Saturation and geometrical scaling -- from small $x$ deep inelastic ep scattering to high energy proton-proton and heavy ion collisions

TL;DR

This paper discusses how gluon saturation leads to geometrical scaling in high-energy collisions, illustrating examples and violations across various reactions, and emphasizing the role of the saturation momentum as a key scale in QCD.

Contribution

It demonstrates the presence and violation of geometrical scaling in different high-energy processes, linking saturation momentum to observable phenomena in QCD.

Findings

Gluon distributions saturate due to non-linear QCD evolution.

Geometrical scaling occurs when saturation momentum is the dominant scale.

Examples of geometrical scaling and its violations are provided across reactions.

Abstract

Gluon distributions of colliding hadrons saturate as a result of the non-linear evolution equations of QCD. As a consequence there exists the so called saturation momentum, which is related to the gluon density per unit rapidity per transverse area. When saturation momentum is the only scale for physical processes, different observables exhibit geometrical scaling (GS). We show a number of examples of GS and its violation in different reactions.