Parton Saturation at Small x and in Large Nuclei
A. H. Mueller
TL;DR
This paper establishes a framework for parton saturation at small x in high-energy hadrons and nuclei by tying quark and gluon densities in the light-cone wavefunction to parton production in current-nucleus scattering. Using a light-cone gauge where final-state interactions vanish, it demonstrates that a Weizsacker-Williams-like picture captures the gluon content and derives one-loop expressions for unintegrated quark and gluon distributions; saturation emerges as a black-disc limit controlled by the saturation momentum $Q_s$. In the quasi-classical regime, explicit formulas show how densities saturate for $\ell^2\ll Q_s^2$ and how the gluon distribution grows with $\ln(1/x)$, evolving to include BFKL dynamics at small x. The work further argues that higher-order corrections convert the $\ln(1/x)$ factor into a $\frac{1}{\alpha}\ln(Q_s^2/\ell^2)$ form, linking the microscopic wavefunction densities to a semiclassical, universal saturation picture with strong implications for high-energy DIS on nuclei and early-stage heavy-ion collisions.
Abstract
Quark and gluon distributions in the light-cone wavefunction of a high energy hadron or nucleus are calculated in the saturation regime. One loop calculations are performed explicitly using the equivalence between the parton distribution in the light-cone wavefunction and the production distribution of that parton in a current-nucleon (nucleus) scattering. We argue that, except for some overall numerical factors, the Weizsacker- Williams wavefunction correctly gives the physics of the gluon distribution in a light-cone wavefunction.