Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus
Yuri V. Kovchegov
TL;DR
The paper derives the classical non-Abelian Weizsäcker-Williams field for a very large ultra-relativistic nucleus and constructs the corresponding two-dimensional color charge density ρ_perp within the McLerran-Venugopalan framework. By evaluating density correlators, it shows that ρ_perp has a Gaussian distribution with a spatially dependent variance μ^2(x), thereby validating the MV averaging prescription for small-x observables and linking μ^2 to the nucleus geometry. The results yield an explicit expression for μ^2(x) and demonstrate that odd-density correlators vanish while even correlators factorize, implying a consistent Gaussian functional weight for all observables of the form O_ρ. This provides a solid field-theoretic basis for calculating Wilson-loop–type observables and gluon distributions in very large nuclei at small x.
Abstract
We consider a very large ultra-relativistic nucleus. Assuming a simple model of the nucleus and weak coupling we find a classical solution for the gluon field of the nucleus and construct the two-dimensional color charge density for McLerran-Venugopalan model out of it. We prove that the density of states distribution, as a function of color charge density, is Gaussian, confirming the assumption made by McLerran and Venugopalan.