Anomalous dimensions of composite operators for off-forward hard scattering processes

Abstract

We consider the renormalization of operator matrix elements for exclusive hard scattering processes in the chiral limit in the MS-bar- scheme. For such processes, mixing with total derivative operators has to be taken into account. By analyzing the renormalization structure of the operators in the chiral limit, we construct a consistency relation between the elements of the corresponding anomalous dimension matrices, which determine the scale-dependence of non-forward parton distributions. This relation, which is valid to all orders in the strong coupling, then forms the basis for an algorithm to reconstruct the off-diagonal elements of such matrices. We apply the algorithm to multiple cases. In the limit of a large number of quark flavors, we determine the anomalous dimension matrices for Wilson operators to fifth order in the strong coupling. In the same approximation, the anomalous dimensions for the transversity operators are presented to fourth order. Finally, we also apply the algorithm to obtain some low-N results for the Wilson operators in full QCD to fifth order in the strong coupling.