy-dependent distortion on the diffuse supernova neutrino background.","keywords":["dynamic neutrino masses","neutrino mass ordering","diffuse supernova neutrino background","MSW resonance","redshift-dependent neutrino properties","neutrino oscillations","supernova neutrinos"],"falsifier":"Compute $P_{ee}(E,z)$ from the paper's three-flavor Schr\\\"odinger evolution at neutrino energies of 5, 10, and 25 MeV for a fixed redshift where a mass splitting changes sign, such as $z\\simeq0.075$ in the normal-ordering benchmark; if the three values differ by more than a few percent, the $P_{ee}(z)$ simplification collapses and the predicted energy-dependent DSNB distortion would change shape.","tokens_in":10345,"feed_emoji":"🌌","tokens_out":5589,"duration_ms":55484,"temperature":0.7,"pith_summary":"Neutrino masses may have been different in the past. This paper argues that if the neutrino mass spectrum changed with cosmic time, so that the ordering today differs from the ordering at higher redshift, the diffuse supernova neutrino background (DSNB) would carry an energy-dependent distortion. The distortion comes from the survival probability of electron neutrinos $P_{ee}(z)$ taking different values at different redshifts, because the sign and size of the mass-squared differences control MSW resonances inside supernovae. The authors conclude that this is a direct probe of dynamical neutrino mass mechanisms, complementary to cosmological bounds, though current astrophysical spectral-shape uncertainties hide the effect from present and near-future detectors.","feed_headline":"Changing neutrino masses could distort the supernova neutrino background","feed_subtitle":"A redshift-dependent mass ordering would alter the DSNB spectrum's energy shape, not just its height, giving a direct probe of dynamic…","key_machinery":"The central object is the electron-neutrino survival probability $P_{ee}(z)$ inside a supernova, set by the redshift-dependent mass-squared differences $\\Delta m^2_{21}(z)$ and $\\Delta m^2_{31}(z)$. The sign of each $\\Delta m^2$ decides whether the MSW (Mikheyev-Smirnov-Wolfenstein) resonance occurs for neutrinos or antineutrinos, and its magnitude decides whether the crossing is adiabatic; both effects control which mass eigenstate leaves the star and hence the flux at Earth. The paper evaluates $P_{ee}$ by numerically solving the Schr\\\"odinger equation for neutrino propagation through a presupernova density profile at each redshift, then lets the masses evolve on the way to Earth. The parameterization $m_i(z)=m_i^\\infty + (m_i^0 - m_i^\\infty)/(1+(z/z_i)^{B_i})$ supplies the toy model for the redshift dependence.","core_discovery":"The central claim is that a redshift-dependent neutrino mass spectrum modifies the DSNB electron-neutrino flux not as a constant rescaling but through an energy-dependent change in shape. In their benchmark, at low energies ($E_\\nu \\lesssim 10$ MeV) the flux approaches the decoherence limit $\\sum_i |U_{ei}|^4 \\simeq 0.547$ times the unoscillated flux, because high-redshift neutrinos were nearly massless; at higher energies, where nearby supernovae dominate, the altered $P_{ee}$ changes the mixture of original $\\nu_e$ and $\\nu_x$ fluxes. The same physics produces a differently shaped modification depending on whether the ordering today is normal or inverted. The paper's conclusion is that such an energy-dependent feature is in principle separable from astrophysical uncertainties, but out of reach until those uncertainties are controlled.","pith_inferences":["Beyond the paper, a future DSNB spectrum with fine energy resolution could be used to discriminate a dynamic mass ordering from other new-physics distortions, such as neutrino decay or sterile-neutrino mixing, which also alter the DSNB energy shape.","A testable extension is to embed the toy $m_i(z)$ parameterization in a specific particle model, such as ultralight dark matter or a dark sector phase transition, and compute the model's predicted $P_{ee}(E,z)$ including energy-dependent adiabaticity; this would convert the demonstration into a quantitative prediction.","The paper's energy-independent $P_{ee}(z)$ assumption is worth checking directly: solving the same Schr\\\"odinger equation at several neutrino energies for a fixed redshift where a mass splitting changes sign would show whether the sharp $P_{ee}$ steps are smoothed by partial adiabaticity."],"forward_implications":["If a future DSNB measurement achieves sufficient spectral precision, the predicted energy-dependent shape could reveal that the neutrino mass ordering was different in the past, including sign changes in $\\Delta m^2_{21}$ and $\\Delta m^2_{31}$.","Cosmological surveys that measure only the total neutrino mass density are not sensitive to this effect, so the DSNB would provide a complementary and direct probe of dynamic neutrino masses.","The modification is not a pure normalization shift, so it is in principle distinguishable from astrophysical uncertainties that rescale the overall flux; reducing supernova-rate uncertainties is the key step.","The paper finds that present and near-future experiments cannot reach the predicted signal, placing the observable in the regime of future DSNB searches.","The same $P_{ee}(z)$ machinery could in principle be applied to other redshift-integrated neutrino sources, although the paper focuses on core-collapse supernovae."],"supporting_citations":[{"why":"Establishes that even a uniform redshift-dependent mass shift can affect supernova neutrino propagation through adiabaticity, the starting point this paper generalizes.","marker":"[42]"},{"why":"Supplies the DSNB flux formalism and the cosmic supernova rate parameters used in the redshift integral.","marker":"[41]"},{"why":"Provides the core-collapse supernova neutrino spectra and the presupernova electron density profile used in the numerical propagation.","marker":"[56]"},{"why":"Gives the MSW resonance density formula that connects the sign and magnitude of the mass-squared differences to flavor conversion.","marker":"[57]"},{"why":"Supplies the fractions of core-collapse and black-hole-forming failed supernovae that enter the unoscillated flux.","marker":"[55]"}],"fun_headline_variants":["Neutrino mass evolution leaves shape imprint on supernova background","Redshift-dependent neutrino masses distort supernova neutrino spectrum","Dynamic neutrino ordering may sculpt the DSNB's energy shape","Energy-dependent DSNB distortion tracks evolving neutrino masses","Supernova neutrinos could reveal redshift-varying mass ordering"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that at each redshift the electron-neutrino survival probability $P_{ee}$ depends only on that redshift, not on neutrino energy, even though the resonance density and adiabaticity condition in Eq. (5) both depend on $E_\\nu$.","fun_headline_variants_meta":{"raw":{"variants":["Neutrino mass evolution leaves shape imprint on supernova background","Redshift-dependent neutrino masses distort supernova neutrino spectrum","Dynamic neutrino ordering may sculpt the DSNB's energy shape","Energy-dependent DSNB distortion tracks evolving neutrino masses","Supernova neutrinos could reveal redshift-varying mass ordering"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000813,"raw_usage":{"total_tokens":3570,"prompt_tokens":957,"completion_tokens":2613,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":573,"completion_tokens_details":{"reasoning_tokens":2533}},"tokens_in":573,"tokens_out":2613,"duration_ms":18590,"temperature":1.0,"reasoning_tokens":2533,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T13:25:49.294800+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute $P_{ee}(E,z)$ from the paper's three-flavor Schr\\\"odinger evolution at neutrino energies of 5, 10, and 25 MeV for a fixed redshift where a mass splitting changes sign, such as $z\\simeq0.075$ in the normal-ordering benchmark; if the three values differ by more than a few percent, the $P_{ee}(z)$ simplification collapses and the predicted energy-dependent DSNB distortion would change shape.","supporting_citations":[{"cited_title":"Results from an extended set of 1d core-collapse simulations for a variety of progenitors canbe found at,","cited_arxiv_id":null,"evidence_quote":"Provides the core-collapse supernova neutrino spectra and the presupernova electron density profile used in the numerical propagation."}],"review_version":1}