Lattice computations of small-xparton 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 ${\mu }^2\sim A^{\frac{1}{3}}$ 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 ($g^2\mu L\ll 5$), where $L$ is the transverse size of the nucleus, the numerical results agree with the analytic lattice weak coupling results. For $g^2\mu L\gg 5$, no solutions exist at $O\left(a^4\right)$ 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.