Randomness in infinitesimal extent in the McLerran-Venugopalan model

TL;DR

This paper examines the discrepancy between analytical and numerical implementations of the McLerran-Venugopalan model, emphasizing the importance of longitudinal randomness in the color source distribution and its impact on simulation accuracy.

Contribution

It highlights the loss of longitudinal randomness in numerical simulations due to lack of path-ordering and discusses how this discrepancy can be mitigated through parameter adjustments.

Findings

Numerical simulations often omit longitudinal randomness due to lack of path-ordering.

Discrepancies between analytical and numerical results can be absorbed into model parameters.

Longitudinal randomness is crucial for accurate modeling of the MV model.

Abstract

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.