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The high energy cosmic ray spectrum from relic particle decay

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.