Perturbative evolution at small x

Abstract

The conventional approach to perturbative evolution is illegal because the expansion in powers of ${\alpha }_s$ of the the DGLAP splitting matrix $\mathbf{P}(\mathbf{z},{\alpha }_{\mathbf{s}})$ breaks down at small $z$. The small-$x$ data for the proton structure function $F_2(x,Q^2)$ and its charm component $F_2^c(x,Q^2)$ show that a hard pomeron, with intercept close to 1.4, must be added to the familar soft pomeron. Conventional perturbative evolution may be applied to the hard-pomeron component and provides a striking test of perturbative QCD.

Lectures at Corfu2001