Computing Quark and Gluon Distribution Functions for Very Large Nuclei

TL;DR

The paper argues that at very small x and for sufficiently large nuclei, quark and gluon distribution functions can be computed using weak-coupling methods by treating a high-density color background as static sources along the light cone. It develops a light-cone Hamiltonian framework with a modified propagator and a density parameter μ^2 controlling color-charge fluctuations, and derives a Weiszacker-Williams form for the gluon distribution at lowest order. The approach converts the problem into a many-body calculation with classical color fields, discusses the regime of validity and potential higher-order corrections, and highlights both ultraviolet and infrared open questions as well as connections to deep inelastic scattering and heavy-ion phenomenology. Quark distributions are outlined as a future extension, with the expectation that similar weak-coupling treatment could illuminate small-x structure in large nuclei. Overall, the work provides a structured path toward perturbative calculations of parton distributions in high-density QCD regimes.

Abstract

We argue that the distribution functions for quarks and gluons are computable at small x for sufficiently large nuclei, perhaps larger than can be physically realized. For such nuclei, we argue that weak coupling methods may be used. We show that the computation of the distribution functions can be recast as a many body problem with a modified propagator, a coupling constant which depends on the multiplicity of particles per unit rapidity per unit area, and for non-abelian gauge theories, some extra media dependent vertices. We explicitly compute the distribution function for gluons to lowest order, and argue how they may be computed in higher order.