{"id":"c87f82d9-4030-460a-a012-00fe169e793c","arxiv_id":"2608.12177","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Neutrino flavour conversion strongly suppresses the diffuse neutrino background from neutrino-dominated accretion flows if the neutrino mass ordering is inverted, leaving a detectable signal only in the normal ordering.","lead":"This paper predicts the diffuse background of neutrinos from black hole accretion disks formed when supernova material falls back, after accounting for neutrino oscillations during the trip to Earth. It finds the signal depends strongly on the still-unknown neutrino mass ordering, making a detection plausible only in the normal ordering.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Optimistic NO event counts may conflict with the Super-K DSNB upper limit quoted in Sec. 3; >100 Hyper-K events in 10 yr implies ~2.4 SK events in 1496 days in the same 18-26 MeV window, above the paper's own <2 bound.","rationale":"The paper's central argument is internally coherent: Eq. (9) with adiabatic MSW survival probabilities \\bar p = |U_e1|^2 (NO) and |U_e3|^2 (IO), combined with the computed ratio between the unoscillated \\bar\\nu_e and \\nu_x spectra, naturally produces a large NO/IO ordering contrast. The reader's identified weakness, collective neutrino oscillations, is real and is explicitly acknowledged in Sec. 4, but it is a model uncertainty that may be suppressed by multi-angle matter effects in dense accretion disks; it does not by itself demonstrate an error in the calculation. The sharper, more checkable problem is the paper's failure to confront its own optimistic NO predictions with the Super-K DSNB upper limit that it quotes. The exposure scaling between Hyper-K and Super-K is simple and uses only quantities given in the paper: the target proton numbers, the 18-26 MeV window common to both the quoted SK limit and the adopted HK analysis, and the 1496-day vs 10-year livetimes. The result is that 100 HK events maps to roughly 2.4 SK events, which is already above the quoted '<2 events' bound. This is not an external consensus-based objection; it is an internal consistency check using the paper's own cited limit. It undermines the 'realistic possibility of detection' phrasing for the most optimistic NO models, although it does not overturn the ordering-dependence conclusion from Eq. (9). The reader's CONDITIONAL verdict already captures the need for additional conditions, so I do not change the verdict; I would add the Super-K consistency check as a required condition for the detectability statement.","tokens_in":14340,"tokens_out":14911,"duration_ms":143089,"concrete_test":"Recompute the expected Super-K event counts for the most optimistic NO models in Figs. 5-6 (e.g., Z/Zsun = 0 with E = 2 B, and Z/Zsun = 0.01 with E = 2 B and 4 B) by scaling the Hyper-K event rates to Super-K's fiducial proton number (N_t ~1.5e33), the same 18-26 MeV analysis window, the same (or SK-specific) signal efficiency, and a 1496-day livetime. If the resulting count exceeds the quoted <2 event upper limit, the optimistic NO models are disfavored at more than ~90% CL by existing Super-K data, and the paper's detectability claim must be revised to state that these models are already constrained rather than merely detectable in the future.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central detectability claim in Sec. 3 is that optimistic normal-ordering models predict more than 100 \\bar\\nu_e IBD events in Hyper-K over ten years, making the DNNB 'may be detectable'. The paper itself quotes the Super-K DSNB upper limit as fewer than two events in the 18-26 MeV window over 1496 days. These two statements are in tension. Using the paper's own numbers, Hyper-K has N_t = 2.5e34 target protons versus Super-K's 22.5 kton fiducial mass, N_t ~1.5e33, a factor ~17; the livetime ratio is 3650/1496 ~2.44, so the total exposure ratio is ~41. A 100-event Hyper-K decade signal therefore corresponds to roughly 2.4 events at Super-K in the quoted 1496-day, 18-26 MeV window, already above the <2 upper limit; 'over one hundred' makes the tension worse. The paper never performs this self-consistency check: the quoted Super-K limit is used only as motivation, not applied to its own optimized models. This does not invalidate the ordering contrast from Eq. (9), but it changes the status of the optimistic NO models from 'future detectable' to 'already constrained by existing SK data' unless the limit is rescaled for efficiency and energy response, which is not shown.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper models the diffuse neutrino background from neutrino-dominated accretion flows (DNNB) using spherically symmetric fallback CCSN simulations, computes unoscillated \\bar{\\nu}_e and \\nu_x spectra for different progenitor masses, metallicities, and explosion energies, and folds them with an IMF-weighted cosmic star formation history. It then applies adiabatic MSW flavour conversion with survival probabilities fixed by JUNO mixing parameters (|U_e1|^2 for NO, |U_e3|^2 for IO) via Eq. (9), yielding DNNB \\bar{\\nu}_e spectra. Event rates are computed for JUNO and Hyper-K over 10 years. The central quantitative result is that NO event rates exceed IO by more than an order of magnitude, and optimistic NO models could produce over 100 IBD events in Hyper-K, while IO is likely undetectable. The paper concludes that DNNB may be detectable in NO and could complement mass-ordering studies.","tokens_in":14601,"tokens_out":5584,"duration_ms":49619,"significance":"If the result holds, this is a useful new prediction: the strong NO/IO ordering contrast emerges naturally from Eq. (9) and the large simulated \\bar{\\nu}_e/\\nu_x ratio, without tuning to DNNB observations. Credit is due for explicitly computing \\nu_x spectra instead of assuming thermal scaling, and for stating the relevant limitations (collective oscillations, outflows, metallicity evolution) in the text. However, because the detection claim rests on optimistic upper-limit rates and a simplified oscillation treatment, the quantitative detectability statement is not yet robust; the paper should be read as an illustrative upper-limit scenario until it is checked against existing bounds.","major_comments":[{"comment":"The claim that optimistic NO models yield more than 100 Hyper-K IBD events in 10 years is in tension with the Super-K DSNB limit quoted in the same section (<2 events in 18-26 MeV over 1496 days). Scaling the Hyper-K exposure to Super-K using the numbers in the text (target protons 2.5e34 vs ~1.5e33, livetime ratio 3650/1496) gives roughly 2.4 events at Super-K for a 100-event Hyper-K decade signal, already above the quoted bound; the tension is worse for larger event numbers. The quoted limit is used only as motivation, not applied to the optimistic models. The authors should either rescale the Super-K limit with the appropriate efficiency and energy response for a like-for-like comparison, or explicitly conclude that the optimistic NO models are already constrained by existing data. This does not undermine the relative NO/IO ordering contrast from Eq. (9), but it directly affects the central detectability conclusion.","section":"Sec. 3, Figs. 5-6"},{"comment":"The central result assumes adiabatic MSW conversion with \\bar{p} = |U_e1|^2 (NO) and |U_e3|^2 (IO), neglecting collective neutrino oscillations. Because the DNNB signal is essentially the \\bar{\\nu}_e survival fraction, any collective \\bar{\\nu}_e <-> \\nu_x swap in the dense accretion disk would change the effective \\bar{p} entering Eq. (9) and hence the predicted ordering contrast and event rates. The paper acknowledges this uncertainty but does not quantify it; the detectability statement in the abstract and conclusion is nevertheless built on the simplified conversion. A concrete estimate of the range of possible survival probabilities, or at least an explicit statement that the ordering contrast is conditional on the absence of collective effects, is needed before the detectability conclusion can be accepted.","section":"Sec. 2.3 and Sec. 4"},{"comment":"The NDAF rate uses Mmin and fNDAF from spherically symmetric, piston-driven simulations and deliberately neglects cosmic metallicity evolution; the paper itself states that actual rates are likely lower and that predicted fluxes should be regarded as upper limits. Since event rates scale linearly with RNDAF, the 'may be detectable' claim in the abstract and Sec. 3 relies on the most optimistic upper-limit rate. The abstract and conclusions should carry this caveat explicitly, and the optimistic event numbers should be labelled as upper limits rather than as central expectations.","section":"Sec. 2.1 and Sec. 4"}],"minor_comments":[{"comment":"The notation \\nu_x in Eq. (9) should be defined as including \\bar{\\nu}_\\mu and \\bar{\\nu}_\\tau; otherwise the appearance term in the IBD flux is ambiguous.","section":"Sec. 2.3"},{"comment":"For consistency with Eq. (10), state whether Ndet in Figs. 5 and 6 already includes the signal efficiency \\epsilon_sig; the figure captions do not say.","section":"Sec. 3"},{"comment":"The JUNO mixing parameters are quoted only as sin^2\\theta_12 and sin^2\\theta_13; give the resulting numerical values of \\bar{p} for NO and IO to help the reader verify Eq. (9).","section":"Sec. 2.3"},{"comment":"The quoted Super-K DSNB upper limit is from 2009; consider updating to the latest published Super-K limit, which would strengthen the comparison.","section":"Sec. 3"}],"recommendation":"major_revision","confidential_remarks":"The core ordering contrast is internally coherent, but the detectability claim needs to be reconciled with the Super-K bound and qualified by the acknowledged uncertainties. This is fixable with a like-for-like limit comparison and a rewording of the claims; I therefore see this as a major revision rather than a rejection. The paper is within scope for MNRAS if the astro-data and modelling side is emphasised."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline is that the paper gives a clean, internally consistent calculation of the heavy-lepton neutrino spectra from NDAFs and shows that MSW flavour conversion makes the DNNB strongly dependent on the neutrino mass ordering. The genuinely new piece is the systematic calculation of unoscillated nu_x spectra as a function of progenitor mass, metallicity, and explosion energy; the ordering dependence itself follows directly from Eq. (9) and the fact that the unoscillated electron antineutrino flux is more than a factor of ten above nu_x. The authors are also honest about the usual caveats.\n\nWhere it gets into trouble is the detectability conclusion. The paper quotes the Super-K DSNB upper limit of fewer than two events in 18-26 MeV over 1496 days, then later claims that the most optimistic NO models exceed one hundred IBD events in Hyper-K over ten years. The exposure ratio between these two detectors and live times is about 41, so 100 HK events corresponds to roughly 2.4 events at SK in that same window. That is already above the quoted limit. 'Over one hundred' pushes it further. The authors never use the limit as a constraint on their own models. This doesn't invalidate the ordering hierarchy from Eq. (9), but it changes the status of the optimistic NO models from 'future detectable' to 'already constrained by existing data' unless the limit is rescaled for efficiency and energy response, which is not shown.\n\nThe other weaknesses are minor in comparison. Collective oscillations are neglected, but they are honestly flagged as uncertain. No uncertainties are propagated through the event-rate calculation, which matters for a detectability claim. The fitting formulae come from prior work without a stated validity range, and the data-sharing policy is weak.\n\nThis paper is for people working on diffuse supernova neutrino backgrounds and future MeV detectors. It gives a useful new set of unoscillated nu_x spectra and a clear illustration of how mass ordering changes a subdominant background. The central argument holds up as a prediction but not as a detection claim. A strong referee report should ask the authors to confront the SK limit head-on and to provide a version of the event rates with uncertainties.\n\nI'd send it to peer review. The nu_x spectra are worth having in the literature even if the brightness of the optimistic NO signal is overstated.","headline":"A coherent, useful calculation of heavy-lepton neutrino spectra from NDAFs, but the optimistic normal-ordering detectability claim collides with the paper's own quoted Super-K upper limit.","tokens_in":15170,"tokens_out":4602,"would_cite":true,"duration_ms":40936,"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":"Neutrino flavour conversion reshapes the diffuse NDAF background so that its detectability hinges on the neutrino mass ordering.","keywords":["diffuse neutrino background","neutrino-dominated accretion flow","neutrino flavour conversion","neutrino mass ordering","MSW effect","core-collapse supernova fallback","Hyper-Kamiokande","JUNO"],"falsifier":"A multi-angle neutrino-transport simulation of an NDAF disk that finds efficient collective oscillations swapping $\\bar{\\nu}_e$ and $\\nu_x$ would invalidate the adiabatic-MSW survival probabilities in Eq. (9) and break the predicted ordering contrast; alternatively, a decade-long Hyper-K exposure that measures a DNNB flux below the normal-ordering prediction, or consistent with inverted ordering, would falsify the central detectability claim.","tokens_in":14082,"feed_emoji":"🔭","tokens_out":8904,"duration_ms":62619,"temperature":0.7,"pith_summary":"The paper argues that neutrino flavour conversion decisively reshapes the diffuse neutrino background from neutrino-dominated accretion flows (NDAFs), so strongly that whether this background can be detected at all depends on the neutrino mass ordering. Because the unoscillated heavy-lepton neutrino ($\\nu_x$) spectra are more than an order of magnitude below the electron antineutrino spectra, the survival probability of $\\bar{\\nu}_e$ after propagation controls the total flux. Under the adiabatic MSW approximation, that survival probability is $|U_{e1}|^2$ in normal ordering and $|U_{e3}|^2$ in inverted ordering, making the predicted normal-ordering flux exceed the inverted-ordering flux by more than an order of magnitude. The authors compute event numbers in JUNO and Hyper-Kamiokande and find that in optimistic normal-ordering models Hyper-K could detect over one hundred $\\bar{\\nu}_e$ events in ten years, while the inverted-ordering signal is too weak for a significant detection. This implies that the DNNB could serve as a complementary probe of the neutrino mass ordering and of NDAF physics.","feed_headline":"Neutrino mass ordering decides the NDAF background's detectability","feed_subtitle":"Normal ordering may yield over a hundred Hyper-K events in a decade; inverted ordering suppresses the signal.","key_machinery":"The central object is the flavour-converted electron antineutrino flux of the DNNB, Eq. (9): $d\\Phi_{\\bar{\\nu}_e}/dE = \\bar{p}\\,d\\Phi^0_{\\bar{\\nu}_e}/dE + (1-\\bar{p})\\,d\\Phi^0_{\\nu_x}/dE$, where $\\bar{p}$ is the adiabatic MSW survival probability of $\\bar{\\nu}_e$, equal to $|U_{e1}|^2$ in normal ordering and $|U_{e3}|^2$ in inverted ordering. The argument works because the unoscillated $\\nu_x$ spectrum is more than an order of magnitude below $\\bar{\\nu}_e$, so the second term is a small correction and the total flux tracks the survival probability. The machinery also includes the fitting formulae for the heavy-lepton neutrino cooling rate and disk temperature as functions of black hole mass, spin, accretion rate, and radius, used to build the $\\nu_x$ spectra from the NDAF evolution data.","core_discovery":"The central discovery is that the diffuse NDAF neutrino background (DNNB) is strongly shaped by neutrino flavour conversion, with its detectability controlled by the neutrino mass ordering. Using fallback core-collapse supernova simulations, the authors compute for the first time the unoscillated heavy-lepton neutrino spectra from NDAFs and find them more than an order of magnitude weaker than the electron antineutrino spectra, reflecting the dominance of Urca processes in the disk. With the adiabatic MSW survival probability $\\bar{p} = |U_{e1}|^2$ for normal ordering and $\\bar{p} = |U_{e3}|^2$ for inverted ordering, the flavour-converted $\\bar{\\nu}_e$ flux is given by Eq. (9), and the resulting DNNB flux in all considered models is more than an order of magnitude higher in the normal ordering than in the inverted ordering. In the most optimistic normal-ordering scenarios, Hyper-Kamiokande could identify over one hundred events in a decade, while the inverted-ordering signal is too weak to claim a detection.","pith_inferences":["The detectability conclusion rests on the adiabatic MSW approximation; if collective neutrino oscillations efficiently swap $\\bar{\\nu}_e$ and $\\nu_x$ in the dense disk, the survival probability entering Eq. (9) would change and the ordering contrast could shrink or reverse.","The same flux-mixing formula could be applied to other astrophysical neutrino backgrounds where the unoscillated heavy-lepton flux is subdominant, turning flavour conversion into a generic mass-ordering diagnostic.","A non-detection of the DNNB in Hyper-K after a decade would not simply rule out NDAFs; it would constrain the fraction of weak explosions and the metallicity distribution of progenitors, since these parameters control the predicted flux.","A testable extension would be a spectral-shape analysis of the DNNB in the 12-30 MeV window with JUNO's energy resolution, which could distinguish normal from inverted ordering by the energy dependence, not just the total rate."],"forward_implications":["If the DNNB is detected under normal ordering, its flux and spectral shape provide a new observational handle on the cosmic rate of NDAFs and the average neutrino emission per event, complementing the diffuse supernova neutrino background.","A JUNO determination of the neutrino mass ordering would select which DNNB prediction is the relevant one, removing the dominant uncertainty in the detectability estimate.","A joint analysis of the DNNB with the stochastic gravitational wave background from NDAFs could constrain the average neutrino emission per NDAF event and help separate the DNNB from the DSNB.","The predicted high-energy spectral hardness of the DNNB, if weak explosions are common, offers a signature that could distinguish it from the conventional DSNB."],"supporting_citations":[{"why":"Supplies the fallback CCSN simulations and the unoscillated electron antineutrino spectra of NDAFs that seed the DNNB calculation.","marker":"Wei et al. (2024)"},{"why":"Provides the global NDAF solutions and fitting formulae for the heavy-lepton neutrino cooling rate and temperature used to build the unoscillated $\\nu_x$ spectra.","marker":"Xue et al. (2013)"},{"why":"Gives the adiabatic MSW survival probability for $\\bar{\\nu}_e$ under normal and inverted mass orderings, setting the $\\bar{p}$ in Eq. (9).","marker":"Dighe & Smirnov 2000"},{"why":"Adopted as the reference for the latest neutrino oscillation parameters and the JUNO detector configuration.","marker":"JUNO Collaboration 2022"},{"why":"Supplies $\\sin^2\\theta_{12} = 0.3092$, the value used for $|U_{e1}|^2$ and $|U_{e3}|^2$ in the survival probabilities.","marker":"Abusleme et al. 2025"},{"why":"Supplies $\\sin^2\\theta_{13} = 0.0223$, used in the mixing matrix.","marker":"Workman et al. 2022"},{"why":"Sets the JUNO signal efficiency and analysis energy window (12-30 MeV) used for event-rate predictions.","marker":"Li et al. (2022)"},{"why":"Sets the Hyper-K signal efficiency and analysis energy window (18-26 MeV) used for event-rate predictions.","marker":"Møller et al. 2018"}],"fun_headline_variants":["Mass ordering flips the NDAF background's detectability","Normal neutrino ordering makes NDAF neutrinos visible","Inverted mass ordering suppresses the NDAF neutrino signal","Neutrino mass ordering decides if we see accretion-flow neutrinos","Hyper-K event count hinges on neutrino mass ordering"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that neutrino flavour conversion in NDAF sources is governed by the adiabatic MSW effect with survival probabilities $|U_{e1}|^2$ (normal ordering) and $|U_{e3}|^2$ (inverted ordering), while collective neutrino oscillations and shock-induced non-adiabatic transitions are neglected.","fun_headline_variants_meta":{"raw":{"variants":["Mass ordering flips the NDAF background's detectability","Normal neutrino ordering makes NDAF neutrinos visible","Inverted mass ordering suppresses the NDAF neutrino signal","Neutrino mass ordering decides if we see accretion-flow neutrinos","Hyper-K event count hinges on neutrino mass ordering"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00082,"raw_usage":{"total_tokens":3644,"prompt_tokens":1054,"completion_tokens":2590,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":670,"completion_tokens_details":{"reasoning_tokens":2509}},"tokens_in":670,"tokens_out":2590,"duration_ms":18451,"temperature":1.0,"reasoning_tokens":2509,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:14:44.593092+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A multi-angle neutrino-transport simulation of an NDAF disk that finds efficient collective oscillations swapping $\\bar{\\nu}_e$ and $\\nu_x$ would invalidate the adiabatic-MSW survival probabilities in Eq. (9) and break the predicted ordering contrast; alternatively, a decade-long Hyper-K exposure that measures a DNNB flux below the normal-ordering prediction, or consistent with inverted ordering, would falsify the central detectability claim.","supporting_citations":[],"review_version":1}