The evolution of ${\sigma }^{\gamma P}$ with coherence length

Abstract

Assuming the form ${\sigma }^{\gamma P}\propto l^{{\lambda }_{\mathrm{eff}}}$ at fixed $Q^2$ for the behavior of the virtual-photon proton scattering cross section, where $l$ is the coherence length of the photon fluctuations, it is seen that the extrapolated values of ${\sigma }^{\gamma P}$ for different $Q^2$ cross for $l\approx 10^8$~fm. It is argued that this behavior is not physical, and that the behavior of the cross sections must change before this coherence length $l$ is reached. This could set the scale for the onset of saturation of parton densities.