Ultra high energy cosmic ray neutrinos

Neutrinos, produced by the collisions of ultra high energy cosmic rays and the 3 K background radiation, require careful treatment of the evolving cosmic ray spectrum. The resulting neutrino differential energy spectrum is flat up to energies of order 10¹⁹eV, thus most events are expected at this energy. The total ν_e-flux should be significantly larger than the proton flux at ~5 × 10¹⁹eV when the recoil proton is correctly treated in photomeson production and when the Bethe-Heitler process (e⁺e^- pair production) is incorporated. Based upon the observed primary proton spectrum we obtain a lower limit on the neutrino flux of ~5.2/km²yr sr implying roughly 0.4 detected upward moving events per year in the present Fly's Eye range of sensitivity.