{"id":"7c9ac273-55f4-4613-bced-3bbc0e686bdc","arxiv_id":"2509.04229","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"Cosmic-ray upscattering of the diffuse supernova neutrino background produces a flux about 20 orders below the galactic diffuse emission and about 18 orders below current limits, making the channel undetectable.","lead":"This paper calculates how often cosmic rays could boost neutrinos from distant supernovas up to very high energies. The result: the boosted signal is many orders of magnitude too weak for any current or planned detector to see.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified: a 10^18–10^20 margin makes the null conclusion robust even under extreme variations of the least-constrained input.","rationale":"The reader's verdict is CONDITIONAL with low correctness risk. My stress-test agrees with the substantive conclusion: with 18–20 orders of magnitude headroom, no single input variation can flip the result. The high-z source density is the weakest link, but weakness of an input is not equivalent to a load-bearing concern for a null result of this margin. The paper is transparent in §5.5. The request to prove a negative is open-ended, but the burden is on a hypothetical mechanism to produce ~10^18 enhancement, and the paper's three scalings bracket plausible astrophysical evolutions. The main presentation issues (missing f(z) in Eq. 26, garbled integrals in Eqs. 18–22, no released code) justify the reader's CONDITIONAL but do not move the verdict.","tokens_in":8702,"tokens_out":11559,"duration_ms":120549,"concrete_test":"If one wants a guard against the residual risk of a hidden algebraic error in the rate integral, independently re-derive Eq. 18 (and Eq. 22) directly from Eq. 14 via a kinematic Monte Carlo (no head-on approximation, full 2→2 phase space). If the production rate differs from the closed-form normalization by more than an order of magnitude, recompute Fig. 5 and the conclusions; otherwise the null result stands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is a null result with an extraordinarily large safety margin: the galactic CR-boosted DSNB flux is ~10^20 below the galactic diffuse neutrino flux, and the extragalactic contribution is ~10^18 below present limits (§6). The least constrained input is the high-redshift evolution of UHECR sources (Eq. 26, Sec. 5.5), and the paper itself concedes that the neutrino flux depends on redshifts not probed by Earth-observed UHECRs. However, closing a factor of 10^18 would require the high-z source density to exceed the SFR/quasar/GRB scalings by ~18 orders of magnitude, which is not physically plausible and is not suggested by any data. Even a factor of 10^6 increase changes 'unmeasurable' to 'still unmeasurable.' Equation 26 references f(z) without displaying it, and Eqs. 18/22 have typographical ambiguities, but these are presentation defects; no internal inconsistency shows a numerical error of the size needed to alter the conclusion. Thus I do not find a load-bearing attack.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper calculates the neutrino flux generated when the diffuse supernova neutrino background (DSNB) is upscattered by cosmic rays, considering both Galactic cosmic rays (producing a flux concentrated near the Galactic plane) and extragalactic ultra-high-energy cosmic rays (producing an isotropic flux). The calculation combines a published parametrization of the DSNB, the Gaisser mixed-composition Galactic cosmic-ray model, PriNCe simulations of UHECR propagation under three assumed source-density evolutions (star-formation rate, quasar rate, gamma-ray-burst rate), and standard neutrino-nucleon, neutrino-nucleus, and DIS cross sections. The central claim is that the resulting CR-boosted DSNB flux is unmeasurably small: about 20 orders of magnitude below current models of the Galactic diffuse neutrino emission and about 18 orders of magnitude below present experimental limits, leading the author to conclude that neither component is detectable in the foreseeable future.","tokens_in":9036,"tokens_out":18959,"duration_ms":185513,"significance":"If the result holds, it constitutes a robust null result for a proposed indirect-detection channel of the DSNB. A strength of the paper is that the small flux is not achieved by tuned parameters: all ingredients are taken from published parametrizations and fits, and three different UHECR source-evolution scenarios are tested. The extremely large safety margin means that even order-of-magnitude variations in the least-constrained inputs, such as the high-redshift scaling of UHECR sources, would not affect the qualitative conclusion. The paper is therefore potentially citable as a definitive negative statement. However, the usefulness of the paper depends on the derivation being transparent and reproducible; in its current form several key equations are inconsistent or malformed, which undermines verification of the numerical result.","major_comments":[{"comment":"The transition from Eq. (17) to Eq. (18) is not justified as written. Eq. (17) contains the factor 2ϵν and dσ/dQ², while Eq. (18) introduces an unexplained Q⁴ factor and a 1/(2ϵs³) prefactor. Using the stated relation Q² = 2ϵνϵs(1−cosψ), the angular integral dΩν = 2π d(cosψ) maps to dQ² with Jacobian −π/(ϵνϵs), yielding (2πc/ϵs)∫dϵν∫dΓCR nν nCR ∫dQ² dσ/dQ², not the expression in Eq. (18). Unless an additional kinematic relation between Q² and the final-state energy ϵs is being used without being stated, the two equations are inconsistent. This is a load-bearing part of the calculation, so the derivation must be corrected or clarified before the numerical results can be checked.","section":"Section 5.1, Eqs. (17)-(18)"},{"comment":"The presentation of the deep-inelastic scattering integral is badly garbled. Eq. (21) has an unshown lower limit on the ΓCR integration and the final double integral appears in the text as '∫ 2ϵνΓCR 0 dϵ∗ν ϵνΓCR 2mp(yϵ∗ν −mπ )−m2πZ 0 dQ2', which is unreadable. Eq. (22) similarly writes the upper limit of the Q² integral as '2mp(ϵ∗ν −ϵs/2ΓCR−mπ )−m2πZ 0 dQ2'. Since the paper states in Sec. 5.3 that the inelastic contribution dominates the emission rate, these integrals are central to the result. They must be typeset correctly with all integration limits and variables defined before the calculation can be reproduced.","section":"Section 5.2, Eqs. (21)-(22)"},{"comment":"Eq. (26) introduces f(z) as 'the scaling of the cosmic-ray source density with redshift z, normalized to 1 at zmin = 2.37×10−6', but f(z) does not appear anywhere in the integrand. The reader is left unable to determine how the three source scalings of Eqs. (5)-(7) enter the extragalactic flux. In addition, the lower limit of the redshift integral is not shown, despite the stated normalization at zmin. Please define f(z) explicitly, state the integration limits, and explain the relation between f(z) and the source density used in the PriNCe simulation.","section":"Section 5.5, Eq. (26)"},{"comment":"The spectral indices in Table 1 are listed with negative signs (γ = −0.8, −1.0, −0.8). Inserting these into Eq. (8), which contains (E/10^9 GeV)^{−γ}, gives an injection spectrum that rises with energy as E^{+0.8}, E^{+1.0}, or E^{+0.8} up to the rigidity cutoff. Such rising source spectra are not physically plausible and would not reproduce the Auger-measured UHECR spectrum shown in Fig. 3. This is very likely a sign typo (the values should presumably be +0.8, +1.0, +0.8), but the authors must correct the table or clarify the sign convention used in their fit.","section":"Table 1 and Eq. (8)"}],"minor_comments":[{"comment":"The units of the normalizations f_A, given as GeV^{-1} cm^{-3} s^{-1}, are not explained. Please clarify whether these are comoving emissivities, and how the fit to the Auger spectrum fixes the overall source normalization.","section":"Sec. 3.2, Table 1"},{"comment":"The line-of-sight integral L(Ω) is presented with units kpc/sr, but a line-of-sight integral of a dimensionless spatial function has units of length. The /sr presumably comes from the definition of the intensity per solid angle; this should be stated explicitly.","section":"Sec. 5.4, Eq. (25)"},{"comment":"The manuscript would benefit from a list of input parameters and their references in one place; currently the cosmological parameters appear only in Sec. 3.2, while the DSNB parameters are in Sec. 2 and the cross-section parameters in Sec. 4 and Appendix A.","section":"General"},{"comment":"The variable y in the upper limit '2mp(yϵ∗ν −mπ)' should presumably be a function of εs, ΓCR, and ε*ν as defined in Eq. (20); the notation is confusing and should be made consistent.","section":"Eq. (21)"}],"recommendation":"major_revision","confidential_remarks":"The conclusion is almost certainly robust given the enormous margins quoted, and the paper is a reasonable null-result contribution. My main concern is that the core derivation is not reproducible as written: Eqs. (17)-(18) appear inconsistent, Eq. (21) is unreadable, Eq. (26) references an undefined f(z), and Table 1 seems to have a sign error. These are fixable in revision, but they are not purely cosmetic because they sit in the equations that produce the numerical claims. I therefore recommend major revision rather than acceptance at this stage."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper's takeaway is simple: cosmic-ray boosted diffuse supernova neutrinos are unobservable, by margins of ~10^20 for the galactic component and ~10^18 for the extragalactic one. That's the result, and it's robust. The author builds the calculation from published DSNB spectra [10], CR models [12], UHECR simulations [15], and standard cross sections [21,23,25], plus the PriNCe propagation for extragalactic sources. Nothing is fitted to produce the small flux; it falls out of the convolution. That's good practice for a null result.\n\nWhat's genuinely new: the earlier boosted-relic-neutrino papers [3,4] didn't treat the DSNB, and they didn't need inelastic scattering because the target energies are so low. Here the DSNB energies are high enough that deep inelastic scattering dominates, and the author handles both elastic and inelastic channels, galactic and extragalactic contributions. The paper is also honest about the blind spot: the extragalactic flux depends on the high-redshift evolution of UHECR sources, which is unconstrained by Earth-observed UHECRs. The author uses three scalings (SFR, QSO, GRB). I agree with the stress test: to change the conclusion you'd need the source density to be ~10^18–10^20 times larger at high z, which is not physically plausible. So that's a real caveat but not a fatal one.\n\nSoft spots are mostly presentation. Eq. (21) has garbled Q^2 limits, Eq. (26) introduces f(z) without defining it, and some of the other formulas have typographical issues. There are no error bars or uncertainty propagation on the final spectra, and no code or data released. For a paper whose central claim is a null result, these are annoying but not damaging; the margins are so large that the conclusion would survive even order-of-magnitude errors.\n\nWho's this for? People working on DSNB detection or on cosmic-ray-boosted dark matter/neutrino signals. It's a useful reference to kill off a proposed detection channel. It won't change anyone's research program. I wouldn't cite it in my own work unless I needed a footnote that this channel is dead.\n\nI'd send it to peer review. It's a serious, careful calculation, even if the result is a door closing rather than a window opening. After fixing the equation slips it would be publishable in a specialist journal.","headline":"A careful, honest null result that closes the door on cosmic-ray-boosted DSNB neutrinos; the calculation is sound but the conclusion is a door closing rather than a window opening.","tokens_in":9456,"tokens_out":2689,"would_cite":false,"duration_ms":24545,"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":"Cosmic-ray scattering cannot make the diffuse supernova neutrino background visible: the calculated flux is 20 orders of magnitude below anything current detectors can see.","keywords":["cosmic-ray boosted neutrinos","diffuse supernova neutrino background","ultra-high-energy cosmic rays","galactic diffuse neutrino emission","neutrino-nucleus scattering","deep inelastic neutrino scattering","cosmogenic neutrinos","indirect neutrino detection"],"falsifier":"Look for galactic-plane-correlated neutrinos at TeV-PeV energies, or an isotropic neutrino flux peaking near a few hundred PeV, with sensitivity pushed far beyond current instruments: a detection matching either predicted spectral shape would refute the paper. Short of that, recomputing the extragalactic flux with a high-redshift source density much larger than the three adopted scalings—for example, growth as (1+z)^5—and showing that it approaches current upper limits would demonstrate that the 'unmeasurable' conclusion rests on the least-constrained assumption.","tokens_in":8640,"feed_emoji":"🌌","tokens_out":12038,"duration_ms":116434,"temperature":0.7,"pith_summary":"The diffuse supernova neutrino background—the accumulated neutrinos from all core-collapse supernovae—has never been detected. This paper asks whether it could be seen indirectly, through cosmic-ray particles scattering off those neutrinos and kicking them up to much higher energies. It computes two contributions: a galactic one, concentrated along the galactic plane, and an isotropic extragalactic one from ultra-high-energy cosmic rays. Both turn out to be enormously small—the galactic flux sits about 20 orders of magnitude below modeled galactic diffuse neutrino emission, and the extragalactic flux about 18 orders below current experimental limits. The conclusion is that this detection channel will not work in the foreseeable future, which closes off one speculative route to the missing supernova-neutrino background.","feed_headline":"Cosmic-ray-boosted supernova neutrinos are about 20 orders too faint","feed_subtitle":"The indirect route to the missing supernova-neutrino background turns out to be undetectably weak.","key_machinery":"The calculation is built from a collision-rate integral: the diffuse supernova neutrino background acts as an isotropic low-energy target, cosmic-ray protons and nuclei act as projectiles, and the upscattered neutrino inherits the cosmic-ray direction in the head-on approximation. For the galactic component, the cosmic-ray spectrum is a multi-population rigidity-cutoff parametrization, and the intensity is obtained by integrating the local emission rate along the line of sight using a sech-shaped spatial distribution of galactic cosmic rays. For the extragalactic component, the cosmic-ray density at each redshift comes from a propagated ultra-high-energy cosmic-ray spectrum, with source dens","core_discovery":"The paper's central claim is that the flux of diffuse supernova neutrinos boosted by cosmic-ray scattering is many orders of magnitude too small to be detected: about 20 orders of magnitude below modeled galactic diffuse neutrino emission for the galactic component, and about 18 orders below current experimental limits for the extragalactic component. The galactic component is brightest toward the galactic center and concentrated around the galactic plane, with a roughly E^-2.4 spectrum; the extragalactic component is isotropic and peaks near a few hundred PeV. Because the upscattered flux is so small, it does not compete with ordinary galactic diffuse neutrino emission, the measured high-en","pith_inferences":["If a future experiment nevertheless sees a TeV-PeV galactic-plane-correlated neutrino flux or an isotropic few-hundred-PeV flux, this calculation says it should not be attributed to cosmic-ray-boosted supernova neutrinos; the interpretation would need astrophysical sources or new physics.","The extragalactic result is only as solid as the assumed high-redshift source density. A source population that grows far more steeply with redshift than star formation, quasars, or gamma-ray bursts could raise the isotropic flux, so scanning such unconstrained evolutions would map the true upper bound of this channel.","The same rate-integral machinery, including both elastic and inelastic channels, can be applied to any diffuse low-energy neutrino target, so the method carries over to relic-neutrino and other boosted-flux estimates."],"forward_implications":["The galactic cosmic-ray-boosted component, though concentrated along the galactic plane and following roughly an E^-2.4 spectrum, is so far below modeled galactic diffuse neutrino emission that it will never be separated as a distinct signal.","The isotropic extragalactic component, peaking near a few hundred PeV, lies about 18 orders of magnitude below current experimental upper limits, placing it beyond the reach of any approved or planned detector.","Because both components are negligible, cosmic-ray-boosted diffuse supernova neutrinos can be ignored as a background in searches for cosmogenic neutrinos.","For supernova neutrinos, inelastic scattering contributes significantly to the boosted flux, unlike the relic-neutrino case where elastic scattering dominates; future boosted-flux estimates should include both channels."],"supporting_citations":[{"why":"Supplies the parametrized diffuse supernova neutrino background spectrum used as the target neutrino population.","marker":"[10]"},{"why":"Supplies the galactic cosmic-ray flux parametrization whose third, extragalactic population is removed for the galactic calculation.","marker":"[12]"},{"why":"Provides the ultra-high-energy cosmic-ray propagation simulation used to obtain the extragalactic cosmic-ray flux.","marker":"[15]"},{"why":"Supplies the measured ultra-high-energy cosmic-ray spectrum used to fit the injected source parameters.","marker":"[19]"},{"why":"Provides the elastic neutrino-proton scattering cross-section parametrization used in the upscattering rate.","marker":"[21]"},{"why":"Supplies the coherent and incoherent elastic neutrino-nucleus scattering cross-sections for nuclear targets.","marker":"[23]"},{"why":"Provides the proton structure-function parametrization used for deep inelastic neutrino-nucleus scattering.","marker":"[25]"},{"why":"Provides the modeled galactic diffuse neutrino emission used as the benchmark showing the boosted flux is about 20 orders lower.","marker":"[5]"},{"why":"Provide the experimental upper limits on ultra-high-energy neutrinos against which the extragalactic boosted flux is compared.","marker":"[7–9]"},{"why":"Supplies one of the three assumed redshift evolutions of the ultra-high-energy cosmic-ray source density, the least constrained input to the extragalactic flux.","marker":"[16]"}],"fun_headline_variants":["Supernova neutrinos boosted by cosmic rays still undetectable","Cosmic-ray boost fails to make supernova neutrinos visible","Diffuse supernova neutrino flux too faint even after cosmic-ray boost","20 orders too faint: cosmic-ray-boosted supernova neutrinos","Missing supernova neutrinos stay hidden after cosmic-ray scattering"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The extragalactic part of the calculation assumes that ultra-high-energy cosmic-ray sources at very large distances became more or less numerous in one of three ways tied to star formation, quasars, or gamma-ray bursts; that distant behavior is not constrained by the cosmic-ray spectrum measured on Earth.","fun_headline_variants_meta":{"raw":{"variants":["Supernova neutrinos boosted by cosmic rays still undetectable","Cosmic-ray boost fails to make supernova neutrinos visible","Diffuse supernova neutrino flux too faint even after cosmic-ray boost","20 orders too faint: cosmic-ray-boosted supernova neutrinos","Missing supernova neutrinos stay hidden after cosmic-ray scattering"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000421,"raw_usage":{"total_tokens":1927,"prompt_tokens":598,"completion_tokens":1329,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":342,"completion_tokens_details":{"reasoning_tokens":1251}},"tokens_in":342,"tokens_out":1329,"duration_ms":9978,"temperature":1.0,"reasoning_tokens":1251,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T10:13:16.304985+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Look for galactic-plane-correlated neutrinos at TeV-PeV energies, or an isotropic neutrino flux peaking near a few hundred PeV, with sensitivity pushed far beyond current instruments: a detection matching either predicted spectral shape would refute the paper. Short of that, recomputing the extragalactic flux with a high-redshift source density much larger than the three adopted scalings—for example, growth as (1+z)^5—and showing that it approaches current upper limits would demonstrate that the 'unmeasurable' conclusion rests on the least-constrained assumption.","supporting_citations":[{"cited_title":"Neutrino nonradiative decay and the diffuse supernova neutrino background","cited_arxiv_id":null,"evidence_quote":"Supplies the parametrized diffuse supernova neutrino background spectrum used as the target neutrino population."},{"cited_title":"Spectrum of cosmic-ray nucleons and the atmospheric muon charge ratio","cited_arxiv_id":null,"evidence_quote":"Supplies the galactic cosmic-ray flux parametrization whose third, extragalactic population is removed for the galactic calculation."},{"cited_title":"A New View on Auger Data and Cosmogenic Neutrinos in Light of Different Nuclear Disintegration and Air-shower Models","cited_arxiv_id":null,"evidence_quote":"Provides the ultra-high-energy cosmic-ray propagation simulation used to obtain the extragalactic cosmic-ray flux."},{"cited_title":"Measurement of the energy spectrum of ultra-high energy cosmic rays using the Pierre Auger Observatory.Proc","cited_arxiv_id":null,"evidence_quote":"Supplies the measured ultra-high-energy cosmic-ray spectrum used to fit the injected source parameters."},{"cited_title":"Measurement of neutrino-proton and antineutrino-proton elastic scattering","cited_arxiv_id":null,"evidence_quote":"Provides the elastic neutrino-proton scattering cross-section parametrization used in the upscattering rate."},{"cited_title":"From eV to EeV: Neutrino cross sections across energy scales","cited_arxiv_id":null,"evidence_quote":"Supplies the coherent and incoherent elastic neutrino-nucleus scattering cross-sections for nuclear targets."},{"cited_title":"Connection of the virtual γ∗ p cross section of ep deep inelastic scattering to real γp scattering, and the implications for νN and ep total cross sections","cited_arxiv_id":null,"evidence_quote":"Provides the proton structure-function parametrization used for deep inelastic neutrino-nucleus scattering."},{"cited_title":"Diffuse Emission of Galactic High-energy Neutrinos from a Global Fit of Cosmic Rays.Astrophys","cited_arxiv_id":null,"evidence_quote":"Provides the modeled galactic diffuse neutrino emission used as the benchmark showing the boosted flux is about 20 orders lower."},{"cited_title":"On the Normalization of the Cosmic Star Formation History","cited_arxiv_id":null,"evidence_quote":"Supplies one of the three assumed redshift evolutions of the ultra-high-energy cosmic-ray source density, the least constrained input to the extragalactic flux."}],"review_version":1}