Ultra High Energy Cosmic Rays Spectra in Top-Down models

In this work we present a detailed computation of the spectra of UHECR in the top-down scenario. We compare the spectra of hadrons obtained by two different methods in QCD and supersymmetric (SUSY) QCD with large primary energies $\sqrt{s}$ up to $10^{16}$ GeV. The two methods discussed are a Monte Carlo (MC) simulation and the evolution of the hadron fragmentation functions as described by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations. The hadron spectra obtained by the two methods agree fairly well in the interesting energy range $10^{-5}M_{X}<E<0.3M_{X}$ ($M_X$ is the energy scale of the process $M_{X}\ge 10^{12}$ GeV). We have also computed the spectra of photons, neutrinos and nucleons obtaining a good agreement with other published results. The consistency of the spectra computed by different methods allows us to consider the spectral shape as a signature of the production model for UHECR, such as the decay of super heavy relic particles or topological defects.