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-Alrarelli-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 dim ensions of composite operators in the complex plane, and finally perfo rming an inverse Mellin transformation. In this way the group property of renormalization is exactly preserved, i.e. performing two successi ve scale transformations coincides exactly with a direct one making pa rton distributions independent of the integration path used to connect two different scales. This is relevant when large scale differences a re involved and makes upward or downward evolution fully equivalent. T hus, it becomes possible to evolve the known parton distributions and leading twist contributions to the structure functions from Q(2) = m(b )(2) to the lowest possible scale imposed by positivity and unitarity. (C) 1998 Elsevier Science B.V.