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REVIEW 4 major objections 4 minor 1 cited by

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.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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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.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection 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. the 4 major comments →

arxiv 2509.04229 v1 pith:CK3O4XXL submitted 2025-09-04 astro-ph.HE hep-ph

Cosmic-Ray Boosted Diffuse Supernova Neutrinos

Alexander Sandrock This is my paper
classification astro-ph.HE hep-ph
keywords cosmic-ray boosted neutrinosdiffuse supernova neutrino backgroundultra-high-energy cosmic raysgalactic diffuse neutrino emissionneutrino-nucleus scatteringdeep inelastic neutrino scatteringcosmogenic neutrinosindirect neutrino detection
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

Core claim

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

What carries the argument

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

Load-bearing premise

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.

What would settle it

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.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • 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.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

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.

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 (4)
  1. [Section 5.1, Eqs. (17)-(18)] 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.
  2. [Section 5.2, Eqs. (21)-(22)] 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.
  3. [Section 5.5, Eq. (26)] 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.
  4. [Table 1 and Eq. (8)] 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.
minor comments (4)
  1. [Sec. 3.2, Table 1] 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.
  2. [Sec. 5.4, Eq. (25)] 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.
  3. [General] 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.
  4. [Eq. (21)] 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.

Circularity Check

0 steps flagged

No significant circularity: the calculation is a convolution of independent external models and standard fits.

full rationale

The paper's central result is a direct convolution of externally published inputs: the DSNB parametrization of Ref. [10] based on Ref. [11], the galactic cosmic-ray parametrization of Ref. [12], and extragalactic UHECR spectra from the PriNCe simulation code [15]. The UHECR injection parameters in Table 1 are explicitly fitted to Pierre Auger data as standard calibration; they are not used as a prediction. The final boosted flux is obtained by evaluating the scattering integrals with these ingredients, and no parameter is adjusted to force the extremely small magnitude—the smallness follows from the tiny DSNB number density and the relevant cross-sections. The only author self-citation, Ref. [3], appears in the introduction merely to note recent interest in boosted relic neutrinos and is not load-bearing for any derivation. The paper also honestly discloses in Sec. 5.5 that the high-redshift source evolution is unconstrained by fitting the Earth-observed UHECR spectrum; this is a modeling uncertainty, not an instance of circularity, because the assumed scalings (SFR, QSO, GRB) are external functional forms and are not defined in terms of the target flux. No step in the derivation reduces to its own inputs by construction. The minor notation issue in Eq. (26) (undefined f(z)) is a presentation defect, not a circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

The paper's central result is a convolution of established ingredients. The only new free numbers are the UHECR injection parameters (Table 1), fitted to Auger data within the paper itself. The DSNB flux, galactic CR model, source evolution shapes, and cross sections are all imported from the cited literature. No new entities are postulated. The main unvalidated assumption is the high-z extrapolation of UHECR sources.

free parameters (3)
  • UHECR injection parameters under SFR source evolution = Rmax=10^9.25 GV; gamma=-0.8; fH=1.0e-45; fHe=4.5e-46; fN=6.2e-47; fSi=4.1e-48; fFe=9.0e-50 GeV-1 cm-3 s-1
    Fitted to Pierre Auger UHECR spectrum data [19] above 6e9 GeV (Table 1, Fig 3). These shape the extragalactic cosmic ray flux that upscatters DSNB neutrinos.
  • UHECR injection parameters under QSO source evolution = Rmax=10^9.20 GV; gamma=-1.0; fH=2.2e-45; fHe=7.7e-46; fN=6.1e-47; fSi=2.3e-48; fFe=6.6e-50 GeV-1 cm-3 s-1
    Second set of UHECR source fits used to bracket the unknown source evolution (Table 1, Fig A1).
  • UHECR injection parameters under GRB source evolution = Rmax=10^9.25 GV; gamma=-0.8; fH=1.7e-46; fHe=4.6e-47; fN=5.5e-47; fSi=3.9e-48; fFe=9.5e-50 GeV-1 cm-3 s-1
    Third set of UHECR source fits used to bracket the unknown source evolution (Table 1, Fig A2).
axioms (6)
  • domain assumption The DSNB flux parametrization of [10] based on [11] gives the total neutrino plus antineutrino flux (Eq. 1, Section 2).
    The central calculation inherits the DSNB model. The paper notes predicted DSNB flux varies by factor 2-5 among models, but that range does not affect the conclusion.
  • domain assumption The galactic cosmic ray flux is described by the three-population parametrization of [12] (Eq. 4), with the third (extragalactic) component removed.
    Section 3.1. The galactic CR flux is an input that sets the normalization of the galactic boosted flux.
  • domain assumption UHECR injection follows the form of [18] and propagation uses PriNCe [15] with TALYS photodisintegration [20] and Gilmore EBL [29].
    Section 3.2. These tools and models determine the extragalactic CR flux at all redshifts.
  • domain assumption The head-on approximation Omega_s = Omega_CR and beta = 1 is valid for the problem because Gamma_CR >> 1 (Section 5.1).
    Used to reduce the rate integrals in Eqs. (14)-(18). Standard for boosted-neutrino calculations, but an approximation.
  • domain assumption The galactic cosmic ray spectrum factorizes as n_CR(E,x) = n_sun(E) f(x), with f from [27] (Eq. 24, Section 5.4).
    This assumes steady state, separable diffusion, negligible energy losses, and escape-dominated losses, as the paper explicitly lists. It sets the angular distribution and normalization of the galactic signal.
  • standard math Standard-model elastic and inelastic neutrino-nucleon/nucleus cross sections from [21,23,24,25,26] (Section 4).
    The cross sections are taken from the literature, not derived. They are well-established and not the source of the tiny flux.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Cosmic-Ray Boosted Diffuse Supernova Neutrinos." pith.science (2026). https://pith.science/paper/CK3O4XXL

@misc{pith2026250904229,
  author       = {Pith},
  title        = {Pith review of: Cosmic-Ray Boosted Diffuse Supernova Neutrinos},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CK3O4XXL}},
  note         = {Machine review of arXiv:2509.04229}
}
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read the original abstract

The subject of boosted fluxes of dark matter or cosmic relic neutrinos via scattering on cosmic rays has received considerable attention recently. This article investigates the boosted neutrino flux from scattering of cosmic rays and the so-far undetected diffuse supernova neutrino background, taking into account both galactic and extragalactic cosmic rays. The calculated flux is many orders of magnitude smaller than either the galactic diffuse neutrino emission, the extragalactic astrophysical flux measured by IceCube, or the cosmogenic neutrino flux expected at the highest energies.

Figures

Figures reproduced from arXiv: 2509.04229 by Alexander Sandrock.

Figure 1
Figure 1. Figure 1: Fiducial spectrum of the diffuse supernova neutrino background from [10] based on simulations by [11]. The spectrum is weighted with the square of the neutrino energy. where Yνl refers to the parametrized neutrino yield, RSN(z, M) = ρ˙∗(z) ϕ(M) dM R 125M⊙ 0.5M⊙ ϕ(M)M dM (2) is the supernova rate, determined from star formation history ρ˙∗ and initial mass function ϕ with M the stellar mass, and [PITH_FULL… view at source ↗
Figure 2
Figure 2. Figure 2: Galactic cosmic ray spectrum according to the mixed composition model from [12], weighted with the third power of the energy per particle. The third generation is set to zero, since the extragalactic cosmic rays are treated differently. Measurements of the all-particls cosmic ray flux from CREAM, IceCube, KASCADE, TUNKA, and the Pierre Auger observatory are shown for comparison (taken from the compilation … view at source ↗
Figure 3
Figure 3. Figure 3: Extragalactic cosmic ray flux fit, assuming a source density scaling as the star formation rate. The fit is to the UHECR measurement data from [19] above a lower energy of 6 × 109 GeV [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Emission rate per volume n˙s at earth for elastic neutrino-nucleon scattering, coherent and incoherent neutrino-nucleus scattering, and deep-inelastic neutrino-nucleus scattering of diffuse supernova neutrinos on galactic cosmic rays. Since the minimal energy in the nucleon rest frame for this process is given by ϵ ∗ min = mπ + m2 π/2mp, the integration region is more constrained compared to the elastic sc… view at source ↗
Figure 5
Figure 5. Figure 5: Energy spectra of the CR-boosted diffuse supernova neutrino flux integrated over angular regions corresponding to the inner and outer galaxy, high latitudes and the whole sky with solid lines; and energy spectra of the extragalactic CR-boosted diffuse supernova neutrino flux for different UHECR source density scalings with dashed lines. Similar to the diffuse galactic neutrino emission produced in cosmic-r… view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 5, 2026.