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Neutrino Interactions at Ultrahigh Energies

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ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Raj Gandhi, Chris Quigg, Mary Hall Reno, Ina Sarcevic

High Energy Physics - Phenomenology · Submitted 6 Jul 1998 · 69 references

Pith's verdict: The cross-section tables and the Eq. (2.10) fits are the durable product and they hold up; the reliability band is asserted with a pointer to the authors' earlier paper rather than derived at the energy where it matters.

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arXiv IDhep-ph/9807264 (version 1)
Pith IDW72FVQOJ, Pith's permanent record of this paper and its review
CitationChris Quigg, Ina Sarcevic, Mary Hall Reno, Raj Gandhi. "Neutrino Interactions at Ultrahigh Energies." arXiv:hep-ph/9807264 (1998). https://pith.science/paper/W72FVQOJ
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The paper

The paper claims

The paper recalculates neutrino-nucleon cross sections from $10^{9}$ to $10^{21}$ eV with updated parton distributions, finding values at most 25% below its own earlier results and fixing the interaction rates that future neutrino observa t

The reading

This paper asks a practical question for neutrino astronomy: how strongly does an ultrahigh-energy neutrino interact with a nucleon, and how much of that answer can be trusted? The authors recompute the charged-current and neutral-current deep-inelastic cross sections over twelve orders of magnitude in neutrino energy, swapping the older CTEQ3 parton distributions for CTEQ4, and tabulate the results so that other groups can use them directly. They then take several published models of extraterrestrial neutrino flux and convert the cross sections into expected event rates in cubic-kilometre water and ice detectors and in a large ground array. The point is not one number but a calibrated input: without a reliable cross section, no claimed detection rate from an active galaxy or a gamma-ray burst can be believed. A sympathetic reader should care because the same cross section simultaneously sets the signal and the shielding — it decides both how often a neutrino converts to a muon and how much of the Earth the neutrino can pass through to reach the detector.

What carries the argument

The load-bearing object is the parton-model expression for the double-differential cross section, $d^2σ/dxdy = 2G_F^2 M E_ν/π · (M_W^2/(Q^2+M_W^2))^2 [xq(x,Q^2) + xbar{q}(x,Q^2)(1-y)^2]$, with a matching neutral-current version built from the chiral couplings $L_u, L_d, R_u, R_d$. The $W$ propagator factor damps the linear rise of the cross section once $Q^2$ approaches $M_W^2$, which is what turns a cross section that grows linearly at low energy into a power law at high energy. The second piece of machinery is the shadow factor $S(E_ν)$, an angular average of $exp[-z(θ)/L_{int}(E_ν)]$ over the column depth of the Earth, which converts an isotropic cosmic flux into the upward-muon rate a detector actually sees. The third is the muon-range probability $P_μ = N_A σ_{CC} ⟨R(E_ν; E_μ^{min})⟩$, which ties the neutrino cross section to the observable threshold energy of the muon.

Extended reading notes

Core claim

The paper's central claim is that the inclusive neutrino-nucleon cross sections computed in the renormalization-group-improved parton model with the CTEQ4-DIS distributions are the appropriate inputs for ultrahigh-energy rate estimates, and that they differ only modestly from the authors' earlier CTEQ3-based numbers. Concretely, at $E_ν = 10^{21}$ eV the new cross sections are about 25% smaller than the earlier ones, because the CTEQ4 sea quarks rise more gently toward small $x$ ($xq_s ∝ x^{-0.227}$ rather than $x^{-0.332}$). Below $10^{16}$ eV every standard parton distribution gives essentially the same answer; above it, the answer depends on unmeasured small-$x$ behaviour, and the authors put the spread at a factor $2^{±1}$ near $10^{20}$ eV. The tabulated cross sections are well described between $10^{16}$ and $10^{21}$ eV by simple power laws, for example $σ_{CC}(νN) = 5.53×10^{-36}(E_ν/1~GeV)^{0.363}~cm^2$. From these numbers follow the paper's physical corollaries: the Earth's diameter exceeds the neutrino interaction length above roughly 40 TeV, and the $W$-boson resonance in $bar{ν}_e e$ scattering at about 6.3 PeV extinguishes an electron-antineutrino beam that crosses the Earth.

Load-bearing premise

Everything above about $10^{16}$ eV rests on extrapolating the fitted small-$x$ behaviour of the sea-quark distributions into a region with no direct experimental constraint, and the authors acknowledge that the resulting uncertainty is at most a factor $2^{±1}$ near $10^{20}$ eV.

Editorial extensions

If this is right

  • For neutrino energies up to about $10^{16}$ eV, the predicted event rates are insensitive to which modern parton distribution set is used, so disagreement between rate predictions in that range must come from the flux models, not the cross section.
  • Because the Earth's diameter exceeds the neutrino interaction length above roughly 40 TeV, upward-going muon searches lose reach as the energy threshold rises, and the fraction of events arriving near the horizon grows — between 77% and 94% of the extraterrestrial signal at a 100 TeV threshold comes from nadir angles between 60 and 90 degrees.
  • A detector with 0.1 km$^2$ effective area should see tens to hundreds of upward muons per year above a 10 TeV threshold for the more generous active-galaxy flux models, while atmospheric neutrinos remain a comparable or larger background at a 1 TeV threshold.
  • Resonant $bar{ν}_e e → W^-$ production at 6.3 PeV will be hard to separate from ordinary neutrino-nucleon charged- and neutral-current events in the same energy window, since the nucleon-interaction background is itself of comparable size.
  • For a large ground array, the most promising neutrino-induced horizontal air showers come from $(ν_e + bar{ν}_e)N$ charged-current interactions, where the shower energy is essentially the full neutrino energy; the rates are a few per year at best for the modern active-galaxy flux estimates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's own variant-distribution checks (CTEQ4-HJ, MRS-D$'$, CTEQ3-DLA) span only about 15 to 30% in the cross section, yet the quoted factor $2^{±1}$ at $10^{20}$ eV is inherited from the earlier paper's more extreme variations. That gap suggests the true uncertainty band is narrower than advertised, and a reader could reasonably treat the $10^{20}$ eV numbers as better determined than the st
  • If the small-$x$ sea rise is the dominant unknown, then the angular distribution of upward muons near the horizon is a more efficient discriminant than the total rate: shadowing maps neutrino energy onto nadir angle, so a measured angular shape at fixed threshold probes the cross section at a specific energy without requiring absolute flux normalisation.
  • The same cross-section tables that feed neutrino astronomy also bound any new physics that would enhance neutrino-nucleon interactions at ultrahigh energy, because a large enhancement would shorten the interaction length and visibly flatten the observed angular distribution of upward events.
  • A future measurement of the proton sea at $x$ between $10^{-6}$ and $10^{-8}$ at $Q^2$ near $M_W^2$ — from a next-generation deep-inelastic experiment or from precision electroweak fits — would convert the paper's extrapolated power law into a constrained input and shrink the high-energy error band directly.
Original abstract

We report new calculations of the cross sections for deeply inelastic neutrino-nucleon scattering at neutrino energies between $10^{9}\ev$ and $10^{21}\ev$. We compare with results in the literature and assess the reliability of our predictions. For completeness, we briefly review the cross sections for neutrino interactions with atomic electrons, emphasizing the role of the $W$-boson resonance in $\bar{\nu}_{e}e$ interactions for neutrino energies in the neighborhood of $6.3\pev$. Adopting model predictions for extraterrestrial neutrino fluxes from active galactic nuclei, gamma-ray bursters, and the collapse of topological defects, we estimate event rates in large-volume water \v{C}erenkov detectors and large-area ground arrays.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,755 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.28 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.58 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We report new calculations of the cross sections for deeply inelastic neutrino-nucleon scattering at neutrino energies between $10^{9}\ev$ and $10^{21}\ev$. We compare with results in the literature and assess the reliability of our predictions. For completeness, we briefly review the cross sections for neutrino interactions with atomic electrons, emphasizing the role of the $W$-boson resonance in $\bar{\nu}_{e}e$ interactions for neutrino energies in the neighborhood of $6.3\pev$. Adopting model predictions for extraterrestrial neutrino fluxes from active galactic nuclei, gamma-ray bursters, and the collapse of topological defects, we estimate event rates in large-volume water \v{C}erenkov detectors and large-area ground arrays.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We report new calculations of the cross sections for deeply inelastic neutrino-nucleon scattering at neutrino energies between $10^{9}\ev$ and $10^{21}\ev$. contribution 0.99 0.95 0.14 asserted 0.99
s1 We compare with results in the literature and assess the reliability of our predictions. method 0.70 0.82 0.04 asserted 0.55
s2 For completeness, we briefly review the cross sections for neutrino interactions with atomic electrons, emphasizing the role of the $W$-boson resonance in $\bar{\nu}_{e}e$ interactions for neutrino energies in the neighborhood of $6.3\pev$. background 0.75 0.24 0.04 asserted 0.72
s3 Adopting model predictions for extraterrestrial neutrino fluxes from active galactic nuclei, gamma-ray bursters, and the collapse of topological defects, we estimate event rates in large-volume water \v{C}erenkov detectors and large-area ground arrays. contribution 0.61 0.87 0.16 asserted 0.95

What kind of paper the classifier reports this is: theoretical result 0.82 · evidence from simulation or computation 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1. Cross sections for
Figure 2. FIG. 2. Ratio of the charged-current cross section shown in F
Figure 3. FIG. 3. Cross sections for ¯ν
Figure 4. FIG. 4. Cross sections for
Figure 5. FIG. 5. Ratio of the charged-current cross section shown in F
Figure 6. FIG. 6. Interaction lengths for neutrino interactions on nu
Figure 7. FIG. 7. Interaction lengths for antineutrino interactions
Figure 8. FIG. 8. Interaction lengths for neutrino interactions on el
Figure 9. FIG. 9. Muon neutrino plus antineutrino fluxes scaled by neut
Figure 10. FIG. 10. Differential shadow factor (1
Figure 11. FIG. 11. Acceptance versus shower energy for nearly horizon

Figures reproduced from arXiv:hep-ph/9807264 by the authors.

References
How later papers used it

98 later papers cite it

Evidence: substantial. 84 of the citing papers share no author with it, and 31 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 151 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 of 6 papers with this label

  • Performed its deep inelastic scattering simulation with Pythia6.4 and CTEQ5d PDFs combined with this paper for cross section calculations.

    The Giant Radio Array for Neutrino Detection (2015) · 0.90 · paraphrased: the licence does not allow quoting

Uses its data or values 3 of 23 papers with this label
How the literature uses it

91 arXiv papers cite this in 143 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 76 sentences without a confident label

Uses its method or tool 5 papers
  • Given our interest in high energies, we calculated the neutrino isoscalar nucleon cross section using the CTEQ6 parton distribution functions [ref] for $E_ν= 50-10^12$ GeV [ref] .

    High energy leptons from muons in transit · Neutrino charged current interactions · 0.88

  • The simulation of the Deep Inelastic Scattering of the neutrinos is performed with Pythia6.4, using the CTEQ5d probability distribution functions (PDF) combined with [ref] for cross section calculations.

    The Giant Radio Array for Neutrino Detection · GRAND layout and neutrino sensitivity · 0.90

  • Thus, the number of events ($N_jk(ν_β)$ for $ν_β$ and $N_jk(ν̅_β)$ for $ν̅_β$) for the energy bin ($E_j<E<E_j+1$) and zenith angle bin ($cosΘ_k<cosΘ<cosΘ_k+1$) can be expressed in terms of the flux $Φ(ν_α, E', Θ')$, the cross section [ref] ($σ_X(E')$ for neutrinos and $σ̅_X(E')$ for antineutrinos, for CC ($X=CC$) and NC ($X=NC$) interactions, respectively) and the detection efficiency $ϵ_X(E,ν_β) (X=CC, NC)$ as follows: [equation] $R_e$ and $R_z$ represent the resolution functions in the neutrino energy and zenith angle, respectively: [equation] where $E'$ and $Θ'$ are the true neutrino energy and zenith angle, respectively, whereas $E$ and $Θ$ are the reconstructed ones, respectively.

    Search for sterile neutrinos by shower events at a future neutrino telescope · Numbers of events · 0.86

Uses its data or values 21 papers
  • For the fluorescence observation mode of POEMMA, its sensitivity [ref] using two different high energy neutrino cross sections, labeled GQRS [ref] and BDH [ref] , is combined with a uniform differential exposure over the entire sky.

    Indirect dark matter searches at ultrahigh energy neutrino detectors · Dark matter annihilation to neutrinos · 0.90

  • where E$_th$ is the threshold energy, $T$ corresponds to the observation time of the flare [ref] , $σ_νN()=6.78×10^-35(/TeV)^0.363$ cm$^2$ is the charged current cross section [ref] , $ρ_ice$=0.9 g cm$^-3$ is the density of the ice and V$_i$ is the effective volume of detector, then the expected number of neutrinos inferred from this flare is

    Could a plasma in quasi-thermal equilibrium be associated to the "orphan" TeV flares ? · High-energy neutrinos · 0.95

  • The effective area of the detector for neutrinos can be defined as [equation] where $ρ_ice =0.9 ^3$, $N_A = 6.022 ×10^23 ^-1$ (to convert grams to nucleons), $σ_νN(E)$ is the neutrino-nucleon cross-section [ref] and $V(E) ≈0.04$ km$^3$ is the effective volume of the DeepCore detector for a neutrino-induced shower of energy $E$ [ref] .

    High-Energy Neutrino Signatures of Dark Matter Decaying into Leptons · Introduction · 0.92

Compares with it 10 papers
Cites it as support 1 paper
Cites it as background 17 papers
  • Among the uncertainties in these tau neutrino flux limits or eventual observation are three elements: the uncertainty in the high energy neutrino cross section [ref] required to convert the tau neutrino to the tau lepton in the Earth, the inelasticity for neutrino scattering with isoscalar nucleons (how much of the neutrino energy is transferred to the tau) and the tau electromagnetic loss [ref] as the tau transits the remaining rock before it emerges to decay into an air shower.

    Tau energy loss and ultrahigh energy skimming tau neutrinos · Introduction · 0.86

  • In the case of the neutrino telescopes described above, the signal arises from the interaction [ref] of a highly energetic neutrino with a nucleon from the target material, typically an H$_2$O molecule.

    Neutrino Telescopes as QCD Microscopes · Introduction · 0.86

  • There is an extensive literature on the high energy extrapolations of the neutrino-nucleon cross section [ref] .

    Cosmic tau neutrino detection via Cherenkov signals from air showers from Earth-emerging taus · Neutrino interactions · 0.99

Discussion

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