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

Abstract

Including the new HERA data, the $γ^* p$ total cross section is analysed in the generalized vector dominance/colour-dipole picture (GVD/CDP) that contains scaling in $η= (Q^2 + m^2_0) / Λ^2 (W^2)$, where $Λ^2 (W^2)$ 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, $σ_{γ^* p} (W^2, Q^2) / σ_{γp} (W^2) \to 1$. The gluon density deduced from the colour-dipole cross section fulfills the leading order DGLAP relationship. Evolution à la DGLAP breaks down for $η\lsim 0.1$.