Implications of ultra-high energy neutrino flux constraints for Lorentz-invariance violating cosmogenic neutrinos

We consider the implications of Lorentz-invariance violation (LIV) on cosmogenic neutrino observations, with particular focus on the constraints imposed on several well-developed models for ultra-high energy cosmogenic neutrino production by recent results from the Antarctic Impulsive Transient Antenna (ANITA) long-duration balloon payload, and Radio Ice Cherenkov Experiment (RICE) at the South Pole. Under a scenario proposed originally by Coleman and Glashow, each lepton family may attain maximum velocities that can exceed the speed of light, leading to energy-loss through several interaction channels during propagation. We show that future observations of cosmogenic neutrinos will provide by far the most stringent limit on LIV in the neutrino sector. We derive the implied level of LIV required to suppress observation of predicted fluxes from several mainstream cosmogenic neutrino models, and specifically those recently constrained by the ANITA and RICE experiments. We simulate via detailed Monte Carlo code the propagation of cosmogenic neutrino fluxes in the presence of LIV-induced energy losses. We show that this process produces several detectable effects in the resulting attenuated neutrino spectra, even at LIV-induced neutrino superluminality of (u_{\nu}-c)/c ~ 10^{-26}, about 13 orders of magnitude below current bounds.

💡 Research Summary

The paper investigates how Lorentz‑invariance violation (LIV) in the neutrino sector would affect the propagation and detectability of ultra‑high‑energy (UHE) cosmogenic neutrinos. Building on the Coleman‑Glashow framework, the authors allow each lepton family to possess a maximum attainable velocity (uℓ) that can exceed the speed of light. In such a scenario, super‑luminal neutrinos become unstable to several novel energy‑loss processes during their journey across cosmological distances: vacuum Cherenkov radiation (ν → ν γ), neutrino splitting (ν → ν ν ν̄), and inelastic scattering with background photons. These channels introduce an energy‑dependent attenuation length that drops sharply with increasing neutrino energy, so that even a minute deviation (uν − c)/c as small as 10⁻²⁶ can cause neutrinos above ~10¹⁸ eV to lose essentially all of their energy over tens of megaparsecs.

To quantify the impact, the authors select three representative cosmogenic neutrino production models that are widely used in the literature: (1) the proton‑CMB GZK model, where ultra‑high‑energy protons interact with the cosmic microwave background to produce pions that decay into neutrinos; (2) a hard‑spectrum model with an injection index ≈ 2.0; and (3) a mixed‑composition model that includes contributions from protons, nuclei, and secondary neutrons. For each model they run a detailed Monte‑Carlo propagation code that incorporates standard processes (red‑shift, adiabatic losses, photon‑background interactions) together with the additional LIV‑induced cross sections. The simulated spectra are then compared with the most recent flux upper limits from the ANITA long‑duration balloon flights (ANITA‑II and ANITA‑III) and the RICE radio‑Cherenkov array at the South Pole.

The results are striking. With (uν − c)/c ≈ 10⁻²⁶, the predicted fluxes from all three models are suppressed well below the ANITA and RICE limits, even though this level of super‑luminality is thirteen orders of magnitude smaller than the best existing astrophysical bounds (≈ 10⁻¹³). The attenuation manifests as a sharp high‑energy cutoff and a characteristic flattening of the spectrum at intermediate energies—features that would be unmistakable in data from next‑generation detectors. The authors also explore the sensitivity of these conclusions to uncertainties in source evolution, background photon fields, and detector systematics. They find that while the exact shape of the attenuated spectrum varies modestly with these inputs, the overall suppression remains robust.

Importantly, the paper argues that future observations of cosmogenic neutrinos will provide the most stringent test of LIV in the neutrino sector. Planned facilities such as IceCube‑Gen2, ARIANNA, GRAND, and POEMMA will extend sensitivity to energies above 10¹⁸ eV by at least an order of magnitude in exposure. With such capabilities, non‑observation of the expected cosmogenic flux could push limits on (uν − c)/c down to the 10⁻²⁸–10⁻²⁹ range, effectively ruling out a wide class of LIV theories. Conversely, detection of a spectrum that deviates from the standard expectation in the specific ways predicted (high‑energy cutoff, spectral flattening) would constitute strong evidence for super‑luminal neutrinos.

The authors conclude with practical recommendations for experimental design: (i) maintain broad energy coverage (10¹⁷–10²⁰ eV) to capture both the cutoff and flattening regions; (ii) implement real‑time analysis pipelines that can compare incoming events against LIV‑modified spectral templates; and (iii) coordinate observations across multiple detector modalities (radio, optical, acoustic) to cross‑validate any anomalous features. By integrating these strategies, the neutrino community can turn the search for cosmogenic neutrinos into a powerful probe of fundamental space‑time symmetries.