The Colour Glass Condensate: An Introduction

TL;DR

The paper introduces the Colour Glass Condensate as the high-density, small-x gluon matter in hadrons and nuclei. It develops a classical Yang-Mills description with random color sources, then derives a renormalization group equation that evolves these sources with rapidity, unifying linear BFKL growth and non-linear saturation through a functional Fokker-Planck framework. Key outcomes include the recovery of BFKL in the weak-field limit, the Balitsky-Kovchegov equation in the large-N_c limit, and a mean-field approach that illuminates high-k⊥ (perturbative) and low-k⊥ (saturation) dynamics. These results explain unitarization via saturation, predict a universal, scale-dependent saturation scale Q_s(τ), and connect small-x evolution to observable quantities such as the gluon distribution and dipole cross-sections, with broad implications for DIS and heavy-ion collisions.

Abstract

In these lectures, we develop the theory of the Colour Glass Condensate. This is the matter made of gluons in the high density environment characteristic of deep inelastic scattering or hadron-hadron collisions at very high energy. The lectures are self contained and comprehensive. They start with a phenomenological introduction, develop the theory of classical gluon fields appropriate for the Colour Glass, and end with a derivation and discussion of the renormalization group equations which determine this effective theory.

Figures (19)

• Figure 1: The cross sections for $pp$ and $p\overline p$ scattering.
• Figure 2: A hadron-hadron collision. The produced particles are shown as circles.
• Figure 3: The rapidity distribution of particles produced in a hadronic collision.
• Figure 4: Feynman scaling of rapidity distributions. The two different lines correspond to rapidity distributions at different energies.
• Figure 5: Deep inelastic scattering of an electron on a hadron.