Color neutrality and the gluon distribution in a very large nucleus

We improve the McLerran-Venugopalan model for the gluon distribution functions in very large nuclei by imposing the condition that the nucleons should be color neutral. We find that enforcing color neutrality cures the infrared divergences in the transverse coordinates which are present in the McLerran-Venugopalan model. Since we obtain well-defined expressions for the distribution functions, we are able to draw unambiguous conclusions about various features of the model. In particular, we show that the gluon distribution functions in the absence of quantum corrections behave as ${1/x}_F$ to all orders in the coupling constant. Furthermore, our distribution functions exhibit saturation at small transverse momenta. The normalization of the distribution function we obtain is not arbitrary but specified in terms of the nucleon structure. We derive a sum rule for the integral of the gluon distribution function over transverse momenta, and show that the non-Abelian contributions serve only to modify the shape of the transverse momentum distribution. We obtain a relatively simple expression for the mean value of the transverse momentum-squared. The connection between the McLerran-Venugopalan model and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation is discussed quantitatively. Finally, we illustrate our results in terms of a simple nuclear model due to Kovchegov.