Unstable superheavy relic particles as a source of neutrinos responsible for ultrahigh-energy cosmic rays

Decays of superheavy relic particles may produce extremely energetic neutri nos. Their annihilations on the relic neutrinos can be the origin of the co smic rays with energies beyond the Greisrn-Zatsepin-Kuzmin cutoff. The reds hift acts as a cosmological filter selecting the sources at some particular value z(e) +/- delta z, for which the present neutrino energy is close to the Z pole of the annihilation cross section. We predict no directional cor relation of the ultrahigh-energy cosmic rays with the galactic halo. At the same time, there can be some directional correlations in the data, reflect ing the distribution of matter at redshift z = z(e) +/- delta z. Both of th ese features are manifest in the existing data. Our scenario is consistent with the neutrino mass reported by super-Kamiokande and requires no lepton asymmetry or clustering of the background neutrinos.