Collective Phenomena in $pp$ and $ep$ Scattering

TL;DR

This paper explores how saturation effects in deep inelastic scattering relate to the slow-down of proton-proton cross section growth, using models like the Van der Waals equation to describe phase transitions.

Contribution

It links saturation phenomena in DIS structure functions with phase transition models, providing a novel perspective on the connection between low-$x$ behavior and cross section saturation.

Findings

Saturation effects in DIS are analogous to phase transitions.

A Van der Waals model describes the saturation in structure functions.

Potential slowdown in $pp$ cross section rise due to saturation effects.

Abstract

Bjorken scaling violation in deep inelastic electron-proton scattering (DIS) is related to the rise of hadronic cross sections by using the additive quark model. Of special interest is the connection between saturation in the low-$x$ behavior of the DIS structure functions (SF) and possible slow-down of the $pp$ cross section rise due to saturation effects. We also identify saturation effects in the DIS SF with phase transition that can be described by the Van der Waals equation of state.