Pith. sign in

REVIEW 1 major objections 1 minor 1 cited by

Implications of a Cosmogenic Origin of KM3-230213A for Ultra-High-Energy Protons

T0 review · 1 major / 1 minor · reviewed 2026-05-25 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A cosmogenic origin for the KM3-230213A neutrino requires strongly evolving ultra-high-energy proton sources unless null results from other detectors are included.

desk verdict The paper gives updated source-evolution bounds for UHE protons only if KM3-230213A is cosmogenic; the ~20% proton fraction at 20 EeV comes mostly from composition data anyway. read the letter →

arxiv 2603.13476 v2 pith:C7NAO6KU submitted 2026-03-13 astro-ph.HE

A. R. Alhebsi , Arjen van Vliet , Domenik Ehlert , Satyendra Thoudam This is my paper · ORCID
classification astro-ph.HE
keywords ultra-high-energycosmicrayscosmogenicneutrinosKM3NeTsourceevolutionprotonfractionactivegalacticnucleimulti-messengerconstraintsUHECRcomposition
verification ladder T0 review T1 audit T2 compute T3 formal

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 paper explores the consequences of interpreting the KM3-230213A neutrino event as produced by ultra-high-energy protons interacting with background photons. It constructs the best-fit spectrum and composition of ultra-high-energy cosmic rays using a two-population model that incorporates this single neutrino detection along with other multi-messenger data. The fit shows that explaining the event with only KM3NeT exposure demands strong redshift evolution of the proton sources, matching expectations for high-luminosity active galactic nuclei. Adding the lack of similar events in Pierre Auger and IceCube observations instead disfavors that strong evolution. Across both scenarios the proton fraction stays near 20 percent at 20 EeV because composition measurements fix it.

What carries the argument

A two-population model of ultra-high-energy cosmic rays consisting of a mixed-composition population and a subdominant ultra-high-energy proton population, whose parameters are jointly constrained by the cosmic-ray spectrum, composition, and the single cosmogenic neutrino event.

What would settle it

A direct measurement establishing that KM3-230213A did not arise from ultra-high-energy proton interactions with background photons, or the detection of a rate of additional cosmogenic neutrinos inconsistent with the rate predicted by the best-fit model.

Watch

Extended reading notes

Core claim

Interpreting KM3-230213A as cosmogenic fixes the parameters of a two-population ultra-high-energy cosmic ray model so that the subdominant proton population must evolve strongly with redshift to produce one event in the KM3NeT exposure; including the null results from Pierre Auger and IceCube disfavors such strong evolution, while the proton fraction remains approximately 20 percent at 20 EeV from composition constraints.

Load-bearing premise

The neutrino event KM3-230213A is of cosmogenic origin produced by interactions of UHE protons with background photons.

Editorial extensions

If this is right

  • Strongly evolving ultra-high-energy proton sources are required to match the single KM3NeT neutrino detection when only that exposure is considered.
  • Null observations from Pierre Auger and IceCube disfavor strongly evolving proton sources.
  • The proton fraction of ultra-high-energy cosmic rays is constrained to approximately 20 percent at 20 EeV by composition data in both cases.
  • The model yields 68 percent confidence-level constraints on the parameters of the two-population ultra-high-energy cosmic ray description.

Reading between the lines

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

  • Additional high-energy neutrino detections would narrow the allowed range of source evolution parameters for the proton population.
  • The 20 percent proton fraction at 20 EeV implies a specific expected rate of cosmogenic neutrinos at still higher energies that future detectors could test.
  • The contrast between the single-event and null-result constraints underscores the importance of accurate exposure calculations across observatories.
Share X Bluesky LinkedIn Reddit HN

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

1 major / 1 minor

Summary. The manuscript claims that interpreting the single KM3-230213A neutrino event (72 PeV–2.6 EeV) as cosmogenic (produced by UHE protons interacting with background photons) allows constraints on a two-population UHECR model (mixed-composition population plus subdominant protons) when fitted simultaneously to UHECR spectrum, composition, and the neutrino event. Under this assumption, the KM3NeT exposure alone requires strongly evolving proton sources (consistent with high-luminosity AGN), while adding null results from Auger and IceCube disfavors strong evolution; in both cases the proton fraction at 20 EeV is ~20% and is stated to be set primarily by composition data rather than the neutrino event.

Significance. If the cosmogenic interpretation holds, the work supplies useful multi-messenger constraints that separate the impact of a single high-energy neutrino detection on source-evolution parameters from the composition-driven limit on the proton fraction. The explicit conditioning on the interpretation and the consistency of the proton-fraction result across the two dataset combinations are strengths.

major comments (1)
  1. [Abstract] Abstract: the central claims on source evolution (strong evolution required by KM3NeT alone; disfavored when Auger/IceCube nulls are added) rest entirely on the assumption that KM3-230213A is cosmogenic. The manuscript provides no quantitative robustness check, likelihood ratio, or odds assessment against non-cosmogenic (astrophysical or background) origins for the event; this assumption is load-bearing for all evolution constraints and therefore requires explicit treatment.
minor comments (1)
  1. The energy range quoted for KM3-230213A should be cross-checked for consistency with the energy binning and exposure calculations used in the fits to the neutrino flux.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claims on source evolution (strong evolution required by KM3NeT alone; disfavored when Auger/IceCube nulls are added) rest entirely on the assumption that KM3-230213A is cosmogenic. The manuscript provides no quantitative robustness check, likelihood ratio, or odds assessment against non-cosmogenic (astrophysical or background) origins for the event; this assumption is load-bearing for all evolution constraints and therefore requires explicit treatment.

    Authors: We agree that the evolution constraints are conditional on the cosmogenic interpretation of KM3-230213A. The manuscript already signals this explicitly via the abstract phrasing 'When interpreted as cosmogenic in origin' and the title. The analysis is framed as deriving implications under that hypothesis rather than determining the origin probability. A full likelihood-ratio or odds assessment against astrophysical or background origins would require detailed modeling of the expected non-cosmogenic neutrino flux and KM3NeT-specific backgrounds, which is outside the present scope. To make the conditional nature more transparent, we will revise the abstract and add a short clarifying paragraph in the introduction (and conclusions) that reiterates the assumption and notes that alternative origins are possible but not quantified here. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; standard multi-messenger fit is self-contained

full rationale

The paper fits a two-population UHECR model (mixed composition plus subdominant protons) to spectrum, composition, and the single KM3NeT event under an explicit conditional interpretation as cosmogenic. Resulting constraints on evolution parameters and the ~20% proton fraction at 20 EeV are direct outputs of that external-data fit, not reductions by construction. No self-definitional equations, no fitted inputs relabeled as predictions, no load-bearing self-citations, and no uniqueness theorems imported from prior author work appear in the provided text. The analysis remains conditional on the cosmogenic assumption but does not exhibit any of the enumerated circular patterns.

Assumptions & free parameters 2 free parameters · 1 assumptions · 0 invented entities

The model relies on a two-population UHECR model with fitted parameters for evolution and composition, assuming cosmogenic origin for the neutrino.

free parameters (2)
  • source evolution parameters
    Parameters describing the redshift evolution of UHE proton sources are fitted to match the neutrino event rate.
  • proton fraction at 20 EeV
    The fraction of protons in UHECRs at 20 EeV is constrained by composition data in the model.
assumptions (1)
  • domain assumption The neutrino event KM3-230213A is of cosmogenic origin from UHE proton interactions.
    This is the central interpretation used to derive constraints on source evolution.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Implications of a Cosmogenic Origin of KM3-230213A for Ultra-High-Energy Protons." pith.science (2026). https://pith.science/paper/C7NAO6KU

@misc{pith2026260313476,
  author       = {Pith},
  title        = {Pith review of: Implications of a Cosmogenic Origin of KM3-230213A for Ultra-High-Energy Protons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C7NAO6KU}},
  note         = {Machine review of arXiv:2603.13476}
}
abstract

A significant neutrino event with an estimated energy between $72\,\mathrm{PeV}$ and $2.6\,\mathrm{EeV}$ was recently observed by the KM3NeT experiment (KM3-230213A). When interpreted as cosmogenic in origin, this event can provide constraints on several phenomenological parameters of UHE proton sources. In this study, we present the best fit to the spectrum and composition of UHECRs that is consistent with multi-messenger constraints, including the detection of a single neutrino event by the KM3NeT detector in the energy range of KM3-230213A. From the best fit, we obtain the 68\% CL constraints on the parameters of a two-population model of UHECRs, comprising a mixed-composition population and a subdominant UHE proton population. Our results indicate that the detection of a single neutrino event in the energy range of KM3-230213A solely with the KM3NeT exposure requires strongly evolving UHE proton sources, consistent with high-luminosity active galactic nuclei. On the other hand, including the null observations from the Pierre Auger and IceCube observatories disfavors such strong evolution. In both cases, the observed proton fraction of UHECRs is primarily constrained by the composition data to be $\sim 20\%$ at $20\,\mathrm{EeV}$.

Figures

Figures reproduced from arXiv: 2603.13476 by the authors.

Figure 1
Figure 1. The CR spectrum (top) and composition observables (bottom) of the KM3NeT-only (left) and joint (right) fits shown alongside data by Auger (P. Abreu et al. 2021; A. Abdul Halim et al. 2023). The contribution of different mass groups is shown with [Amin, Amax], and colored bands indicate the 68% CL range. The Galactic component is added to our model from S. Thoudam et al. (2016), albeit with a free normalization. In t… view at source ↗
Figure 2
Figure 2. Cosmogenic neutrinos (solid lines) and diffuse electromagnetic-cascade gamma rays (dashed lines) of the KM3NeT-only (left) and joint (right) fits. All neutrino fluxes are per-flavor, assuming flavor equipartition post-propagation. Contributions from the mixed and pure-proton populations are shown in purple and orange, respectively, with bands indicating the 68% CL range. We show the IGRB measured by Fermi-LAT, IceCu… view at source ↗
Figure 3
Figure 3. The 68% CL range in the model-predicted in￾tegral flux of UHE gamma rays and current 95% CL upper limits posed by Auger (P. Abreu et al. 2023; A. Abdul Halim et al. 2024b) and the Telescope Array (R. U. Abbasi et al. 2019). the KM3-230213A event could constrain two important properties of UHECRs: the observed fraction of UHE protons and the cosmological evolution of their sources. We have adopted a scenario in which… view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The soft volume of ultra-high energy neutrinos experiments

    hep-ph 2026-07 conditional novelty 6.0 of 10

    A drift-diffusion approximation of muon energy loss maps ultra-high-energy neutrino fluxes to through-going track rates, with a soft volume several times the instrumented volume.

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages · cited by 1 Pith paper

  1. [1]

    Depth of maximum of air-shower profiles at the Pierre Auger Observatory

    Aab, A., Abreu, P., Aglietta, M., et al. 2014, Physical Review D, 90, 122006, doi: 10.1103/PhysRevD.90.122006

    work page doi:10.1103/physrevd.90.122006 2014

  2. [2]

    Combined fit of spectrum and composition data as measured by the Pierre Auger Observatory.JCAP, 04:038, 2017

    Aab, A., Abreu, P., Aglietta, M., et al. 2017, Journal of Cosmology and Astroparticle Physics, 2017, 038, doi: 10.1088/1475-7516/2017/04/038

    work page doi:10.1088/1475-7516/2017/04/038 2017

  3. [3]

    Aab et al

    Aab, A., Abreu, P., Aglietta, M., et al. 2019, Journal of Cosmology and Astroparticle Physics, 2019, 022, doi: 10.1088/1475-7516/2019/10/022

    work page doi:10.1088/1475-7516/2019/10/022 2019

  4. [4]

    , year = 2018, month = sep, volume =

    Aartsen, M. G., Ackermann, M., Adams, J., et al. 2018, Physical Review D, 98, 062003, doi: 10.1103/PhysRevD.98.062003

    work page doi:10.1103/physrevd.98.062003 2018

  5. [5]

    G., Abbasi, R., Ackermann, M., et al

    Aartsen, M. G., Abbasi, R., Ackermann, M., et al. 2021a, Nature, 591, 220, doi: 10.1038/s41586-021-03256-1

    work page doi:10.1038/s41586-021-03256-1

  6. [6]

    IceCube-Gen2: The window to the extreme universe,

    Aartsen, M. G., Abbasi, R., Ackermann, M., et al. 2021b, Journal of Physics G: Nuclear and Particle Physics, 48, 060501, doi: 10.1088/1361-6471/abbd48

    work page doi:10.1088/1361-6471/abbd48

  7. [7]

    2021, Physical Review D, 104, 022002, doi: 10.1103/PhysRevD.104.022002

    Abbasi, R., Ackermann, M., Adams, J., et al. 2021, Physical Review D, 104, 022002, doi: 10.1103/PhysRevD.104.022002

    work page doi:10.1103/physrevd.104.022002 2021

  8. [8]

    , keywords =

    Abbasi, R., Ackermann, M., Adams, J., et al. 2022, The Astrophysical Journal, 928, 50, doi: 10.3847/1538-4357/ac4d29

    work page doi:10.3847/1538-4357/ac4d29 2022

Show all 84 references
  1. [9]

    2025, Physical review letters, 135, 031001, doi: 10.1103/PhysRevLett.135.031001

    Abbasi, R., Ackermann, M., Adams, J., et al. 2025, Physical review letters, 135, 031001, doi: 10.1103/PhysRevLett.135.031001

    2025 doi

  2. [10]

    U., Abe, M., Abu-Zayyad, T., et al

    Abbasi, R. U., Abe, M., Abu-Zayyad, T., et al. 2019, Astroparticle physics, 110, 8, doi: 10.1016/j.astropartphys.2019.03.003 Abdul Halim, A., Abreu, P., Aglietta, M., et al. 2023, in 38th International Cosmic Ray Conference (ICRC2023)-Cosmic-Ray Physics (Indirect, CRI), 319, d...

    2019 doi

  3. [11]

    2013, Journal of Cosmology and Astroparticle Physics, 2013, doi: 10.1088/1475-7516/2013/02/026

    Abreu, P., Aglietta, M., Ahlers, M., et al. 2013, Journal of Cosmology and Astroparticle Physics, 2013, doi: 10.1088/1475-7516/2013/02/026

    2013 doi

  4. [12]

    M., et al

    Abreu, P., Aglietta, M., Albury, J. M., et al. 2021, The European Physical Journal C, 81, 1, doi: 10.1140/epjc/s10052-021-09700-w

    2021 doi

  5. [13]

    2023, Journal of cosmology and astroparticle physics, 2023, 021, doi: 10.1088/1475-7516/2023/05/021

    Abreu, P., Aglietta, M., Allekotte, I., et al. 2023, Journal of cosmology and astroparticle physics, 2023, 021, doi: 10.1088/1475-7516/2023/05/021

    2023 doi

  6. [14]

    2015, The Astrophysical Journal, 799, 86, doi: 10.1088/0004-637X/799/1/86

    Ackermann, M., Ajello, M., Albert, A., et al. 2015, The Astrophysical Journal, 799, 86, doi: 10.1088/0004-637X/799/1/86

    2015 doi

  7. [15]

    2016, Physical Review Letters, 116, 151105, doi: 10.1103/PhysRevLett.116.151105

    Ackermann, M., Ajello, M., Albert, A., et al. 2016, Physical Review Letters, 116, 151105, doi: 10.1103/PhysRevLett.116.151105

    2016 doi

  8. [16]

    2025a, arXiv preprint arXiv:2511.13886, doi: 10.48550/arXiv.2511.13886

    Adriani, O., Albert, A., Alhebsi, A., et al. 2025a, arXiv preprint arXiv:2511.13886, doi: 10.48550/arXiv.2511.13886

    doi

  9. [17]

    2025b, The Astrophysical Journal Letters, 984, L41, doi: 10.3847/2041-8213/adcc29

    Adriani, O., Aiello, S., Albert, A., et al. 2025b, The Astrophysical Journal Letters, 984, L41, doi: 10.3847/2041-8213/adcc29

    doi

  10. [18]

    2025c, arXiv preprint arXiv:2502.08387, doi: 10.48550/arXiv.2502.08387

    Adriani, O., Aiello, S., Albert, A., et al. 2025c, arXiv preprint arXiv:2502.08387, doi: 10.48550/arXiv.2502.08387

    doi

  11. [19]

    2025d, Physical Review X, 15, 031016, doi: 10.1103/yypk-zmb8

    Adriani, O., Aiello, S., Albert, A., et al. 2025d, Physical Review X, 15, 031016, doi: 10.1103/yypk-zmb8

    doi

  12. [20]

    A., Allison, P., Beatty, J., et al

    Aguilar, J. A., Allison, P., Beatty, J., et al. 2021, Journal of Instrumentation, 16, P03025, doi: 10.1088/1748-0221/16/03/P03025

    2021 doi

  13. [21]

    A., & Sarkar, S

    Ahlers, M., Anchordoqui, L. A., & Sarkar, S. 2009, Physical Review D—Particles, Fields, Gravitation, and Cosmology, 79, 083009, doi: 10.1103/PhysRevD.79.083009

    2009 doi

  14. [22]

    2024, The European Physical Journal C, 84, 885, doi: 10.1140/epjc/s10052-024-13137-2

    Aiello, S., Albert, A., Alshamsi, M., et al. 2024, The European Physical Journal C, 84, 885, doi: 10.1140/epjc/s10052-024-13137-2

    2024 doi

  15. [23]

    R., et al

    Aiello, S., Albert, A., Alhebsi, A. R., et al. 2025, Nature, 638, 376, doi: 10.1038/s41586-024-08543-1

    2025 doi

  16. [24]

    2012, The Astrophysical Journal, 751, 108, doi: 10.1088/0004-637X/751/2/108

    Ajello, M., Shaw, M., Romani, R., et al. 2012, The Astrophysical Journal, 751, 108, doi: 10.1088/0004-637X/751/2/108

    2012 doi

  17. [25]

    2013, The Astrophysical Journal, 780, 73, doi: 10.1088/0004-637X/780/1/73 11

    Ajello, M., Romani, R., Gasparrini, D., et al. 2013, The Astrophysical Journal, 780, 73, doi: 10.1088/0004-637X/780/1/73 11

    2013 doi

  18. [26]

    2023, Bulletin of the Russian Academy of Sciences: Physics, 87, 1059, doi: 10.3103/S1062873823702817

    Allakhverdyan, V., Avrorin, A., Avrorin, A., et al. 2023, Bulletin of the Russian Academy of Sciences: Physics, 87, 1059, doi: 10.3103/S1062873823702817

    2023 doi

  19. [27]

    2005, The Astrophysical Journal, 625, 249, doi: 10.1086/429615 Alvarez-Muˇ niz, J., Filipˇ ciˇ c, A., Lundquist, J

    Aloisio, R., & Berezinsky, V. 2005, The Astrophysical Journal, 625, 249, doi: 10.1086/429615 Alvarez-Muˇ niz, J., Filipˇ ciˇ c, A., Lundquist, J. P., et al. 2025, in UHECR 2024, The 7th International Symposium on Ultra-High-Energy Cosmic Rays, doi: 10.22323/1.484.0025 ´Alvarez...

    2005 doi

  20. [28]

    2025, arXiv preprint arXiv:2502.08484, doi: 10.48550/arXiv.2502.08484

    Baldini, P., Buchner, J., Erkenov, A., et al. 2025, arXiv preprint arXiv:2502.08484, doi: 10.48550/arXiv.2502.08484

    2025 doi

  21. [29]

    A., De Almeida, R

    Batista, R. A., De Almeida, R. M., Lago, B., & Kotera, K. 2019, Journal of Cosmology and Astroparticle Physics, 2019, 002, doi: 10.1088/1475-7516/2019/01/002

    2019 doi

  22. [30]

    2016, Astroparticle Physics, 84, 52, doi: 10.1016/j.astropartphys.2016.08.007

    Berezinsky, V., Gazizov, A., & Kalashev, O. 2016, Astroparticle Physics, 84, 52, doi: 10.1016/j.astropartphys.2016.08.007

    2016 doi

  23. [31]

    2021, PoS, ICRC2021, 338, doi: 10.22323/1.395.0338

    Bergman, D. 2021, PoS, ICRC2021, 338, doi: 10.22323/1.395.0338

    2021 doi

  24. [32]

    Bister, T., & Farrar, G. R. 2024, The Astrophysical Journal, 966, 71, doi: 10.3847/1538-4357/ad2f3f

    2024 doi

  25. [33]

    2025, Physical Review D, 111, 123022, doi: 10.1103/shsw-mct6

    Borah, D., Das, N., Okada, N., & Sarmah, P. 2025, Physical Review D, 111, 123022, doi: 10.1103/shsw-mct6

    2025 doi

  26. [34]

    2019, in EPJ Web of Conferences, Vol

    Castellina, A. 2019, in EPJ Web of Conferences, Vol. 210, EDP Sciences, 06002, doi: 10.1051/epjconf/201921006002

    2019 doi

  27. [35]

    2025, arXiv preprint arXiv:2507.11993, doi: 10.48550/arXiv.2507.11993

    Evoli, C. 2025, arXiv preprint arXiv:2507.11993, doi: 10.48550/arXiv.2507.11993

    2025 doi

  28. [36]

    2026, Nuclear Instruments and Methods in Physics Research Section A:

    Chen, M., Collaboration, H., et al. 2026, Nuclear Instruments and Methods in Physics Research Section A:

    2026

  29. [37]

    Accelerators, Spectrometers, Detectors and Associated Equipment, 171374, doi: 10.1016/j.nima.2026.171374

    2026 doi

  30. [38]

    R., & Muzio, M

    Comisso, L., Farrar, G. R., & Muzio, M. S. 2024, Astrophys. J. Lett., 977, L18, doi: 10.3847/2041-8213/ad955f

    2024 doi

  31. [39]

    2025, The Astrophysical Journal, 991, 96, doi: 10.3847/1538-4357/adf8de de Clairfontaine, G

    Das, S., Zhang, B., Razzaque, S., & Xu, S. 2025, The Astrophysical Journal, 991, 96, doi: 10.3847/1538-4357/adf8de de Clairfontaine, G. F., Perucho, M., & Mart´ ı, J. 2025, Monthly Notices of the Royal Astronomical Society, staf1929, doi: 10.1093/mnras/staf1929

    2025 doi

  32. [40]

    2023, Physical Review D, 107, 103045, doi: 10.1103/PhysRevD.107.103045

    Ehlert, D., Oikonomou, F., & Unger, M. 2023, Physical Review D, 107, 103045, doi: 10.1103/PhysRevD.107.103045

    2023 doi

  33. [41]

    2024, Journal of Cosmology and Astroparticle Physics, 2024, 022, doi: 10.1088/1475-7516/2024/02/022

    Ehlert, D., van Vliet, A., Oikonomou, F., & Winter, W. 2024, Journal of Cosmology and Astroparticle Physics, 2024, 022, doi: 10.1088/1475-7516/2024/02/022

    2024 doi

  34. [42]

    J., & Cousins, R

    Feldman, G. J., & Cousins, R. D. 1998, Physical review D, 57, 3873, doi: 10.1103/PhysRevD.57.3873

    1998 doi

  35. [43]

    C., Somerville, R

    Gilmore, R. C., Somerville, R. S., Primack, J. R., & Dom´ ınguez, A. 2012, Monthly Notices of the Royal Astronomical Society, 422, 3189, doi: 10.1111/j.1365-2966.2012.20841.x

    2012 doi

  36. [44]

    2017, The Astrophysical journal letters, 839, L22, doi: 10.3847/2041-8213/aa6af0 Gonz´ alez, J

    Globus, N., Allard, D., Parizot, E., & Piran, T. 2017, The Astrophysical journal letters, 839, L22, doi: 10.3847/2041-8213/aa6af0 Gonz´ alez, J. M., Mollerach, S., & Roulet, E. 2021, Phys. Rev. D, 104, 063005, doi: 10.1103/PhysRevD.104.063005

    2017 doi

  37. [45]

    1966, Physical Review Letters, 16, 748, doi: 10.1103/PhysRevLett.16.748

    Greisen, K. 1966, Physical Review Letters, 16, 748, doi: 10.1103/PhysRevLett.16.748

    1966 doi

  38. [46]

    A., Abreu, P., Aglietta, M., et al

    Halim, A. A., Abreu, P., Aglietta, M., et al. 2023, Journal of Cosmology and Astroparticle Physics, 2023, 024, doi: 10.1088/1475-7516/2023/05/024

    2023 doi

  39. [47]

    2005, Astronomy & Astrophysics, 441, 417, doi: 10.1051/0004-6361:20042134

    Hasinger, G., Miyaji, T., & Schmidt, M. 2005, Astronomy & Astrophysics, 441, 417, doi: 10.1051/0004-6361:20042134

    2005 doi

  40. [48]

    2016, The Astrophysical Journal, 825, 122, doi: 10.3847/0004-637X/825/2/122

    Heinze, J., Boncioli, D., Bustamante, M., & Winter, W. 2016, The Astrophysical Journal, 825, 122, doi: 10.3847/0004-637X/825/2/122

    2016 doi

  41. [49]

    2019, The Astrophysical Journal, 873, 88, doi: 10.3847/1538-4357/ab05ce

    Heinze, J., Fedynitch, A., Boncioli, D., & Winter, W. 2019, The Astrophysical Journal, 873, 88, doi: 10.3847/1538-4357/ab05ce

    2019 doi

  42. [50]

    Hopkins, A. M. 2004, The Astrophysical Journal, 615, 209, doi: 10.1086/424032

    2004 doi

  43. [51]

    M., & Beacom, J

    Hopkins, A. M., & Beacom, J. F. 2006, The Astrophysical Journal, 651, 142, doi: 10.1086/506610

    2006 doi

  44. [52]

    2012, The Astrophysical Journal, 753, 69, doi: 10.1088/0004-637X/753/1/69

    Horiuchi, S., Murase, K., Ioka, K., & Meszaros, P. 2012, The Astrophysical Journal, 753, 69, doi: 10.1088/0004-637X/753/1/69

    2012 doi

  45. [53]

    E., Kuzmin, V

    Kalashev, O. E., Kuzmin, V. A., Semikoz, D. V., & Sigl, G. 2002, Physical Review D, 66, 063004, doi: 10.1103/PhysRevD.66.063004

    2002 doi

  46. [54]

    2016, Monthly Notices of the Royal Astronomical Society, 461, 371, doi: 10.1093/mnras/stw1290

    Kochanek, C. 2016, Monthly Notices of the Royal Astronomical Society, 461, 371, doi: 10.1093/mnras/stw1290

    2016 doi

  47. [55]

    K., & Sahu, N

    Kohri, K., Paul, P. K., & Sahu, N. 2025, Physical Review D, 112, L031703, doi: 10.1103/vvqq-1z2t

    2025 doi

  48. [56]

    J., Hilaire, S., & Duijvestijn, M

    Koning, A. J., Hilaire, S., & Duijvestijn, M. C. 2007, in International Conference on Nuclear Data for Science and Technology, EDP Sciences, 211–214, doi: 10.1051/ndata:07767

    2007 doi

  49. [58]

    Y., Petrov, N

    Kuznetsov, M. Y., Petrov, N. A., & Savchenko, Y. S. 2025b, arXiv preprint arXiv:2509.09590, doi: 10.48550/arXiv.2509.09590

    doi arXiv

  50. [59]

    2014, The Astrophysical Journal, 783, 24, doi: 10.1088/0004-637X/783/1/24

    Lien, A., Sakamoto, T., Gehrels, N., et al. 2014, The Astrophysical Journal, 783, 24, doi: 10.1088/0004-637X/783/1/24

    2014 doi

  51. [60]

    Lisanti, M., Mishra-Sharma, S., Necib, L., & Safdi, B. R. 2016, The Astrophysical Journal, 832, 117, doi: 10.3847/0004-637X/832/2/117

    2016 doi

  52. [61]

    2014, Annual Review of Astronomy and Astrophysics, 52, 415, doi: 10.1146/annurev-astro-081811-125615

    Madau, P., & Dickinson, M. 2014, Annual Review of Astronomy and Astrophysics, 52, 415, doi: 10.1146/annurev-astro-081811-125615

    2014 doi

  53. [62]

    2024, Universe, 10, 53, doi: 10.3390/universe10020053

    Malecki, P. 2024, Universe, 10, 53, doi: 10.3390/universe10020053

    2024 doi

  54. [63]

    A., Abreu, P., et al

    Mayotte, E., Halim, A. A., Abreu, P., et al. 2024, in 38th International Cosmic Ray Conference (ICRC2023)-Cosmic-Ray Physics (Indirect, CRI), Sissa Medialab, 365, doi: 10.22323/1.444.0365

    2024 doi

  55. [64]

    2020, Physical Review D, 101, 103024, doi: 10.1103/PhysRevD.101.103024

    Mollerach, S., & Roulet, E. 2020, Physical Review D, 101, 103024, doi: 10.1103/PhysRevD.101.103024

    2020 doi

  56. [65]

    S., Unger, M., & Farrar, G

    Muzio, M. S., Unger, M., & Farrar, G. R. 2019, Physical Review D, 100, 103008, doi: 10.1103/PhysRevD.100.103008

    2019 doi

  57. [66]

    S., Unger, M., & Wissel, S

    Muzio, M. S., Unger, M., & Wissel, S. 2023, Physical Review D, 107, 103030, doi: 10.1103/PhysRevD.107.103030

    2023 doi

  58. [67]

    S., Yuan, T., & Lu, L

    Muzio, M. S., Yuan, T., & Lu, L. 2025, arXiv preprint arXiv:2502.06944, doi: 10.48550/arXiv.2502.06944

    2025 doi

  59. [68]

    2025, arXiv preprint arXiv:2502.12986, doi: 10.48550/arXiv.2502.12986

    Neronov, A., Oikonomou, F., & Semikoz, D. 2025, arXiv preprint arXiv:2502.12986, doi: 10.48550/arXiv.2502.12986

    2025 doi

  60. [69]

    2025, Astroparticle Physics, 103201, doi: 10.1016/j.astropartphys.2025.103201

    Nozzoli, F. 2025, Astroparticle Physics, 103201, doi: 10.1016/j.astropartphys.2025.103201

    2025 doi

  61. [70]

    V., & Sigl, G

    Ostapchenko, S., Garzelli, M. V., & Sigl, G. 2023, Physical Review D, 107, 023014, doi: 10.1103/PhysRevD.107.023014

    2023 doi

  62. [71]

    1961, Il Nuovo Cimento (1955-1965), 22, 800, doi: 10.1007/BF02783106

    Peters, B. 1961, Il Nuovo Cimento (1955-1965), 22, 800, doi: 10.1007/BF02783106

    1961 doi

  63. [72]

    2015, The Astrophysical Journal, 806, 44, doi: 10.1088/0004-637X/806/1/44

    Petrosian, V., Kitanidis, E., & Kocevski, D. 2015, The Astrophysical Journal, 806, 44, doi: 10.1088/0004-637X/806/1/44

    2015 doi

  64. [73]

    A., Abreu, P., et al

    Petrucci, C., Halim, A. A., Abreu, P., et al. 2024, in 38th International Cosmic Ray Conference (ICRC2023)-Cosmic-Ray Physics (Indirect, CRI), 1520, doi: 10.22323/1.444.1520

    2024 doi

  65. [74]

    2021, Physical review letters, 126, 191101, doi: 10.1103/PhysRevLett.126.191101 Smolˇ ci´ c, V., Zamorani, G., Schinnerer, E., et al

    Winter, W. 2021, Physical review letters, 126, 191101, doi: 10.1103/PhysRevLett.126.191101 Smolˇ ci´ c, V., Zamorani, G., Schinnerer, E., et al. 2009, The Astrophysical Journal, 696, 24, doi: 10.1088/0004-637X/696/1/24

    2021 doi

  66. [75]

    Rachen, J. P. 2000, Physical Review D, 62, 093005, doi: 10.1103/PhysRevD.62.093005

    2000 doi

  67. [76]

    2009, Astroparticle Physics, 31, 201, doi: 10.1016/j.astropartphys.2009.01.006

    Takami, H., Murase, K., Nagataki, S., & Sato, K. 2009, Astroparticle Physics, 31, 201, doi: 10.1016/j.astropartphys.2009.01.006

    2009 doi

  68. [77]

    M., Ahlers, M., & Hooper, D

    Taylor, A. M., Ahlers, M., & Hooper, D. 2015, Physical Review D, 92, 063011, doi: 10.1103/PhysRevD.92.063011

    2015 doi

  69. [78]

    2016, Astronomy & Astrophysics, 595, A33, doi: 10.1051/0004-6361/201628894

    Thoudam, S., Rachen, J., Van Vliet, A., et al. 2016, Astronomy & Astrophysics, 595, A33, doi: 10.1051/0004-6361/201628894

    2016 doi

  70. [79]

    Watson, M. G. 2014, The Astrophysical Journal, 786, 104, doi: 10.1088/0004-637X/786/2/104

    2014 doi

  71. [80]

    2003, The Astrophysical Journal, 598, 886, doi: 10.1086/378940 van Vliet, A., Batista, R

    Ueda, Y., Akiyama, M., Ohta, K., & Miyaji, T. 2003, The Astrophysical Journal, 598, 886, doi: 10.1086/378940 van Vliet, A., Batista, R. A., & H¨ orandel, J. R. 2019, Physical Review D, 100, 021302, doi: 10.1103/PhysRevD.100.021302

    2003 doi

  72. [81]

    2010, Monthly Notices of the Royal Astronomical Society, 406, 1944, doi: 10.1111/j.1365-2966.2010.16787.x

    Wanderman, D., & Piran, T. 2010, Monthly Notices of the Royal Astronomical Society, 406, 1944, doi: 10.1111/j.1365-2966.2010.16787.x

    2010 doi

  73. [82]

    Wittkowski, D., Albuquerque, I. F. d. M., Catalani, F., et al. 2017, Proceedings of Science, 301, 563, doi: 10.22323/1.301.0563

    2017 doi

  74. [83]

    2023, Nature Astronomy, 7, 1497, doi: 10.1038/s41550-023-02087-6 Y¨ uksel, H., Kistler, M

    Ye, Z., Hu, F., Tian, W., et al. 2023, Nature Astronomy, 7, 1497, doi: 10.1038/s41550-023-02087-6 Y¨ uksel, H., Kistler, M. D., Beacom, J. F., & Hopkins, A. M. 2008, The Astrophysical Journal Letters, 683, L5, doi: 10.1086/591449

    2023 doi

  75. [84]

    T., & Kuz’min, V

    Zatsepin, G. T., & Kuz’min, V. A. 1966, Soviet Journal of Experimental and Theoretical Physics Letters, 4, 78

    1966

  76. [85]

    2025, Astroparticle Physics, 171, 103123, doi: 10.1016/j.astropartphys.2025.103123

    Zhang, H., Cui, Y., Huang, Y., et al. 2025, Astroparticle Physics, 171, 103123, doi: 10.1016/j.astropartphys.2025.103123

    2025 doi

Pith tools

Reviewed May 25, 2026 · model on record in the stance chip above.