Implication of the non-detection of gzk neutrinos

The IceCube telescope has detected diffuse neutrino emission up to a deposited energy of 2.6 PeV. Neutrinos with higher energies are expected from the Greisen Ztsepin Kuzmin (GZK) effect, namely the interaction of ultrahigh-energy cosmic rays (UHECRs) with the cosmic microwave background (CMB) and the extragalactic background light (EBL), but have not yet been detected. Models for GZK neutrinos vary greatly due to different assumptions on the UHECR elemental composition, as well as on the cosmological evolution of their sources and of the EBL. We show that the high ratio of EeV to PeV neutrinos in essentially all GZK models excludes the currently detected PeV neutrinos from being due to the GZK effect, because many additional higher-energy neutrinos should have been detected but were not. The non-detection of GZK neutrinos, despite more than essentially 1800 observing days, already rules out at 95% confidence all of the models that predict rates of 0.6 neutrinos yr^-1 or more. The non-detection is further used here to quantify the confidence at which classes of GZK models can be ruled out, and to compute the additional IceCube observing time required in order to rule them out with 95% confidence, if no detection is made. Finally, the number of GZK neutrinos expected from various classes of models in the future neutrino telescopes ARA and KM3NeT is estimated.