IceCube's contained-event measurement of the astrophysical neutrino flavor ratio (11.4 years of Medium Energy Starting Events, published as Phys. Rev. Lett. 137, 081002 (2026)) determined an energy-averaged composition fe:fμ:fτ=0.30:0.37:0.33f_e:f_\mu:f_\tau=0.30:0.37:0.33 between TeV and PeV energies, but the measurement is limited in two linked ways: the double-cascade tau-neutrino sample is only 9 events at about 70% purity so ντ\nu_\tau statistics dominate the errors; and the flavor ratio is assumed energy-independent across the full range. The open problem is to turn this single averaged number into a precision, energy-resolved determination of the three-flavor composition of the diffuse astrophysical flux — with an enlarged, high-purity tau-tagged sample and an explicit test or measurement of energy dependence.

Background

The diffuse astrophysical neutrino flux discovered by IceCube spans TeV to PeV energies, and the proportions of the three neutrino flavors at Earth — the flavor composition fe:fμ:fτf_e:f_\mu:f_\tau with fe+fμ+fτ=1f_e+f_\mu+f_\tau=1 — encode how and where the neutrinos were produced. In standard source scenarios (full pion-decay chain, muon-damped pion decay, neutron beta decay, or heavy-meson/charm production), neutrino oscillations over cosmic baselines average out and map each source composition onto a nearly unique Earth composition near 1:1:11:1:1; measured deviations from that expectation would indicate non-standard source physics or new physics in propagation (sterile mixing, neutrino decay, quantum decoherence, Lorentz violation, or non-standard interactions).

IceCube, a cubic-kilometer Cherenkov detector at the South Pole, infers flavor from event morphology. Neutrino interactions with vertices contained in the instrumented volume produce three topologies: cascades (mostly νe\nu_e charged-current and neutral-current events), tracks (νμ\nu_\mu charged-current events), and double cascades (ντ\nu_\tau charged-current events in which the hadronic shower and the shower from the subsequent tau-lepton decay, separated by roughly 50 m per PeV of tau energy, are both resolved). Resolving double cascades is intrinsically hard because the horizontal spacing of the digital optical modules (DOMs, the photomultiplier-tube sensors embedded in the ice) is about 125 m, generally larger than the tau decay length below PeV energies. The Medium Energy Starting Events (MESE) sample selects contained events above about 1 TeV and includes all three topologies processed consistently; the High-Energy Starting Events (HESE) sample is a higher-threshold analogue.

The measurement lineage: IceCube first identified two double-cascade tau candidates in 7.5 years of HESE data (Proceedings of Science, PoS(ICRC2019)1015; Eur. Phys. J. C 82, 1031 (2022)); a convolutional-neural-network search then found seven tau candidates in 9.7 years and excluded the absence of astrophysical ντ\nu_\tau at 5σ5\sigma (Phys. Rev. Lett. 132, 151001 (2024)). This measurement — presented at ICRC 2025 (arXiv:2507.07212) and published as Phys. Rev. Lett. 137, 081002 (2026) — used 11.4 years of MESE data classified by a deep neural network into cascades, tracks, and double cascades, giving the first flavor measurement down to the TeV scale: fe:fμ:fτ=0.30:0.37:0.33f_e:f_\mu:f_\tau=0.30:0.37:0.33, with each fraction constrained above zero at more than 90% confidence level (CL) assuming a broken power law (BPL) astrophysical spectrum.

Two limitations of that measurement define the open problem. First, the tau sample is statistically dominant in the errors: 9 observed double cascades against 7.0±0.97.0\pm0.9 expected under the BPL fit, with a selection purity of only about 70%, so ντ\nu_\tau-related observables carry the largest statistical uncertainties. Second, the analysis assumes a single flavor ratio across the whole energy range; a possible energy dependence of the composition — expected, for example, if production mechanisms change with energy — is untested in this sample. A further caveat, which the source treats as handled rather than open, concerns the assumed spectral shape: the flavor confidence contours shift with the spectral model — a single power law (SPL) fit pulls the contours along the ντ\nu_\tau axis relative to the BPL baseline — and the published analysis adopts its BPL baseline from IceCube's dedicated spectral measurements, which establish that the all-flavor spectrum from 5 TeV to 10 PeV rejects an SPL at more than 4σ4\sigma in favor of a BPL or log-parabola (Phys. Rev. Lett. 136, 121002 (2026); Phys. Rev. D 113, 062002 (2026)), with an SPL cross-check reporting consistent best fits.

Problem Statement

Determine the three-flavor composition of the diffuse astrophysical neutrino flux as a function of energy across the TeV-to-PeV range, removing the limitations identified by the contained-event IceCube measurement. Concretely, the analysis must: (1) identify a substantially larger and higher-purity sample of ντ\nu_\tau events (beyond the current 9 double cascades at about 70% purity), so that ντ\nu_\tau statistics no longer dominate the flavor uncertainty; and (2) test for and measure, or bound, energy dependence of the flavor composition fe:fμ:fτf_e:f_\mu:f_\tau over the measured energy range, replacing the single energy-averaged ratio. The two components serve one objective: a precision, energy-resolved flavor measurement of the astrophysical flux at Earth (and, by propagation back through oscillations, at its sources). The result is an energy-resolved composition — flavor-ratio constraints in at least two energy bins spanning the measured TeV-to-PeV range (each at least about a decade wide) or a parametrized energy dependence with calibrated confidence levels, including a well-calibrated null result bounding any energy dependence — obtained with an enlarged tau-tagged sample whose ντ\nu_\tau-channel contribution is no longer the dominant statistical term (operationally, smaller than the leading non-tau contribution to the statistical uncertainty of at least one flavor fraction), together with the systematics treatment (ice optical model, DOM optical efficiency) needed to keep detector uncertainties from masking the result.

References

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