Origin of the emerging neutrino flux above 5 PeV: single power-law continuation or ultrahigh-energy-cosmic-ray production, and the high-rigidity proton population it requires

The KM3NeT/ARCA event KM3-230213A, with a spectrum-dependent energy estimate of $220^{+570}_{-110}$ PeV, together with three IceCube events above 5 PeV, hints at an astrophysical neutrino flux above 5 PeV. A first joint fit of IceCube and KM3NeT neutrino data with the Pierre Auger Observatory's ultrahigh-energy cosmic ray (UHECR) spectrum and composition (Muzio, Yuan & Lu, 2025) shows that both a single-power-law continuation and a UHECR-produced recovery can describe current data; the energy scale of the recovery, and whether an additional high-rigidity pure-proton source population must be invoked beyond the mixed-composition population seen by Auger, hinges on the true energy of KM3-230213A (near 100 PeV or approaching 1 EeV). The open problem is to determine the origin of the >5 PeV flux — single power law versus UHECR-linked recovery — to fix the event's energy, to confirm or falsify the extra proton population against Auger composition data, and to identify or constrain the accompanying EeV-scale cosmogenic (GZK) neutrino component. The problem remains open: no second ultrahigh-energy event has been detected, the proton fraction is constrained but not settled, and a live ~2.9 sigma IceCube–KM3NeT tension persists.

Background

Astrophysical neutrinos are produced when accelerated hadrons interact with gas or radiation fields, either inside their sources or while propagating through intergalactic space; because neutrinos are electrically neutral they travel essentially undeflected, so they trace the highest-energy cosmic accelerators. The IceCube Neutrino Observatory has measured the diffuse astrophysical neutrino flux from TeV to multi-PeV energies; in its high-energy starting event (HESE) sample the flux is described by a single power law (SPL), $d\Phi/dE \propto E^{-\gamma}$ with $\gamma \approx 2.9$, and only three events above 5 PeV have been recorded in over a decade of operation. Ultrahigh-energy cosmic rays (UHECRs; energies $\gtrsim 0.1$ EeV, where 1 EeV $= 10^{18}$ eV) are observed by the Pierre Auger Observatory (Auger), which measures the cosmic-ray energy spectrum and, for air showers observed with its fluorescence detector, the depth of shower maximum $X_{\max}$ (the atmospheric depth where a cosmic-ray air shower deposit peaks). The mean and dispersion $\sigma(X_{\max})$ of $X_{\max}$ constrain the primary mass composition, but their interpretation requires predicting showers with hadronic interaction models such as SIBYLL or EPOS and forward-folding model distributions through detector acceptance; Auger's $\sigma(X_{\max})$ indicates a mixed, increasingly heavy composition at the highest energies. A key accelerator quantity is rigidity, the energy per unit charge $E/Z$: in most acceleration scenarios each nucleus is cut off at a rigidity scale set by the source, so reaching neutrino energies near 1 EeV by photopion production requires protons of rigidity well above 10 EeV. Cosmogenic (GZK) neutrinos are produced when UHECR protons undergo photopion interactions with the cosmic microwave background (CMB) and extralactic background light during propagation; they are the long-predicted, still-unconfirmed smoking gun of UHECR propagation.

On 13 February 2023 the ARCA detector of KM3NeT (a neutrino telescope under construction in the Mediterranean) recorded a muon-track event, KM3-230213A, whose neutrino energy the collaboration estimates at $220^{+570}_{-110}$ PeV assuming an $E^{-2}$ spectrum, making it plausibly the highest-energy neutrino ever observed (KM3NeT Collaboration, Nature 638, 376, 2025). Because the estimate depends on the assumed spectrum and flavor, and the uncertainties span an order of magnitude, any conclusion conditional on the event energy remains ambiguous.

Muzio, Yuan & Lu (arXiv:2502.06944, 2025) performed the first simultaneous fit of IceCube and KM3NeT neutrino data together with Auger's UHECR spectrum and $X_{\max}$ distributions, testing a common-origin hypothesis in which a phenomenological source model (a UFA-type source embedding the accelerator in an environment where nuclei photodisintegrate, followed by propagation through the CMB and background light) produces both the cosmic rays and the neutrinos. They find that a model of this type can describe the combined data, and that the neutrino spectrum above roughly 10 PeV either continues as an SPL or transitions into a UHECR-linked recovery of the energy flux peaking near 30 PeV (source-produced neutrinos) or near 1 EeV (cosmogenic neutrinos), depending on whether the KM3NeT event's true energy is near 100 PeV or near 1 EeV. Only the EeV-scale case requires, in addition to the mixed-composition population, a second source population of pure protons with maximum rigidity above 10 EeV. That extra proton component predicts a recovery of the proton spectrum at Earth above about 10 EeV, which broadens the predicted $\sigma(X_{\max})$ above roughly 20 EeV and is in tension with Auger's moment-based measurements, a tension sensitive to the hadronic model (SIBYLL 2.3c) and to the forward-folding treatment at low $X_{\max}$ statistics. The authors also show, with an Asimov test (a fit to statistically idealized mock data) for the proposed IceCube-Gen2 observatory (an expansion of IceCube's optical array to at least eight cubic kilometers plus a radio antenna array), that next-generation detectors should be able to distinguish the SPL expectation from a UHECR-produced recovery, while AugerPrime (Auger's upgrade, adding scintillator detectors for composition measurement at the highest energies) can improve the composition input. The predicted EeV-scale cosmogenic flux itself remains model-dependent (source evolution and in-source interactions could raise or lower it).

Problem Statement

Determine the origin of the astrophysical neutrino flux emerging above 5 PeV and its implications for ultrahigh-energy cosmic ray sources, as posed by the joint IceCube-KM3NeT-Auger analysis of Muzio, Yuan & Lu (2025). Concretely: (i) establish, from combined neutrino data (IceCube, KM3NeT/ARCA, and other detectors) folded together with the UHECR spectrum and composition measured by Auger, whether the flux above 5 PeV continues as a single power law or exhibits a UHECR-produced recovery (in-source or cosmogenic), with a quantified statistical discrimination between the two hypotheses; (ii) determine the true energy of KM3-230213A — near 100 PeV or approaching 1 EeV — since only the EeV-scale case decisively requires, beyond the mixed-composition population observed by Auger, an additional high-rigidity pure-proton source population; (iii) test the predicted signature of that extra proton component — a recovery of the proton spectrum at Earth above about 10 EeV broadening $\sigma(X_{\max})$ above roughly 20 EeV — against improved UHECR composition measurements (including AugerPrime and surface-detector-based $\sigma(X_{\max})$ inferences), with the hadronic-model and forward-folding systematics quantified; and (iv) determine the accompanying EeV-scale cosmogenic (GZK) neutrino flux and whether it can be identified as a distinct population, folding detector systematics and energy-reconstruction uncertainties into global multimessenger fits. These four components jointly answer one question — whether the highest-energy neutrinos and the highest-energy cosmic rays share a common origin and what source populations that requires — and an answer is complete when the flux-shape discrimination, the event-energy branch, the existence or absence of the extra proton population, and the identification or constraint of the accompanying EeV-scale cosmogenic (GZK) neutrino component are settled with quantified significance and systematics.

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