IMPLICATION OF THE NON-DETECTION OF GZK NEUTRINOS

Abstract

The IceCube telescope has detected diffuse neutrino emission, 20 events of which were reported to be above 60~TeV. In this paper, we fit the diffuse neutrino spectrum using Poisson statistics, which are the most appropriate for the low counts per energy bin. We extend the fitted energy range and exploit the fact that no neutrinos were detected above 2~PeV, despite the high detector sensitivity around the Glashow resonance at 6.3\,PeV and beyond. A best-fit power-law slope of $\alpha=2.9\pm 0.3$ is found with no evidence for a high-energy cutoff. This slope is steeper than $\alpha=2.3\pm 0.3$ found by the IceCube team using a different fitting method. Such a steep spectrum facilitates the identification of high energy ($\gg$ PeV) neutrinos, if detected, to be due to the GZK effect of cosmic-ray protons interacting with the Extragalactic Background Light. We use the ratio of EeV to PeV neutrinos in GZK models to show that the currently detected PeV neutrinos could not be due to the GZK effect, because this would imply many more higher-energy neutrinos that should have been detected, but were not. The non-detection of GZK neutrinos by IceCube despite more than essentially 1200 observing days, has already ruled out (at 95\% confidence) models that predict rates of $\sim1$ neutrino/yr or more. We use this non-detection to quantify the confidence at which GZK models are ruled out, and compute the additional IceCube and (in the future) ARA observing time that would rule them out with 95\% confidence if no detection is made.