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 parton distributions in large nuclei as correlation functions of a two-dimensional Euclidean field theory. The theory has the dimensionful coupling g(2) mu, where mu(2)-A(1/3) is the valence quark color charge squared per unit area. We use a lattice regularization to investigate these correlation functions both analytically and numerically for the simplified case of SU(2) gauge theory. In weak coupling (g(2) mu L much less than 5), where L is the transverse size of the nucleus, the numerical 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 for the two-dimensional theory. A recent proposal of Jalilian-Marian, Kovner, McLerran, and Weigert for an analytic solution of the classical problem is discussed briefly.