We consider the possibility that a large fraction of the ultrahigh energy cosmic rays are decay products of Z bosons which were produced in the scattering of ultrahigh energy cosmic neutrinos on cosmological relic neutrinos .
We compare the observed ultrahigh energy cosmic ray spectrum with the one predicted in the above Z-burst scenario and determine the required mass of the heaviest relic neutrino as well as the necessary ultrahigh energy cosmic neutrino flux via a maximum likelihood analysis .
We show that the value of the neutrino mass obtained in this way is fairly robust against variations in presently unknown quantities , like the amount of neutrino clustering , the universal radio background , and the extragalactic magnetic field , within their anticipated uncertainties .
Much stronger systematics arises from different possible assumptions about the diffuse background of ordinary cosmic rays from unresolved astrophysical sources .
In the most plausible case that these ordinary cosmic rays are protons of extragalactic origin , one is lead to a required neutrino mass in the range 0.08 eV \leq~ { } m _ { \nu } \leq~ { } 1.3 eV at the 68 % confidence level .
This range narrows down considerably if a particular universal radio background is assumed , e.g .
to 0.08 eV \leq~ { } m _ { \nu } \leq~ { } 0.40 eV for a large one .
The required flux of ultrahigh energy cosmic neutrinos near the resonant energy should be detected in the near future by AMANDA , RICE , and the Pierre Auger Observatory , otherwise the Z-burst scenario will be ruled out .