High-energy cosmic neutrino observations provide a sensitive test of Lorentz invariance violation (LIV), which may be a consequence of quantum gravity theories. We consider a class of nonrenormalizable, Lorentz invariance violating operators that arise in an effective field theory (EFT) description of Lorentz invariance violation in the neutrino sector inspired by Planck-scale physics and quantum gravity models. We assume a conservative generic scenario for the redshift distribution of extragalactic neutrino sources and employ Monte Carlo techniques to describe superluminal neutrino propagation, treating kinematically allowed energy losses of superluminal neutrinos caused by both vacuum pair emission (VPE) and neutrino splitting. We consider EFTs with both nonrenormalizable $\mathcal{C}\mathcal{P}\mathcal{T}$-odd and nonrenormalizable $\mathcal{C}\mathcal{P}\mathcal{T}$-even operator dominance. We then compare the spectra derived using our Monte Carlo calculations in both cases with the spectrum observed by IceCube in order to determine the implications of our results regarding Planck-scale physics. We find that if the dropoff in the neutrino flux above $\sim 2\mathrm{PeV}$ is caused by Planck-scale physics, rather than by a limiting energy in the source emission, a potentially significant pileup effect would be produced just below the dropoff energy in the case of $\mathcal{C}\mathcal{P}\mathcal{T}$-even operator dominance. However, such a clear dropoff effect would not be observed if the $\mathcal{C}\mathcal{P}\mathcal{T}$-odd, $\mathcal{C}\mathcal{P}\mathcal{T}$-violating term dominates.

• Received 24 November 2014

DOI:https://doi.org/10.1103/PhysRevD.91.045009