Production of ultra-energetic cosmic rays through the decay of super-heavy X particles

We present a new and complete numerical analysis of the decay of super-heavy X particles, assumed to be the origin of cosmic rays with energy beyond the GZK cut-off. The decay of X initiates a ``parton shower'', where we include all degrees of freedom contained in the Minimal Supersymmetric Standard Model (MSSM). Since at energies near $M_X$ all gauge couplings are of similar magnitude, we include all of them, as well as third generation Yukawa couplings. Technically the shower development is described through the DGLAP evolution of the relevant fragmentation functions (FFs). We also carefully treat the decay of the superparticles as well as heavy SM particles created in the shower. Nonperturbative physics is parameterized through the input values of the FFs, which we take from the literature. The final result is the the complete spectrum of all stable particles at the very end of the shower : protons, electrons, neutrinos, photons and neutralinos, for an energy range from $10^{-7} M_X$ to $M_X$. In particular, the flux of high-energy neutralinos is sizable ; it might serve as ``smoking gun'' signature for this kind of scenario.