  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 - 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 - 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.
