LATTICE COMPUTATIONS OF SMALL-X PARTON DISTRIBUTIONS IN A MODEL OF PARTON DENSITIES IN VERY LARGE NUCLEI

Using weak coupling methods McLerran and Venugopalan expressed the par ton distributions in large nuclei as correlation functions of a two-di mensional Euclidean field theory. The theory has the dimensionful coup ling g(2) mu, where mu(2)-A(1/3) is the valence quark color charge squ ared per unit area. We use a lattice regularization to investigate the se correlation functions both analytically and numerically for the sim plified case of SU(2) gauge theory. In weak coupling (g(2) mu L much l ess than 5), where L is the transverse size of the nucleus, the numeri cal results agree with the analytic lattice weak coupling results. For g(2) mu L much less than 5, no solutions exist at O(a(4)) where a is the lattice spacing. This suggests an ill-defined infrared behavior fo r the two-dimensional theory. A recent proposal of Jalilian-Marian, Ko vner, McLerran, and Weigert for an analytic solution of the classical problem is discussed briefly.