On 13 February 2023 the KM3NeT/ARCA detector recorded KM3-230213A, a nearly horizontal down-going track event with a median reconstructed neutrino energy of about 220 PeV — the most energetic neutrino ever observed. Its detection rate is in tension with the absence of comparable events in IceCube, the Pierre Auger Observatory and the in-ice radio arrays, and with the four anomalous near-horizon events of ANITA-IV, and no astrophysical interpretation is accepted. The problem is to determine quantitatively the origin of this event — cosmogenic neutrinos from a specified ultrahigh-energy cosmic-ray source population, an astrophysical point-source or transient population, an exotic component such as superheavy dark-matter decay, or a detector-systematics or background effect — through a model that simultaneously reproduces the single detected event and the non-detections elsewhere, remains consistent with cosmic-ray spectrum and composition data and diffuse gamma-ray bounds, and derives the implied all-flavor ultrahigh-energy neutrino flux and source-population parameters. The 2025-2026 literature proposes mutually incompatible explanations, none of which is accepted, so the problem is open.

Background

Ultrahigh-energy (UHE) neutrinos, with energies above roughly 101710^{17} eV, are expected mainly as cosmogenic neutrinos — the Greisen–Zatsepin–Kuzmin (GZK) prediction: neutrinos, photons and electron-positron pairs produced when ultrahigh-energy cosmic rays (UHECRs) interact with the cosmic microwave and infrared background photons during intergalactic propagation. Their flux depends on the UHECR injection spectrum, the mass composition at the source, the maximum acceleration energy, and the redshift evolution of the sources. Two observables anchor UHECR physics: the energy spectrum measured by the Pierre Auger Observatory and Telescope Array, and the atmospheric depth of shower maximum Xmax⁡X_{\max} and its RMS spread, which diagnose the primary mass but depend on hadronic-interaction models extrapolated far beyond accelerator energies. A central degeneracy (the 'Peters cycle') links the comoving number density of sources with their luminosity evolution with redshift: sparse bright strongly-evolving sources and numerous weak weakly-evolving sources can fit the same UHECR spectrum while predicting very different cosmogenic neutrino fluxes, and predictions are further sensitive to extragalactic magnetic fields and to the assumed maximum source distance.

On 13 February 2023 the deep-sea Cherenkov telescope KM3NeT/ARCA (Astroparticle Research with Cosmics in the Abyss, off Sicily) detected a track-like event consistent with a UHE muon produced by a neutrino of about 220 PeV median energy (90% range roughly 72 PeV to 2.6 EeV), arriving almost horizontally, marginally down-going — at the time the highest-energy neutrino ever recorded. The implied quasi-diffuse flux (the 'gray cross' in the observational-strategy literature) sits above the upper limits on a diffuse UHE neutrino flux set by IceCube at the South Pole and by the Auger surface detector, which have run longer with comparable or larger exposure at these energies; the four near-horizon events of ANITA-IV (the Antarctic Impulsive Transient Antenna, a long-duration balloon-borne radio antenna array) add a further tension. Kotera et al. (2025) — a study of 'wide and shallow' versus 'deep and narrow' UHE neutrino observing strategies — discuss among their open issues this cluster: the source density-luminosity-evolution degeneracy controlling cosmogenic and source diffuse-flux predictions, the role of hadronic and air-shower model uncertainties in interpreting Xmax⁡X_{\max}, the lack of any clear astrophysical interpretation of KM3-230213A, and poorly constrained transient-population parameters. Candidate explanations in the literature include: cosmogenic neutrinos from strongly evolving proton sources or from Fanaroff–Riley II (FRII) radio-galaxy lobes (the extended lobes of classical double radio galaxies); blazar or transient populations; Galactic-origin scenarios; decays of superheavy dark matter with masses above 100 PeV; and instrumental or atmospheric-muon-bundle misreconstruction. Multi-messenger consistency requirements are strong: any hadronic production scenario must not overshoot the Fermi-LAT isotropic diffuse gamma-ray background (the cascade bound), and any UHECR source scenario must fit the Auger spectrum and Xmax⁡X_{\max} data.

Problem Statement

Determine the origin of the ultra-high-energy neutrino event KM3-230213A and the diffuse ultrahigh-energy neutrino flux it implies. The origin is to be determined by identifying the origin class — cosmogenic neutrinos from a specified UHECR source population, an astrophysical point-source or transient population, an exotic component such as superheavy dark-matter decay, or a detector-systematics/atmospheric-background effect — and by demonstrating, quantitatively and with a stated statistical significance, that the identified explanation is simultaneously consistent with the full observed event-rate pattern — the detection of one KM3-230213A-like event in the ARCA exposure, zero comparable events in IceCube, Auger and the in-ice radio arrays, and the four near-horizon ANITA-IV events — where 'comparable' means comparable in reconstructed neutrino energy to KM3-230213A, using the published effective areas (each experiment's energy- and direction-dependent effective detection area) and exposures, that it is consistent, for any hadronic production scenario, with the UHECR spectrum and composition data (including Xmax⁡X_{\max} and its RMS) and with the Fermi-LAT isotropic diffuse gamma-ray background, and that it yields the implied all-flavor UHE neutrino spectrum — or, for a detector-systematics/atmospheric-background explanation, the quantitative bound on that spectrum implied by the explanation — and, for any explanation invoking an astrophysical or exotic source population, the source-population parameters (number density, luminosity evolution with redshift, maximum energy, beaming or decay parameters as appropriate) with their uncertainties, including how the source density-luminosity evolution degeneracy is broken or bounded.

References

  1. K. Kotera, M. Mukhopadhyay, R. Alves Batista, D. Fox, O. Martineau-Huynh, K. Murase, S. Wissel, A. Zeolla (2025, arXiv; published in JCAP 01 (2026) 027), 'Observational strategies for ultrahigh-energy neutrinos: the importance of deep sensitivity for detection and astronomy', arXiv:2504.08973, DOI 10.1088/1475-7516/2026/01/027, https://arxiv.org/abs/2504.08973
  2. KM3NeT Collaboration (2025), 'Observation of an ultra-high-energy cosmic neutrino with KM3NeT', Nature 638, 376-382, DOI 10.1038/s41586-024-08543-1, https://doi.org/10.1038/s41586-024-08543-1
  3. The KM3NeT Collaboration (2025), 'Can KM3-230213A be compatible with a cosmogenic origin?', arXiv:2510.23287, https://arxiv.org/abs/2510.23287
  4. Dibya S. Chattopadhyay, Carlos A. Argüelles, Vedran Brdar (2026), 'Four, One, and None: Quantifying the Ultra-High-Energy Neutrino Anomaly Across ANITA-IV, KM3NeT, and IceCube', arXiv:2607.19487, https://arxiv.org/abs/2607.19487
  5. A. R. Alhebsi, Arjen van Vliet, Domenik Ehlert, Satyendra Thoudam (2026), 'Implications of a Cosmogenic Origin of KM3-230213A for Ultra-High-Energy Protons', arXiv:2603.13476, https://arxiv.org/abs/2603.13476
  6. M. Yu. Kuznetsov, N. A. Petrov, Y. S. Savchenko (2025, arXiv; published in JETP Letters 123, 287-297 (2026)), 'Ultra-high energy event KM3-230213A as a cosmogenic neutrino in light of minimal UHECR flux models', arXiv:2509.09590, DOI 10.1134/S0021364025610061, https://arxiv.org/abs/2509.09590
  7. Denis Allard, Bruny Baret, Noémie Globus, Etienne Parizot (2026), 'Cosmogenic neutrinos from FRII galaxies as potential origin of the ultra-high-energy KM3-230213A event', arXiv:2608.16540, https://arxiv.org/abs/2608.16540
  8. Alessandro Cermenati, Antonio Ambrosone, Roberto Aloisio, Denise Boncioli, Carmelo Evoli (2025), 'Scrutinizing the cosmogenic origin of the KM3-230213A event: A Multimessenger Perspective', arXiv:2507.11993, https://arxiv.org/abs/2507.11993
  9. D. Fargion (2025), 'Paucity of downward UHE neutrino tracks in IceCube versus unexpected huge KM3-230213A event: solving the puzzles?', PoS(ICRC2025) 092, arXiv:2512.07042, DOI 10.22323/1.501.0925, https://arxiv.org/abs/2512.07042
  10. KM3NeT Collaboration (2026), 'Testing Heavy Dark Matter Decay as the Origin of KM3-230213A', arXiv:2606.09986, https://arxiv.org/abs/2606.09986
  11. The KM3NeT Collaboration (2025), 'Blazars as a Potential Origin of the KM3-230213A Event', arXiv:2511.13886, https://arxiv.org/abs/2511.13886