Ultra-high-energy (UHE) astrophysical neutrinos, above roughly 10 PeV, are expected to arrive at Earth with an approximately 1:1:1 ratio of electron, muon, and tau flavors, and deviations from this pattern encode both source physics and possible beyond-Standard-Model propagation effects. Earth-skimming tau-neutrino telescopes detect only tau leptons emerging from the Earth, but Garcia Soto, Zhelnin, Safa, and Argüelles (Phys. Rev. Lett. 128, 171101, 2022) showed that interactions of electron- and muon-neutrinos inside the Earth generate a secondary tau-neutrino flux that can rival the primary one above 10 PeV. Consequently, the observed rate of emerging taus is degenerate between different primary flavor compositions — e.g., a canonical (1:1:1) flux and a flux with zero primary tau component — so a technique whose observable is that emerging-tau rate cannot set strong constraints on either the flavor composition or the normalization of the UHE flux without assumptions about the other. The open problem, stated explicitly in that work and in the 2024 thesis of Safa it underpins, is to break this degeneracy so that the primary flavor ratios and the flux normalization can be inferred free of it. As of August 2026 this remains unachieved observationally: 2026 studies have produced a first three-technology sensitivity forecast and a Glashow-resonance channel study, but no UHE flavor-tagged measurement exists.

Background

Neutrinos of astrophysical origin span energies from TeV to EeV. At the highest energies (above ~100 PeV), the dominant expected component is cosmogenic neutrinos, produced when ultra-high-energy cosmic rays scatter on cosmic microwave background photons; their flux normalization is itself uncertain by orders of magnitude. Standard three-flavor neutrino oscillations over astronomical baselines are expected to shape any source flavor mixture into an approximately democratic 1:1:1 ratio of (νe:νμ:ντ)(\nu_e:\nu_\mu:\nu_\tau) at Earth, so a measured departure from this pattern would carry information about the production mechanism at the source (e.g., pppp versus pγp\gamma collisions, or neutron beta decay) or about new physics during propagation, such as neutrino decay or mixing with sterile states. Three detection technologies cover this energy range: in-ice optical Cherenkov telescopes (IceCube and its upgrade IceCube-Gen2), which record the light of charged particles in Antarctic ice and can statistically distinguish flavor topologies up to a few PeV; in-ice radio arrays (ARA, ARIANNA, RNO-G, the IceCube-Gen2 radio array), which detect the Askaryan radio emission — coherent radiation from the charge-excess shower front — from neutrino interactions in the ice at EeV energies but identify flavor only crudely; and Earth-skimming tau-neutrino telescopes (TAMBO, POEMMA, Trinity, BEACON, GRAND, the Pierre Auger Observatory), which point at mountain walls or the Earth's limb and detect the extensive air shower — the cascade of particles in the atmosphere — produced when a tau lepton emerges from the Earth after a tau-neutrino charged-current interaction and decays. Earth-skimming experiments are therefore uniquely sensitive to tau neutrinos above the horizon-crossing energies where the Earth becomes opaque. However, as muon- and electron-neutrinos traverse the Earth they can produce on-shell WW bosons, which decay to τ ντ\tau\,\nu_\tau about 10% of the time; the relevant channels are the Glashow resonance (νˉee−→W−\bar{\nu}_e e^- \to W^-), neutrino-nucleus and neutrino-electron WWWW-boson production, and top-quark production, whose rate is tied to the sea-bottom parton distribution functions of the nucleon. This secondary production is distinct from tau regeneration — the ντ\nu_\tau charged-current chain ντ→τ→ντ\nu_\tau \to \tau \to \nu_\tau, which makes the Earth effectively transparent to tau neutrinos — and from the prompt decay of charmed hadrons, which sets the atmospheric tau-neutrino background that the secondary flux is compared against. Garcia Soto, Zhelnin, Safa, and Argüelles (2022) computed this secondary tau-neutrino flux with a Monte Carlo simulation of propagation through Earth (the NupropEarth framework, with tau energy losses from PROPOSAL and the related open TauRunner lepton-propagation code) and found it exceeds the atmospheric background above ~300 TeV and can reach ~50% of the primary astrophysical flux above ~10 PeV. That fraction depends mainly on the primary spectrum and on the column depth traversed, so it is larger for steeper trajectories. Two consequences follow, both derived in the primary source and in Chapter 2 of Safa's thesis ('Tau Neutrinos Require Some Care', Sec. 4 'Production of Tau Neutrinos in Earth'): (i) Earth-skimming telescopes will observe emerging taus even if the primary flux contains no tau neutrinos at all; and (ii) the emerging-tau yield is degenerate between, e.g., a smaller canonical (1:1:1) flux and a larger (1:1:0)-type flux, so a single-flavor technique cannot set strong constraints on the normalization of the flux without assumptions about its flavor composition. The same authors noted the two escape routes that define the current problem: nascent reconstruction of muon-induced air-shower Cherenkov emission would make Earth-skimming telescopes sensitive to multiple flavors, and all-flavor-sensitive radio/optical experiments are unaffected by the degeneracy, so a combined analysis is fundamental. The Glashow resonance — the channel νˉee−→W−\bar{\nu}_e e^- \to W^- at 6.3 PeV, whose W→τ νˉτW \to \tau\,\bar{\nu}_\tau branch produces a tau air shower — plays a double role here: it is one of the channels generating the secondary tau-neutrino flux, and (as explored in the 2026 study of Ding and Liu) a potential in-technique handle on the electron-antineutrino component. The observational context makes the problem concrete: IceCube has measured the three-flavor composition only at TeV–PeV energies and observed seven astrophysical tau candidates at a median parent energy near 200 TeV (2024), and the KM3NeT collaboration reported the first hundreds-of-PeV event, KM3-230213A, with no flavor identification. No experiment has yet measured flavor composition at ultra-high energy.

Problem Statement

Determine, from observations, the flavor composition and normalization of the ultra-high-energy (Eν≳10E_\nu \gtrsim 10 PeV) neutrino flux at Earth, disentangling primary tau neutrinos from the secondary tau neutrinos generated inside the Earth by electron- and muon-neutrino interactions. Throughout, the target regime is Eν≳10E_\nu \gtrsim 10 PeV, where the secondary tau component reaches ~50% of the primary astrophysical flux; the cosmogenic-dominated regime above ~100 PeV is the part of this window in which most models place the largest flux, and flavor-sensitive channels below 10 PeV (e.g., the Glashow resonance at 6.3 PeV) enter only as inputs to an analysis of this window. As established by Garcia Soto et al. (Phys. Rev. Lett. 128, 171101, 2022), a technique whose observable is the emerging-tau yield — in particular an Earth-skimming telescope that sees only emerging tau air showers — suffers a degeneracy: an observed tau rate can be matched by a smaller canonical (1:1:1) flux or by a larger flux with zero primary tau component, so the normalization cannot be constrained without assumptions about the flavor composition. The problem is to break this degeneracy: to separate the primary and secondary tau contributions and infer the UHE flavor ratios and the flux normalization without assumptions about the other, carrying through the propagation and detector modeling this requires: the WW-boson channels that generate the secondary tau neutrinos (Glashow resonance, WWWW-boson production, top-quark production) together with tau regeneration along Earth trajectories, including their energy and emergence-angle dependence, and per-event tau-identification efficiencies and misidentification rates in the likelihood. The degeneracy is broken when quantified constraints on the UHE flavor ratios and flux normalization — obtained from a likelihood built on realistic tau-neutrino identification criteria and on the energy and angular information of operating or forthcoming instruments rather than on idealized sensitivity assumptions, and including the secondary tau contribution — no longer allow a (1:1:1) flux and a (1:1:0)-type flux to mimic each other at an explicitly stated confidence level with statistical and systematic uncertainties propagated. The degeneracy is broken only if the constraints span the flavor ratios and the normalization, rather than separating those two compositions alone.

References

  1. A. Garcia Soto, P. Zhelnin, I. Safa, C. A. Argüelles, 'Tau Appearance from High-Energy Neutrino Interactions', Phys. Rev. Lett. 128, 171101 (2022), DOI:10.1103/PhysRevLett.128.171101, arXiv:2112.06937, https://arxiv.org/abs/2112.06937
  2. I. Safa, 'New Physics with PeV Astrophysical Neutrino Beams', PhD thesis (2024), DOI:10.48550/arXiv.2402.19393, arXiv:2402.19393, https://arxiv.org/abs/2402.19393
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  4. T. Ding, Q. Liu, 'Probing Neutrino Flavor Composition with the Glashow Resonance at Tau Air-Shower Neutrino Telescopes' (2026), DOI:10.48550/arXiv.2607.26128, arXiv:2607.26128, https://arxiv.org/abs/2607.26128
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