NLO evolution for large scale distances, positivity constraints and the low-energy model of the nucleon

We present a computationally reliable and accurate method for solving the Gribov-Lipatov-Altarelli-Parisi equations at next to leading order, both in the non-singlet and in the singlet case. It requires solving numerically the renormalization group equations for the anomalous dimensions of composite operators in the complex plane, and finally performing an inverse Mellin transformation. In this way the group property of renormalization is exactly preserved, i.e. performing two successive scale transformations coincides exactly with a direct one making parton distributions independent of the integration path used to connect two different scales. This is relevant when large scale differences are involved and makes upward or downward evolution fully equivalent. Thus, it becomes possible to evolve the known parton distributions and leading twist contributions to the structure functions from Q2=mb2 to the lowest possible scale imposed by positivity and unitarity. (orig.)