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Ultra-high-energy neutrinos boosted from the cosmic neutrino background are within reach of current and future neutrino telescopes.

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2026-08-03 10:29 UTC pith:ARCWGNPT

load-bearing objection Genuinely new NC DIS channel makes IceCube's existing UHE limits the strongest current cosmological CνB constraint, but the headline η bound leans on a pure-proton UHECR assumption that could soften it by an order of magnitude. the 4 major comments →

arxiv 2601.09790 v2 pith:ARCWGNPT submitted 2026-01-14 hep-ph astro-ph.COastro-ph.HE

The Cosmic Neutrino Background is within Reach of Future Neutrino Telescopes

Gonzalo Herrera , Shunsaku Horiuchi , Xiaolin Qi , Ian M. Shoemaker This is my paper
classification hep-ph astro-ph.COastro-ph.HE
keywords cosmic neutrino backgroundboosted neutrinosdeep inelastic scatteringneutrino telescopesneutrino overdensityultra-high-energy neutrinosrelic neutrinosUHECR
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 paper tries to establish that the cosmic neutrino background (CνB)—the relic neutrinos left over from the early Universe—can be observed indirectly by current and future high-energy neutrino telescopes. It shows that cosmic rays scattering off relic neutrinos across cosmic distances boost them to ultra-high energies, and that including deep-inelastic scattering, not just elastic scattering, raises the predicted flux substantially. With this channel, existing neutrino-telescope data already cap the cosmological relic-neutrino overdensity at roughly one hundred to one thousand for a lightest neutrino mass above 0.1 eV. The planned next-generation telescope could test overdensities of order one to ten, and a network of ten comparable instruments could reach the density that standard cosmology predicts. A sympathetic reader would care because direct detection of the CνB would open a window to the Universe one second after the Big Bang and probe neutrino masses and clustering.

Core claim

The central claim is that the diffuse boosted cosmic neutrino background (DBCνB)—the flux of relic neutrinos upscattered by cosmic-ray protons at all redshifts—is dominated at the highest energies by neutral-current deep-inelastic scattering, a channel neglected in earlier work. For a lightest neutrino mass mν ≳ 0.1 eV, protons near the GZK cutoff scatter on relic neutrinos with center-of-mass energies in the DIS regime, producing a sharp flux of boosted neutrinos at Eν ≈ 10^10 GeV. Comparing this flux to current upper limits, the authors find IceCube already excludes relic-neutrino overdensities η ≳ O(100–1000) on cosmological scales; IceCube-Gen2 could test η ~ O(1–10), and a combination o

What carries the argument

The load-bearing object is the cosmic-ray boosted relic-neutrino flux integral, Eq. (1), which sums scattering events over all redshifts, cosmic-ray energies, and assumed source evolutions. It is evaluated with three ingredients: a broken power-law proton spectrum normalized to Earth observations; three assumed redshift evolutions of cosmic-ray sources (star formation, quasars/FR-II, and gamma-ray bursts); and Standard Model proton–neutrino cross sections for neutral-current elastic, charged-current quasi-elastic, and neutral-current deep-inelastic scattering. The DIS cross section uses parton distribution functions and becomes dominant above proton energies E_th ≃ 1.9×10^10 GeV for mν = 0.1

Load-bearing premise

The strongest limits rely on the highest-energy cosmic rays being protons whose source spectra are extrapolated from local observations to z ≈ 6 through a few assumed evolution models; the paper states this explicitly. If very-high-energy cosmic rays are mostly heavy nuclei with a different high-redshift population, the deep-inelastic boosted flux—and the derived overdensity limits—would weaken substantially.

What would settle it

Measure the composition of ultra-high-energy cosmic rays above ~2×10^10 GeV: if they are dominated by nuclei with charge Z ≳ 6 rather than protons, the DIS-boosted flux falls by an order of magnitude or more, and the claimed IceCube limit on η no longer holds. Conversely, a future neutrino telescope that sees a non-democratic, mass-eigenstate flavored flux at Eν ≈ 10^10 GeV in excess of the cosmogenic prediction would confirm the boosted-CνB mechanism.

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

If this is right

  • If the calculation is right, current IceCube data already constrain the relic-neutrino overdensity at cosmological scales to ≲10^3, a scale no other probe has reached.
  • IceCube-Gen2 alone would push the reach down to η ~ 1–10 for mν ≳ 0.1 eV, turning the CνB from an untestable relic into a near-term target.
  • A network of ten comparable telescopes could test the ΛCDM-predicted CνB density, i.e., η ~ 1, for neutrino masses within the sharpest laboratory bound.
  • The boosted CνB constitutes an irreducible 'neutrino fog' that any future ultra-high-energy neutrino detection—cosmogenic or exotic—must be disentangled from.
  • The flavor composition of the boosted CνB, non-democratic and set by mass eigenstates, differs from cosmogenic neutrinos, providing a discrimination handle.

Where Pith is reading between the lines

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

  • It is plausible that the same DIS-boosting mechanism applies to cosmic rays scattering off other relic particles, so a null result in future searches could translate directly into constraints on new physics in the neutrino sector—an extension the paper only gestures at.
  • A natural extension would be to replace the pure-proton assumption with mixed-composition UHECRs: heavy nuclei would suppress both cosmogenic and boosted fluxes, but likely asymmetrically, so the relative sensitivity could survive or even improve.
  • The paper's neglect of τ production in charged-current scattering is conservative; including it would raise the predicted flux and tighten the η limits, making the claimed reach a lower bound on the discovery potential.
  • If the CνB is detected this way, the inferred η would directly test models of neutrino clustering and structure formation on megaparsec scales, giving a new cosmological handle beyond CMB and BBN measurements.

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 / 5 minor

Summary. The paper computes the diffuse flux of cosmic neutrino background (CνB) neutrinos boosted by cosmic-ray protons through neutral-current elastic, charged-current quasi-elastic, and neutral-current deep-inelastic scatterings, integrated over redshift. It then uses existing ultra-high-energy neutrino upper limits from IceCube, Auger, and ANITA to convert the flux into upper limits on the CνB overdensity η as a function of lightest neutrino mass (Eq. (1), Fig. 3). The authors find that IceCube already constrains η at O(100–1000) for mν ≳ 0.1 eV, that IceCube-Gen2 could reach O(1–10), and that a combination of 10 comparable future telescopes could test the ΛCDM-expected density. The paper also emphasizes that this probe can beat the Pauli-exclusion bound and constitutes an irreducible 'neutrino fog' for ultra-high-energy neutrino searches.

Significance. The significance is high if the central assumptions hold. The NC DIS channel is a genuine new contribution that moves the reach from local/single-galaxy scales to cosmological-scale overdensities and improves the projected sensitivity by orders of magnitude. The derivation is transparent and uses standard cross sections and public PDFs (Appendix B), and the paper carefully separates the ES and DIS limits (Appendix D). The statement that the boosted CνB forms a 'neutrino fog' for other UHE neutrino signals is a useful conceptual contribution. However, the headline claims are conditional on a pure-proton UHECR spectrum and on a specific high-z source evolution, and the paper itself defers a composition treatment to future work. Given that the DIS channel dominates the limits precisely in the energy range where UHECR composition is poorly known, the quantitative results as presented are not yet robust enough for the abstract's strong claims.

major comments (4)
  1. [Deep inelastic scattering / Eq. (4) / Fig. 3 (left)] The DIS contribution, which drives the most stringent η limit for mν ≳ 0.06 eV, is computed under the assumption that UHECRs are purely protons. For mν=0.1 eV the threshold E_p^th ≃ 1.876×10^10 GeV lies in the composition-transition region, where Auger and TA data imply a mixed composition with a reduced proton fraction. Since the DIS flux is proportional to the proton flux and the η limit scales as η ∝ 1/flux, a proton fraction of 10–30% at these energies would weaken the IceCube limit from O(100–1000) to O(10^3–10^4). The Conclusion acknowledges a pure-proton limitation but does not quantify it. I request a quantitative composition benchmark (e.g., a mixed-composition model with rigidity cutoff, or even a constant rescaling) and the corresponding η limits. Without this, the headline reach cannot be evaluated.
  2. [Diffuse Boosted Cosmic Neutrino Background / Appendix A] The flux integral in Eq. (1) relies on three source-evolution functions with fixed spectral indices α=2.5 (SFR), 2.3 (QSO), 2.4 (GRB), taken from Ref. [46], and integrates to z_max=6. These indices were derived by fitting a propagated pure-proton spectrum to local UHECR data; they do not include the uncertainty in the high-z source population or in the injection spectrum. The band in Fig. 2 only spans the three f_i(z), not the uncertainty in α or z_max. Since the DIS flux accumulates over the full redshift range, the projected O(1–10) reach and the 10-telescope ΛCDM test depend on these choices. Please provide a systematic scan (e.g., α∈[2.0,2.8], z_max∈[4,10]) or an error budget on η.
  3. [Deep inelastic scattering / Abstract] The abstract and introduction claim that the paper computes the total DBCνB 'accounting for neutral current and charged current elastic and deep inelastic scatterings.' In the DIS section, however, only NC DIS is included; CC DIS and neutrinos from secondary-hadron decays are dropped with the argument that they are subdominant. This is plausible, but it is an assumption, not a demonstrated result. Because 'total' is a central selling point, the omitted channels should be estimated at least at the level of a rough cross-section ratio, or the wording should be changed to specify that only NC DIS plus CC quasi-elastic are computed. Otherwise the claim of totality is inaccurate.
  4. [Projected limits from future neutrino telescopes / Fig. 3 (right)] The 10-telescope projection assumes comparable sensitivities and scales the combined limit as N^{-1/2} (or by exposure in the background-free regime). The listed future instruments operate in different energy windows and have very different effective areas, backgrounds, and systematics; the 'similar sensitivity' assumption is ideal. The statement that 10 such instruments would test the ΛCDM CνB density is therefore a scaling exercise rather than a detector-level projection. I recommend stating this explicitly and, ideally, replacing or supplementing the idealized combination with a convolution of published differential sensitivities.
minor comments (5)
  1. [Fig. 2 / main text] There is an inconsistency between 'Anita I-IV' (Fig. 2 and Ref. [42]) and 'Anita I-V' (limits section). Also, the Fig. 2 caption contains the typo 'dooted' for 'dotted'.
  2. [Fig. 3 / caption] The NH/IH abbreviations in the legend are not decoded in the caption, and the caption text states 'normal (inverted) neutrino mass hierarchies in solid (dashed)' while the legend ordering appears reversed in the discussion. Please check consistency.
  3. [Appendix D heading] The heading 'F uture neutrino telescopes' contains a spacing typo.
  4. [Appendix F / Fig. 3 (left)] The Pauli-principle limit η≤2×10^4 is quoted for massless neutrinos, while the formula above it is mν-dependent. Clarify which curve is shown in Fig. 3 and why the massless bound is relevant for the mν ≳ 0.1 eV claims.
  5. [Eq. (1) / text after Eq. (1)] Define η explicitly in the text (it appears to be the overdensity relative to the cosmological average nν=336 cm^-3) and clarify whether the boosted neutrino energy Tν in the Θ function is the observed energy after redshift or the energy at scattering redshift.

Circularity Check

0 steps flagged

No significant circularity: the η limits are a linear re-scaling of external UHE-neutrino flux limits, not a re-fit of the target parameter.

full rationale

The derivation is self-contained with respect to the target parameter. The DBCνB flux in Eq. (1) is linearly proportional to the overdensity η (factor η nν in the integrand); the paper then derives upper limits by requiring this flux not to exceed externally measured IceCube/Auger/ANITA flux limits (Sec. 'Limits from current neutrino telescopes'). This is the standard way to convert an external upper limit into a constraint on a linear parameter, not a fitted input renamed as a prediction. The CR spectrum uses a broken power law normalized to Earth observations and source-evolution functions from the literature [46,51-53]; the spectral indices α are fixed by propagation through the CMB, independent of the CνB or neutrino-telescope data. The only self-citations are [34] for the master integral Eq. (1) and [16] for single-galaxy boosted fluxes; [34] is prior work by overlapping authors, but Eq. (1) is a generic cosmological line-of-sight integral and the new NC DIS/CC contributions are evaluated with standard cross sections and external PDFs. No uniqueness theorem or ansatz is imported from self-citation to force the result, and no equation reduces to itself or to a fitted version of η. Composition uncertainties (pure-proton assumption) affect the normalization but are a correctness risk, not circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

No new particles, forces, or dimensions are introduced; all channels are Standard Model. The DBCνB 'fog' is a label for the computed flux, not a new physical entity. The main external inputs are the SM cross sections, the UHECR spectrum model, the source evolution functions, and the experimental sensitivity curves.

free parameters (5)
  • η (CνB overdensity) = constrained upper limit O(100–1000) for mν≳0.1 eV; ΛCDM expectation 1
    Multiplies the homogeneous relic-neutrino density in Eq. (1); it is the target of the derived limits, not a fitted constant.
  • CR high-energy spectral index α = 2.5 (SFR), 2.3 (QSO), 2.4 (GRB)
    Chosen following [46] so the propagated UHECR spectrum matches local observations; directly sets the DIS-boosted flux and the η limits.
  • Cosmic-ray source evolution f_i(z) = SFR, QSO, GRB parameterizations (Appendix A)
    Three alternative source redshift distributions from [51–53]; the spread across them is the main systematic band in Figs. 2–3.
  • z_min and z_max = z_min=2.37e-6, z_max=6
    Integration range in Eq. (1); z_min corresponds to the Milky Way scale, z_max is nominal.
  • Benchmark neutrino mass = 0.1 eV
    Used for flux figures and for quoting the DIS threshold; limits are scanned over m_lightest from 1e-4 to 1 eV.
axioms (6)
  • domain assumption SM neutrino–nucleon cross sections (NC elastic, CC quasi-elastic, NC DIS) and the PDFs from ManeParse are correct in the energy ranges considered.
    Central to Eq. (1) and Appendix B; PDF uncertainties are quoted as ~2%.
  • ad hoc to paper UHECRs are purely protons.
    Assumed after Eq. (2); the authors note heavy nuclei would change results.
  • domain assumption The local broken power-law CR spectrum and the three source-evolution functions can be extrapolated to z≈6 without additional propagation losses beyond the α choice.
    Underlies Eq. (1) and Appendix A; high-z UHECR flux is unmeasured.
  • domain assumption The CνB is homogeneous with a single redshift-independent overdensity η on cosmological scales.
    Allows Eq. (1) to pull η out of the integral; clustering is only a factor ≤10 at galaxy scales (Appendix F).
  • ad hoc to paper τ-production CC, charged-current DIS, and neutrinos from secondary hadron decays are subdominant and can be neglected.
    Stated in the DIS and CC sections; argued kinematically, not by a full calculation.
  • standard math Standard ΛCDM background evolution (H0=67.4, Ωm=0.315, ΩΛ=0.685) and FLRW redshift integral.
    Eq. (1) uses the Hubble factor from Planck [4].

pith-pipeline@v1.3.0-alltime-deepseek · 13923 in / 17471 out tokens · 168628 ms · 2026-08-03T10:29:58.044935+00:00 · methodology

0 comments
read the original abstract

The cosmic neutrino background (C$\nu$B) can be boosted to high energies due to scatterings with energetic cosmic rays (CRs) across cosmological scales. Previous calculations focused on neutral current incoherent and coherent elastic scatterings of cosmic-ray protons off relic neutrinos. However, charged current interactions and deep inelastic scatterings are also expected to occur, which enhances the boosted relic neutrino fluxes on Earth. Here, we compute the \textit{total} diffuse boosted cosmic neutrino background (DBC$\nu$B) arising from CRs at all redshifts in the Universe, accounting for neutral current and charged current elastic and deep inelastic scatterings. We find that IceCube already places an upper limit on the cosmic neutrino background overdensity in cosmological scales of ~$\mathcal{O}(100-1000)$ at $E_{\nu}=10^{10}$ GeV, for a lightest neutrino mass of $m_{\nu} \gtrsim 0.1$ eV. We further show that IceCube-Gen2 could test $\mathcal{O}(1-10)$ C$\nu$B overdensities, and the combination of $10$ future neutrino telescopes with similar sensitivity would allow us to test the $\Lambda$CDM expected C$\nu$B density for a lightest neutrino mass compatible with the KATRIN bound.

Figures

Figures reproduced from arXiv: 2601.09790 by Gonzalo Herrera, Ian M. Shoemaker, Shunsaku Horiuchi, Xiaolin Qi.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the cosmic-ray boosted relic neutrino mechanism. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

discussion (0)

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Forward citations

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