Evolution at small x_bj: The Color Glass Condensate

TL;DR

This work introduces the Color Glass Condensate as a dense gluon regime at small x, where nonlinear evolution (JIMWLK) and dipole-based observables capture saturation physics through a universal saturation scale Q_s. It develops the formalism via Wilson-line correlators, the Balitsky hierarchy, and its BK reduction, and provides both a Fokker-Planck/Langevin interpretation and a bridge to jet physics through analogies with non-global observables. Key results include geometric scaling, a scaling window above Q_s, and the impact of running coupling on Q_s evolution, supported by numerical JIMWLK and BK studies. The phenomenology connects to HERA DIS, initial gluon production in heavy-ion collisions, and Cronin effect suppression, with implications for RHIC/LHC and future EIC experiments.

Abstract

When probed at very high energies or small Bjorken x_bj, QCD degrees of freedom manifest themselves as a medium of dense gluon matter called the Color Glass Condensate. Its key property is the presence of a density induced correlation length or inverse saturation scale R_s=1/Q_s. Energy dependence of observables in this regime is calculable through evolution equations, the JIMWLK equations, and characterized by scaling behavior in terms of Q_s. These evolution equations share strong parallels with specific counterparts in jet physics. Experimental relevance ranges from lepton proton and lepton nucleus collisions to heavy ion collisions and cross correlates physics at virtually all modern collider experiments.

Figures (27)

• Figure 1: Kinematics in DIS of leptons off protons or nuclei
• Figure 2: Kinematic variables in a Minkowski diagram. Projectile and target are separated by a large boost factor $\frac{1}{{x_{\text{bj}}}}=e^Y$. $x^\pm:=\frac{1}{\sqrt{2}}(x^0\pm x^3)$ are the lightlike directions in the $x^0$-$x^3$ plane often referred to as "$+$" and "$-$" directions.
• Figure 3: Qualitative growth of gluon distributions as from typical DGLAP fits of DIS at HERA ($e A$) for different $Q^2$.
• Figure 4: Left: Partons in the $Y,\ln Q^2$ plane represented as dots of size $1/Q^2$. Numbers grow both with $Q^2$ and $\ln(1/{x_{\text{bj}}})$. Going to sufficiently small ${x_{\text{bj}}}$ at fixed $Q^2$ partons start to overlap. Right: corresponding regions of phase space with qualitatively different behavior. The lower boudary of the CGC region is determined by $Q_s({x_{\text{bj}}})$. The extendeded scaling region will be explaind in Sec. \ref{['sec:scaling-window']}.
• Figure 5: $q\Bar q$ pairs interacting with a nuclear target at small ${x_{\text{bj}}}$. (a) shows the situation in the targets infinite momentum frame with fully Lorentz-contracted target fields, (b) shows the situation in the target rest frame in which the $\gamma^* q\Bar q$ vertex is far outside the target at a distance proportional to the relative boost factor $1/{x_{\text{bj}}} = e^Y$.