Soft and hard pomerons

Abstract

Regge theory provides an excellent description of small-$x$ structure-function data from $Q^2=0$ up to the highest available values. The large-$Q^2$ data should also be described by perturbative QCD: the two descriptions must agree in the region where they overlap. However, at present there is a serious lack in our understanding of how to apply perturbative QCD at small $x$. The usual lowest-order or next-to-lowest order expansion is not valid, at least not until $Q^2$ becomes much larger than is usually assumed; a resummation is necessary, but as yet we do not know how to do this resummation.

8 pages, plain tex, with 6 figures embedded using epsf. Lecture at Workshop on New Trends in HERA Physics, Ringberg (june 1999)