The origin of highest energy cosmic rays is yet unknown .
An appealing possibility is the so-called Z-burst scenario , in which a large fraction of these cosmic rays are decay products of Z bosons produced in the scattering of ultrahigh energy neutrinos on cosmological relic neutrinos .
The comparison between the observed and predicted spectra constrains the mass of the heaviest neutrino .
The required neutrino mass is fairly robust against variations of the presently unknown quantities , such as the amount of relic neutrino clustering , the universal photon radio background and the extragalactic magnetic field .
Considering different possibilities for the ordinary cosmic rays the required neutrino masses are determined .
In the most plausible case that the ordinary cosmic rays are of extragalactic origin and the universal radio background is strong enough to suppress high energy photons , the required neutrino mass is 0.08 eV \leq~ { } m _ { \nu } \leq~ { } 0.40 eV .
The required ultrahigh energy neutrino flux should be detected in the near future by experiments such as AMANDA , RICE or the Pierre Auger Observatory .