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Emergence of a neutrino flux above 5 PeV and implications for ultrahigh energy cosmic rays

T0 review · 5 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Four neutrino events above 5 PeV, fit jointly with Auger cosmic-ray data, point to a common origin in ultrahigh-energy cosmic-ray sources, with the KM3NeT event being either a 30 PeV source component or the first GZK neutrino.

desk verdict Useful joint fit of >5 PeV neutrinos and UHECRs, but the two headline conclusions hinge on an unvalidated ARCA effective-area proxy and on testing only 100 PeV and 1 EeV for the KM3NeT event. read the letter →

arxiv 2502.06944 v2 pith:Y3WO34RY submitted 2025-02-10 astro-ph.HE

Marco S. Muzio , Tianlu Yuan , Lu Lu This is my paper · ORCID
classification astro-ph.HE
keywords astrophysicalneutrinosultrahigh-energycosmicrayscosmogenicGZKeffectmulti-messengerastronomyIceCubeKM3NeT/ARCAPierreAugerObservatory
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

This paper tries to establish that the four neutrino events detected above 5 PeV—three by IceCube and one by KM3NeT/ARCA—are the first indications of a distinct neutrino flux linked to ultrahigh-energy cosmic rays. The authors build a single phenomenological model of cosmic-ray sources and fit it simultaneously to the neutrino data, to the Pierre Auger cosmic-ray spectrum, and to the full distributions of air-shower depths of maximum. The resulting model describes all three datasets, and its predicted neutrino flux shows a spectral recovery: around 30 PeV if the KM3NeT event truly has an energy of 100 PeV, or around 1 EeV if that event is actually at 1 EeV, in which case a second pure-proton source population is required. In the 1 EeV case the KM3NeT event would be the first observed cosmogenic, GZK neutrino, and protons above 10 EeV would reappear in the cosmic-ray flux. The result matters because it shows that a handful of high-energy events can already discriminate between neutrinos produced inside cosmic-ray sources and neutrinos produced during propagation, and it sharpens the prediction for next-generation detectors.

What carries the argument

The load-bearing object is the paper's phenomenological UHECR source model: an injected cosmic-ray spectrum with a rigidity-dependent cutoff, a parameterized source environment that reprocesses nuclei and produces neutrinos, and pre-tabulated propagation through the cosmic microwave and extragalactic background light. The neutrino flux is not added by hand; it follows from the same interactions that shape the cosmic-ray spectrum and composition, which is why a joint fit to Auger and the neutrino data is a genuine test of common origin. For the 1 EeV scenario a pure-proton component with a much higher rigidity cutoff is added. The statistical machinery is a joint deviance that sums a saturated Poisson likelihood for the four events above 5 PeV, a multinomial likelihood over the full Xmax distributions from Auger, and a gamma-distribution likelihood for IceCube's measured flux from 30 TeV to 2 PeV.

What would settle it

A statistically significant measurement of the neutrino flux above 5 PeV by IceCube-Gen2—showing a smooth single power law continuing from lower energies with no recovery near 30 PeV and no excess near 1 EeV—would rule out the paper's common-origin UHECR interpretation as the dominant source of these neutrinos.

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Extended reading notes

Core claim

The central claim is that the combined IceCube, KM3NeT/ARCA, and Auger datasets can be described by a common-origin model in which ultrahigh-energy cosmic rays generate the neutrinos, so the >5 PeV events are not a separate phenomenon. Under the 100 PeV interpretation of the KM3NeT event, the model's neutrino flux has a recovery peaking around 30 PeV, produced by cosmic-ray interactions with the extragalactic background light. Under the 1 EeV interpretation, the baseline sources cannot make such an energetic neutrino, so the model adds a second population of pure protons with rigidity above 10 EeV; that population produces a proton recovery at Earth above 10 EeV and a cosmogenic neutrino component, making the KM3NeT event the first observed GZK neutrino. The paper thus asserts that, although the statistics are minimal, the existing multimessenger data already favor a UHECR-linked flux above 5 PeV and can differentiate the two production channels.

Load-bearing premise

The load-bearing premise is that the KM3NeT/ARCA event's true energy is either 100 PeV or 1 EeV, with its effective area approximated as twenty percent of IceCube's northern-track sample; if the true energy is near the reconstructed best fit of 220 PeV, or if that effective-area approximation is wrong, the predicted recovery shifts and the case for an additional proton population weakens.

Editorial extensions

If this is right

  • The four events above 5 PeV and the Auger spectrum and composition can be simultaneously described by one source model, so the >5 PeV events do not by themselves require a new class of sources unless the KM3NeT event is at the highest energies.
  • If the KM3NeT event is at 100 PeV, the model predicts a neutrino spectral recovery peaking around 30 PeV from cosmic-ray interactions with the extragalactic background light, and current data cannot yet distinguish this from a single power law.
  • If the KM3NeT event is at 1 EeV, the model requires a second pure-proton source population with rigidity above 10 EeV, which yields a proton recovery above 10 EeV and makes the event the first observed GZK neutrino.
  • IceCube-Gen2, with 15 years of optical and radio data, is predicted to detect enough events above 5 PeV to discriminate between a single power law and the 30 PeV or EeV-scale recovery.

Reading between the lines

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

  • The paper tests only two discrete energies for the KM3NeT event; the reconstructed best fit of 220 PeV lies between them, so the real physical scenario is likely intermediate, and future analyses should treat the energy as a continuous nuisance parameter.
  • If the 1 EeV scenario is correct, the same pure-proton population that makes GZK neutrinos should also produce a small flux of ultrahigh-energy gamma rays through photopion and Bethe-Heitler interactions, offering an independent multimessenger test the paper does not carry out.
  • Because the 'emergence' of the >5 PeV flux rests on four events, its shape is not yet measured; single additional events at tens of PeV from IceCube or ARCA in the next few years will be more decisive than re-fitting the current sample.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper analyzes the four reported neutrino events above 5 PeV (three IceCube events and one KM3NeT/ARCA candidate) together with the lower-energy IceCube astrophysical flux and the Pierre Auger Observatory's UHECR spectrum and composition data. It uses a phenomenological UHECR source model that accounts for in-source and propagation neutrino production, and it presents joint likelihood fits under two assumed energies for the KM3NeT event: 100 PeV, which yields a source-neutrino peak near 30 PeV, and 1 EeV, which requires an additional pure-proton UHECR population and leads the authors to interpret the KM3NeT event as the first observed GZK neutrino. The paper also presents a model-independent segmented flux that shows an emerging flux above 5 PeV and projects IceCube-Gen2 sensitivity to discriminate between the scenarios.

Significance. If the quantitative results held, this would be a valuable first combined UHECR-neutrino fit and a useful framework for next-generation detectors. The paper has clear strengths: it uses the latest public Auger Xmax distributions rather than only their moments, constructs an explicit saturated-Poisson likelihood for the sparse high-energy neutrino sample, and tests two physically motivated energy scenarios. However, the quantitative conclusions rest on an approximate, unvalidated ARCA effective area and on fixing the single KM3NeT event's energy to two extreme values while ignoring the published best fit. The 1 EeV scenario introduces a new proton component after the fact and fits it to the same event it is used to explain. The paper is therefore best viewed as an exploratory scenario study rather than a measurement of the >5 PeV flux, despite the abstract's stronger wording.

major comments (5)
  1. [The highest-energy events from IceCube and KM3NeT] The ARCA21 effective area is approximated as 'roughly 20% of the NT effective area' with no uncertainty, validation, or reference to a KM3NeT effective-area calculation. In Eq. (6), the high-energy likelihood is a saturated Poisson sum over the four events, and the expected count for the KM3NeT event scales linearly with this effective area. A factor-of-two error in the area therefore changes the derived flux normalization by roughly a factor of two and changes Dν,hi by O(1), which is comparable to the model-discrimination differences in Table 2 (Dν,hi of 36.4 vs. 38.6 for 100 PeV and 40.1 vs. 45.3 for 1 EeV). Because this proxy directly sets the weight of the single KM3NeT event, the 'measurement' of the flux above 5 PeV is not robust unless the proxy is validated or its uncertainty is propagated. The paper should either use published ARCA acceptance information or present the flux with an uncertainty that accounts for this approximation, and soften the measurement claim accordingly.
  2. [Diffuse joint fit with UHECR and neutrinos] Table 1 tests only Eν = 100 PeV and Eν = 1 EeV for the KM3NeT event, while the cited KM3NeT analysis [13] gives a best-fit energy of 220+570-110 PeV under an E^-2 spectrum assumption. These two hypotheses are not minor variants; they lead to opposite physical conclusions, namely a ~30 PeV source-neutrino peak versus an EeV-scale cosmogenic component. The 220 PeV best fit is never considered, and no energy-resolution smearing or posterior marginalization is applied. Since the single KM3NeT event dominates Dν,hi, the analysis should marginalize over the published energy reconstruction, or at minimum include the 220 PeV hypothesis and show how the conclusions vary continuously with the assumed energy, before claiming that either scenario is favored.
  3. [1 EeV case: Implications for the cosmogenic neutrino flux] The additional pure-proton population is introduced only in the 1 EeV scenario and adds three free parameters (Methods: 'This second proton component adds 3 additional free parameters'). It is fit to the same combined dataset that motivated its introduction, including the single 1 EeV event. The statement that the KM3NeT event 'would be interpreted as the first observed GZK neutrino' is therefore not a prediction of the model but a consistency check of a post-hoc component. The text should clearly label this as a scenario test rather than evidence for a GZK origin, and the conclusion should not present the GZK interpretation as a discovery-level implication.
  4. [Table 2 and statistical significance] The preference for the UHECR model over the single-power-law neutrino model in the high-energy channel is ΔDν,hi = 2.2 for the 100 PeV case and 5.2 for the 1 EeV case, based on only four events above 5 PeV. These differences are well within Poisson fluctuations and are not accompanied by a significance estimate. The abstract's claim that the detections 'underscore the existence of a flux' at these energies and the conclusion's 'hints of an emerging population' are not supported by a quantitative threshold. A p-value or profile-likelihood significance for the excess over a no-flux or single-power-law hypothesis is needed before the result can be called a flux measurement rather than an upper-limit-driven hint.
  5. [Methods and Table 2] The total joint deviances are large: D = 2354.1 with Ndof = 1689 for the 100 PeV UHECR model and D = 1939.4 with Ndof = 1686 for the 1 EeV model. No goodness-of-fit discussion is provided, and the paper does not address whether the excess deviance reflects underestimated systematic uncertainties in the Auger spectrum and Xmax data or a genuine model inadequacy. Given the claim that the model 'is able to describe the combined data', this issue should be addressed explicitly, for instance by showing the contribution of each dataset to the deviance and discussing the role of energy-scale and hadronic-model systematics.
minor comments (5)
  1. [The highest-energy events from IceCube and KM3NeT] The section heading contains a typo: 'T able 1' should be 'Table 1'.
  2. [Table 1] The KM3NeT row lists the energy as '100, 1000' PeV while the text uses '100 PeV and 1 EeV'; for consistency, either use PeV throughout or explicitly state that 1 EeV = 1000 PeV.
  3. [Figs. 2 and 3] The legend entries 'IceCube Cascades 2020 (used)' and 'IceCube Cascades 2020 (not used)' are not defined in the figure captions; the text explains that blue points are included and gray upper limits excluded, but the captions should state this explicitly.
  4. [Methods, Eq. (5)] For upper limits the text sets yi = σ−i = 0, which makes the first equation (αi − 1)θi = 0; please specify how αi and θi are determined in this degenerate case.
  5. [General notation] The paper uses 'E2' in figure axis labels without a superscript; this is a formatting issue, but it would be clearer to render it as E² or E^2 consistently.

Circularity Check

2 steps flagged · score 5.0 of 10

The GZK-neutrino and 30-PeV-recovery 'predictions' are partly in-sample: the UHECR model, and in the 1 EeV case an added pure-proton component, are fit to the same >5 PeV events they are then said to predict, so the KM3NeT event both motivates and normalizes the proton component.

  1. fitted input called prediction [This occurs in the main-text section '1 EeV case: Implications for the cosmogenic neutrino flux' and in the Methods paragraph introducing the additional proton component.]
    "To test this, we include an additional proton component that escapes its source environment with a maximum rigidity above 10 EeV. ... Under this model, the KM3NeT/ARCA event would be interpreted as the first observed GZK neutrino, suggesting that a wealth of EeV-scale neutrinos will be observed by the next-generation of neutrino detectors."

    The pure-proton population is introduced only after assuming a 1 EeV KM3NeT event, and its three additional free parameters are fit with Dν,hi (Eq. 6) containing that same event. The plotted cosmogenic flux is therefore normalized to the event, so calling the event the 'first observed GZK neutrino' is an in-sample consequence of the fit, not an independent prediction.

  2. fitted input called prediction [This occurs in the Figure 2 caption and in the Methods paragraph defining the total deviance D = DCR,J + DCR,X + Dν,lo + Dν,hi.]
    "The left panel shows the predicted neutrino flux for the model that best describes the combined neutrino and cosmic ray data."

    The UHECR model parameters are fit by minimizing a deviance that includes Dν,hi, the saturated Poisson likelihood for the four >5 PeV events (Eq. 6). Thus the 'predicted' >5 PeV flux in the left panel is adjusted against those same events; its agreement with them is partially enforced by construction rather than being an out-of-sample prediction from UHECR data alone.

full rationale

The paper's central operation is a joint maximum-likelihood fit of a phenomenological UHECR source model to Auger spectrum and Xmax data plus IceCube and KM3NeT neutrino data. That operation is not intrinsically circular, and the paper is transparent that it 'simultaneously fit[s]' all datasets. The model is developed in the authors' prior work, but the citations [35, 39, 40, 51] are ordinary model references, not an invoked uniqueness theorem, so no self-citation load-bearing circularity is present. The ARCA effective-area proxy (about 20% of IceCube NT) and the choice to test 100 PeV and 1 EeV while not testing the 220 PeV best fit are assumptions that affect the likelihood and the conclusions, but they are correctness or robustness concerns, not circularity. Two places do shade into fitted-input-called-prediction. First, the 'predicted' UHECR-model neutrino flux in Figures 2 and 3 is obtained after fitting model parameters to Dν,hi (Eq. 6), which contains the same >5 PeV events shown as evidence for the flux; the agreement is partly built into the fit. Second, and more strongly, the 1 EeV scenario introduces a new pure-proton component only after assuming the KM3NeT event is at 1 EeV, fits that component using the event, and then interprets the event as the first GZK neutrino; the event both motivates and normalizes the component, so the GZK interpretation is not an independent confirmation. These are partial circularities, not complete ones, because the UHECR spectrum and full Xmax distributions provide independent constraints and the fits are not guaranteed to succeed; the model could have failed to describe the combined data. Overall score 5.

Assumptions & free parameters 7 free parameters · 3 assumptions · 1 invented entities

The model contains 19-22 fitted parameters, an ad hoc ARCA exposure scaling, and two energy hypotheses for the KM3NeT event. The proposed proton source population is an invented entity with testable but not yet observed consequences.

free parameters (7)
  • UHECR injected spectrum parameters (7)
    Slope gamma, cutoff Ecut,p, and relative abundances of 5 mass groups, fit to Auger spectrum and composition.
  • Source environment parameters (5)
    Photon-to-gas density, magnetic field strength and coherence length, source size; control photohadronic neutrino production. Fit to data.
  • Galactic CR nuisance component (4)
    Normalization, slope, cutoff, composition of a Galactic component to model the transition.
  • Low-energy neutrino nuisance component (3)
    Single power law with cutoff and assumed 1:1:1 flavor ratio to capture the low-to-high energy transition.
  • Second proton component (3) [1 EeV scenario]
    Normalization, slope, cutoff for an additional pure-proton source population at the highest energies; introduced ad hoc to explain the 1 EeV KM3NeT event.
  • ARCA effective area scaling factor = 20% of NT effective area
    Chosen by hand to approximate the partially built ARCA21 detector; directly scales the expected KM3NeT event rate.
  • KM3NeT event energy hypotheses = 100 PeV and 1 EeV
    Two ad hoc choices spanning the uncertain reconstructed energy (best-fit 220 PeV); conclusions are conditional on these.
assumptions (3)
  • domain assumption UFA source model with SFR evolution
    The model of UHECR sources (injected power law with sech cutoff, Peters cycle rigidity cutoff, source environment, SFR evolution) is assumed from refs 35, 39, 40; invoked throughout, especially Eq. (1).
  • domain assumption Sibyll2.3c hadronic model with +20 g/cm2 shift
    Used to compute Xmax distributions from the generalized Gumbel model; the shift is from ref 28. Invoked in Methods.
  • domain assumption Negligible backgrounds above 5 PeV
    Assumes atmospheric muons and neutrinos are effectively rejected by veto and overburden; stated in Methods.
invented entities (1)
  • Additional pure-proton source population at the highest energies independent evidence
    purpose: To explain a 1 EeV KM3NeT event as a cosmogenic GZK neutrino and produce a proton recovery above 10 EeV.
    The population yields falsifiable predictions: a proton tail in Auger Xmax distributions above 20 EeV and an EeV-scale neutrino flux observable by IceCube-Gen2; however, it is introduced ad hoc and fit to the data it explains.

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Cite this review

Pith. "Pith review of Emergence of a neutrino flux above 5 PeV and implications for ultrahigh energy cosmic rays." pith.science (2026). https://pith.science/paper/Y3WO34RY

@misc{pith2026250206944,
  author       = {Pith},
  title        = {Pith review of: Emergence of a neutrino flux above 5 PeV and implications for ultrahigh energy cosmic rays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Y3WO34RY}},
  note         = {Machine review of arXiv:2502.06944}
}
abstract

The rare detections of astrophysical neutrinos with energies above 5~PeV by two neutrino telescopes underscore the existence of a flux at these energies. In addition to over a decade of data taken by the IceCube Neutrino Observatory, the KM3NeT neutrino telescope has recently highlighted their discovery of a possible $\mathcal{O}(100~PeV)$ neutrino candidate. A connection between the highest-energy astrophysical neutrinos and the highest-energy cosmic rays is expected, and well-established theoretically. Here, for the first time, we simultaneously fit the neutrino data from IceCube and KM3NeT, as well as the ultrahigh-energy cosmic ray spectrum and composition data from the Pierre Auger Observatory (Auger), to test a common-origin hypothesis. We show that a phenomenological model is able to describe the combined data across these three observatories, and, depending on the true energy of the event detected by KM3NeT, suggests an additional cosmic ray source population not yet robustly detected by Auger. Although a measurement of the neutrino flux in this energy regime is at the sensitivity limit of cubic-kilometer-scale neutrino telescopes, next-generation observatories, such IceCube-Gen2, will have the sensitivity to make a significant detection of this flux.

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Forward citations

Cited by 6 Pith papers

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

  1. The Highest-Energy Neutrino Event Constrains Dark Matter-Neutrino Interactions

    hep-ph 2025-06 conditional novelty 6.0 of 10

    KM3-230213A limits dark matter-neutrino scattering to below about 1e-22 cm^2/GeV at 220 PeV, but most simple dark matter models are excluded by unitarity above MeV masses.

  2. Astrophysical flux of dark particles as a solution to the KM3NeT and IceCube tension over KM3-230213A

    hep-ph 2025-05 conditional novelty 6.0 of 10

    A transient astrophysical dark-particle flux can explain the KM3NeT 70 PeV muon via in-Earth upscattering and decay to muon pairs, while predicting no IceCube counterpart.

  3. Clash of the Titans: ultra-high energy KM3NeT event versus IceCube data

    astro-ph.HE 2025-02 conditional novelty 6.0 of 10

    A single KM3NeT event above 10 PeV is in 2.9 to 3.6 sigma tension with IceCube's non-observation under all standard source models, pointing toward a new astrophysical source.

  4. Scrutinizing the cosmogenic origin of the KM3-230213A event: A Multimessenger Perspective

    astro-ph.HE 2025-07 conditional novelty 5.0 of 10

    A multimessenger transport calculation finds that KM3-230213A is plausibly cosmogenic only if it originates from hard-spectrum protons above the ankle with source evolution close to (1+z)^3.

  5. Interpreting the KM3-230213A PeV Neutrino Event via Vector Dark Matter Decay and Its Multi-Messenger Signatures

    hep-ph 2025-07 conditional novelty 4.0 of 10

    A U(1)_X vector dark matter model explains the KM3-230213A PeV neutrino via DM decay and predicts a cosmic string gravitational wave background consistent with PTA observations, but with several parameters fitted to the data.

  6. Road through Dark$\nu$ess: Probing dark matter-neutrino interactions using KM3-230213A

    hep-ph 2025-06 conditional novelty 4.0 of 10

    Using the 220 PeV event KM3-230213A, the authors set the highest-energy constraints to date on dark matter-neutrino scattering, and for energy-dependent cross sections they report some of the strongest existing limits.

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Reviewed August 8, 2026 · model on record in the stance chip above.