  We study discrepancy between the analytical definition and the numerical
implementation of the McLerran-Venugopalan (MV) model. The infinitesimal extent
of a fast-moving nucleus should retain longitudinal randomness in the color
source distribution even when the longitudinal extent approximates zero due to
the Lorentz contraction, which is properly taken into account in the analytical
treatment. We point out that the longitudinal randomness is lost in numerical
simulations because of lack of the path-ordering of the Wilson line along the
longitudinal direction. We quantitatively investigate how much the results with
and without longitudinal randomness differ from each other. We finally mention
that the discrepancy could be absorbed in a choice of the model parameter in
the physical unit, and nevertheless, it is important for a full theory
approach.
