Susy QCD and High Energy Cosmic Rays 1. Fragmentation functions of Susy QCD

The supersymmetric evolution of the fragmentation functions (or timelike evolution) within N=1 $QCD$ is discussed and predictions for the fragmentation functions of the theory (into final protons) are given. We use a backward running of the supersymmetric DGLAP equations, using a method developed in previous works. We start from the usual QCD parameterizations at low energy and run the DGLAP back, up to an intermediate scale -assumed to be supersymmetric- where we switch-on supersymmetry. From there on we assume the applicability of an N=1 supersymmetric evolution (ESAP). We elaborate on possible application of these results to High Energy Cosmic Rays near the GZK cutoff.