  It has been speculated that the recently detected ultra-high energy cosmic
rays may originate from the decays of relic particles with mass of order
$10^{12}$ GeV clustered in the halo of our Galaxy. This hypothesis can be
tested through forthcoming measurements of the spectra of both high energy
cosmic nucleons and neutrinos, which are determined in this model by the
physics of QCD fragmentation, with no astrophysical uncertainties. We evolve
fragmentation spectra measured at LEP energies up to the scale of the decaying
particle mass by numerical solution of the DGLAP equations. This enables
incorporation of the effects of supersymmetry on the development of the cascade
and we also allow for decays into many-particle states. The calculated spectral
shape agrees well with present cosmic ray data beyond the
Greisen-Zatsepin-Kuzmin energy.
