The evolution of $σ^{γP}$ with coherence length

Assuming the form $σ^{γP} \propto l^{λ_{\rm eff}}$ 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 $σ^{γP}$ 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.

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