Scaling in $\gamma^* p$ total cross sections, saturation and the gluon density

Abstract

Including the new HERA data, the $\gamma^* p$ total cross section is analysed in the generalized vector dominance/colour-dipole picture (GVD/CDP) that contains scaling in $\eta = (Q^2 + m^2_0) / \Lambda^2 (W^2)$, where $\Lambda^2 (W^2)$ is an increasing function of $W^2$. At any $Q^2$, for $W^2 \to \infty$, the cross sections for virtual and real photons become identical, $\sigma_{\gamma^* p} (W^2, Q^2) / \sigma_{\gamma p} (W^2) \to 1$. The gluon density deduced from the colour-dipole cross section fulfills the leading order DGLAP relationship. Evolution \`a la DGLAP breaks down for $\eta \lsim 0.1$.