Green's Functions in the Color Field of a Large Nucleus

TL;DR

The paper formulates a MV-like framework for a large nucleus at small x, reducing the problem to a two-dimensional ultraviolet-finite theory by averaging over Gaussian color-charge densities. It derives and solves scalar, fermion, and gluon propagators in the background color field and links these Green's functions to sea-quark distributions, providing explicit results in the perturbative kt window and showing saturation of the sea component for light quarks. It finds that in the dominant region the sea quark distribution saturates as a mass-independent constant while the sea-to-gluon ratio is suppressed by $\alpha_s/\pi$, laying groundwork for first radiative corrections and potential high-energy enhancements. The work also discusses limitations, the need for extending to larger kt and Q^2 evolution, and the potential relevance to hadronic structure functions and Lipatov-like effects.

Abstract

We compute the Green's functions for scalars, fermions and vectors in the color field associated with the infinite momentum frame wavefunction of a large nucleus. Expectation values of this wavefunction can be computed by integrating over random orientations of the valence quark charge density. This relates the Green's functions to correlation functions of a two dimensional, ultraviolet finite, field theory. We show how one can compute the sea quark distribution functions, and explictly compute them in the kinematic range of transverse momenta, $α_s^2 μ^2 << k_t^2 << μ^2$, where $μ^2$ is the average color charge squared per unit area. When $m_{quark}^2 << μ^2 \sim A^{1/3}$, the sea quark contribution to the infinite momentum frame wave function saturates at a value that is the same as that for massless sea quarks.