The Evolution of Unpolarized and Polarized Structure Functions at Small x∗

A survey is given of recent developments on the resummed small-x evolution, in a framework based on the renormalization group equation, of non–singlet and singlet structure functions in both unpolarized and polarized deep–inelastic scattering. The available resummed anomalous dimensions are discussed for all these cases, and the most important analytic and numerical results are compiled. The quantitative effects of these small-x resummations on the evolution of the various parton densities and structure functions are presented, and their present uncertainties are investigated. An application to QED radiative corrections is given. ∗ Based on invited talks presented by J. Blümlein at the International Workshop on Deep Inelastic Scattering and Related Phenomena (DIS’96), Rome, Italy, April 1996; and by A. Vogt at the 1996 Zeuthen Workshop on Elementary Particle Theory: QCD and QED in Higher Orders, Rheinsberg, Germany, April 1996. To appear in the Proceedings of the Rheinsberg Workshop, Nucl. Phys. B (Proc. Suppl.).