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

TL;DR

The paper examines how the virtual-photon proton scattering cross section evolves with coherence length, suggesting a change in behavior occurs before reaching extremely large lengths, indicating the onset of parton saturation.

Contribution

It proposes that the observed extrapolation of cross sections at large coherence lengths is unphysical and identifies a potential scale for parton saturation onset.

Findings

Extrapolated cross sections cross at coherence length ~10^8 fm.

Behavior change in cross sections is necessary before reaching this length.

This scale may indicate the onset of parton density saturation.

Abstract

Assuming the form $\sigma^{\gamma P} \propto l^{\lambda_{\rm eff}}$ 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 $\sigma^{\gamma P}$ 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.