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arxiv: 2603.13476 · v2 · pith:C7NAO6KUnew · submitted 2026-03-13 · 🌌 astro-ph.HE

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

A. R. Alhebsi , Arjen van Vliet , Domenik Ehlert , Satyendra Thoudam This is my paper

Pith reviewed 2026-05-25 07:22 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords ultra-high-energy cosmic rayscosmogenic neutrinosKM3NeTsource evolutionproton fractionactive galactic nucleimulti-messenger constraintsUHECR composition
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The pith

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

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

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.

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.

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.

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.

Where Pith is reading between the lines

These are 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.

Load-bearing premise

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

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.

Figures

Figures reproduced from arXiv: 2603.13476 by A. R. Alhebsi, Arjen van Vliet, Domenik Ehlert, Satyendra Thoudam.

Figure 1
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 normaliza… view at source ↗
Figure 2
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-… view at source ↗
Figure 3
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 scenari… view at source ↗
read the original 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 $20\,\mathrm{EeV}$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

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

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.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 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.
axioms (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.

pith-pipeline@v0.9.0 · 5805 in / 1335 out tokens · 26221 ms · 2026-05-25T07:22:34.033062+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. KM3-230213A and potential astrophysical sources

    astro-ph.HE 2026-05 unverdicted novelty 4.0

    KM3NeT reports the first astrophysical neutrino above 100 PeV, reviews tensions with other observatories, and explores source scenarios using the inferred diffuse flux.

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages · cited by 1 Pith paper · 2 internal anchors

  1. [1]

    2014, Physical Review D, 90, 122006, doi: 10.1103/PhysRevD.90.122006

    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]

    2017, Journal of Cosmology and Astroparticle Physics, 2017, 038, doi: 10.1088/1475-7516/2017/04/038

    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]

    2019, Journal of Cosmology and Astroparticle Physics, 2019, 022, doi: 10.1088/1475-7516/2019/10/022

    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]

    G., Ackermann, M., Adams, J., et al

    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]

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

    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]

    2022, The Astrophysical Journal, 928, 50, doi: 10.3847/1538-4357/ac4d29

    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

  9. [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

    work page doi:10.1103/physrevlett.135.031001 2025

  10. [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, doi: 10.22323/1.444.0319 Abdul Halim, A., Abreu, P., Aglietta, M., et al. 2024a, ...

    work page doi:10.1016/j.astropartphys.2019.03.003 2019

  11. [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

    work page doi:10.1088/1475-7516/2013/02/026 2013

  12. [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

    work page doi:10.1140/epjc/s10052-021-09700-w 2021

  13. [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

    work page doi:10.1088/1475-7516/2023/05/021 2023

  14. [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

    work page doi:10.1088/0004-637x/799/1/86 2015

  15. [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

    work page doi:10.1103/physrevlett.116.151105 2016

  16. [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

    work page doi:10.48550/arxiv.2511.13886

  17. [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

    work page doi:10.3847/2041-8213/adcc29 2041

  18. [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

    work page doi:10.48550/arxiv.2502.08387

  19. [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

    work page doi:10.1103/yypk-zmb8

  20. [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

    work page doi:10.1088/1748-0221/16/03/p03025 2021

  21. [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

    work page doi:10.1103/physrevd.79.083009 2009

  22. [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

    work page doi:10.1140/epjc/s10052-024-13137-2 2024

  23. [23]

    R., et al

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

    work page doi:10.1038/s41586-024-08543-1 2025

  24. [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

    work page doi:10.1088/0004-637x/751/2/108 2012

  25. [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

    work page doi:10.1088/0004-637x/780/1/73 2013

  26. [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

    work page doi:10.3103/s1062873823702817 2023

  27. [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-Mu˜ niz, J., Alves Batista, R., Balagopal V, A., et al. 2020, Science China Phy...

    work page doi:10.1086/429615 2005

  28. [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

    work page doi:10.48550/arxiv.2502.08484 2025

  29. [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

    work page doi:10.1088/1475-7516/2019/01/002 2019

  30. [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

    work page doi:10.1016/j.astropartphys.2016.08.007 2016

  31. [31]

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

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

    work page doi:10.22323/1.395.0338 2021

  32. [32]

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

    work page doi:10.3847/1538-4357/ad2f3f 2024

  33. [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

    work page doi:10.1103/shsw-mct6 2025

  34. [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

    work page doi:10.1051/epjconf/201921006002 2019

  35. [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

    work page doi:10.48550/arxiv.2507.11993 2025

  36. [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:

    work page 2026

  37. [37]

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

    work page doi:10.1016/j.nima.2026.171374 2026

  38. [38]

    R., & Muzio, M

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

    work page doi:10.3847/2041-8213/ad955f 2024

  39. [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

    work page doi:10.3847/1538-4357/adf8de 2025

  40. [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

    work page doi:10.1103/physrevd.107.103045 2023

  41. [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

    work page doi:10.1088/1475-7516/2024/02/022 2024

  42. [42]

    J., & Cousins, R

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

    work page doi:10.1103/physrevd.57.3873 1998

  43. [43]

    and Shibahashi , H

    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

    work page doi:10.1111/j.1365-2966.2012.20841.x 2012

  44. [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

    work page doi:10.3847/2041-8213/aa6af0 2017

  45. [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

    work page doi:10.1103/physrevlett.16.748 1966

  46. [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

    work page doi:10.1088/1475-7516/2023/05/024 2023

  47. [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

    work page doi:10.1051/0004-6361:20042134 2005

  48. [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

    work page doi:10.3847/0004-637x/825/2/122 2016

  49. [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

    work page doi:10.3847/1538-4357/ab05ce 2019

  50. [50]

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

    work page doi:10.1086/424032 2004

  51. [51]

    M., & Beacom, J

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

    work page doi:10.1086/506610 2006

  52. [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

    work page doi:10.1088/0004-637x/753/1/69 2012

  53. [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

    work page doi:10.1103/physrevd.66.063004 2002

  54. [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

    work page doi:10.1093/mnras/stw1290 2016

  55. [55]

    K., & Sahu, N

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

    work page doi:10.1103/vvqq-1z2t 2025

  56. [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

    work page doi:10.1051/ndata:07767 2007

  57. [58]

    Ultra-high energy event KM3-230213A as a cosmogenic neutrino in light of minimal UHECR flux models

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

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2509.09590

  58. [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

    work page doi:10.1088/0004-637x/783/1/24 2014

  59. [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

    work page doi:10.3847/0004-637x/832/2/117 2016

  60. [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

    work page internal anchor Pith review doi:10.1146/annurev-astro-081811-125615 2014

  61. [62]

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

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

    work page doi:10.3390/universe10020053 2024

  62. [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

    work page doi:10.22323/1.444.0365 2024

  63. [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

    work page doi:10.1103/physrevd.101.103024 2020

  64. [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

    work page doi:10.1103/physrevd.100.103008 2019

  65. [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

    work page doi:10.1103/physrevd.107.103030 2023

  66. [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

    work page doi:10.48550/arxiv.2502.06944 2025

  67. [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

    work page doi:10.48550/arxiv.2502.12986 2025

  68. [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

    work page doi:10.1016/j.astropartphys.2025.103201 2025

  69. [70]

    V., & Sigl, G

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

    work page doi:10.1103/physrevd.107.023014 2023

  70. [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

    work page doi:10.1007/bf02783106 1961

  71. [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

    work page doi:10.1088/0004-637x/806/1/44 2015

  72. [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

    work page doi:10.22323/1.444.1520 2024

  73. [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

    work page doi:10.1103/physrevlett.126.191101 2021

  74. [75]

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

    work page doi:10.1103/physrevd.62.093005 2000

  75. [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

    work page doi:10.1016/j.astropartphys.2009.01.006 2009

  76. [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

    work page doi:10.1103/physrevd.92.063011 2015

  77. [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

    work page doi:10.1051/0004-6361/201628894 2016

  78. [79]

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

    work page doi:10.1088/0004-637x/786/2/104 2014

  79. [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

    work page doi:10.1086/378940 2003

  80. [81]

    J., Reeves J

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

    work page doi:10.1111/j.1365-2966.2010.16787.x 2010

Showing first 80 references.