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There may be a high-energy cutoff of neutrino events in IceCube data. In particular, IceCube does not observe either continuum events above 2PeV, or the Standard Model Glashow-resonance events expected at 6.3PeV. There are also no higher energy neutrino signatures in the ANITA and Auger experiments. This absence of high-energy neutrino events motivates a fundamental restriction on neutrino energies above a few PeV. We postulate a simple scenario to terminate the neutrino spectrum that is Lorentz-invariance violating, but with a limiting neutrino velocity that is always smaller than the speed of light. If the limiting velocity of the neutrino appliesmore » also to its associated charged lepton, then a significant consequence is that the two-body decay modes of the charged pion are forbidden above two times the maximum neutrino energy, while the radiative decay modes are suppressed at higher energies. Finally, such stabilized pions may serve as cosmic ray primaries.« less

We have previously shown that the decay of high-energy neutrinos from distant astrophysical sources would be revealed by flavor ratios that deviate strongly from the $$\phi_{\nu_e}:\phi_{\nu_\mu}:\phi_{\nu_\tau} = 1:1:1$$ expected from oscillations alone. Here we show that the deviations are significantly larger when the mixing angle $$\theta_{13}$$ and the CP phase $$\delta$$ are allowed to be nonzero. If neutrinos decay, this could allow measurement of $$\theta_{13}$$ and $$\delta$$ in IceCube and other near-term neutrino telescopes.

We discuss the prospects for next generation neutrino telescopes, such as IceCube, to measure the flavor ratios of high-energy astrophysical neutrinos. The expected flavor ratios at the sources are $$\phi_{\nu_e}:\phi_{\nu_{\mu}}:\phi_{\nu_{\tau}} = 1:2:0$$, and neutrino oscillations quickly transform these to $1:1:1$. The flavor ratios can be deduced from the relative rates of showers ($$\nu_e$$ charged-current, most $$\nu_\tau$$ charged-current, and all flavors neutral-current), muon tracks ($$\nu_\mu$$ charged-current only), and tau lepton lollipops and double-bangs ($$\nu_\tau$$ charged-current only). The peak sensitivities for these interactions are at different neutrino energies, but the flavor ratios can be reliably connected by a reasonable measurement of themore » spectrum shape. Measurement of the astrophysical neutrino flavor ratios tests the assumed production mechanism and also provides a very long baseline test of a number of exotic scenarios, including neutrino decay, CPT violation, and small-$$\delta m^2$$ oscillations to sterile neutrinos.« less

Existing limits on the non-radiative decay of one neutrino to another plus a massless particle (e.g., a singlet Majoron) are very weak. The best limits on the lifetime to mass ratio come from solar neutrino observations, and are $$\tau/m \agt 10^{-4}$$ s/eV for the relevant mass eigenstate(s). For lifetimes even several orders of magnitude longer, high-energy neutrinos from distant astrophysical sources would decay. This would strongly alter the flavor ratios from the $$\phi_{\nu_e}:\phi_{\nu_{\mu}}:\phi_{\nu_{\tau}} = 1:1:1$$ expected from oscillations alone, and should be readily visible in the near future in detectors such as IceCube.

Neutrinos may be pseudo-Dirac states, such that each generation is actually composed of two maximally-mixed Majorana neutrinos separated by a tiny mass difference. The usual active neutrino oscillation phenomenology would be unaltered if the pseudo-Dirac splittings are $$\delta m^2 \alt 10^{-12}$$ eV$^2$: in addition, neutrinoless double beta decay would be highly suppressed. However, it may be possible to distinguish pseudo-Dirac from Dirac neutrinos using high-energy astrophysical neutrinos. By measuring flavor ratios as a function of $L/E$, mass-squared differences down to $$\delta m^2 \sim 10^{-18}$$ eV$^2$ can be reached. We comment on the possibility of probing cosmological parameters with neutrinos.