The McLerran-Venugopalan (MV) model is a Gaussian effective theory of color charge fluctuations at small-x in the limit of large valence charge density, i.e., a large nucleus made of uncorrelated color charges. In this work, we explore the effects of the first non-trivial (even C-parity) non-Gaussian correction on the color charge density to the MV model (“quartic” term) in SU(2) and SU(3) color group in the non-perturbative regime. We compare our (numerical) non-perturbative results to (analytical) perturbative ones in the limit of small or large non-Gaussian fluctuations. The couplings in the non-Gaussian action, $\overline{\mu }$ for the quadratic and ${\kappa }_4$ for the quartic term, need to be renormalized in order to match the two-point function in the Gaussian theory. We investigate three different choices for the renormalization of these couplings: i) ${\kappa }_4$ is proportional to a power of $\overline{\mu }$; ii) ${\kappa }_4$ is kept constant and iii) $\overline{\mu }$ is kept constant. We find that the first two choices lead to a scenario where the small-x action evolves towards a theory dominated by large non-Gaussian fluctuations, regardless of the system size, while the last one allows for controlling the deviations from the MV model.

McLerran-Venugopalan（MV）模型是在高价电荷密度（即，由不相关的色电荷构成的大核）的限制下，小x处的色电荷波动的高斯有效理论。在这项工作中，我们探索了SU（2）和SU（3）颜色中的MV模型（“四次”项）的第一个非平凡（甚至C奇偶校验）非高斯校正对色电荷密度的影响非扰动政体中的群体。在较小或较大的非高斯波动的范围内，我们将（数值）非摄动结果与（解析）摄动结果进行比较。非高斯作用下的耦合$\overline{\mu }$ 对于二次和 ${\kappa }_4$对于四次项，需要重新归一化以匹配高斯理论中的两点函数。我们研究了这些耦合的重新归一化的三种不同选择：${\kappa }_4$ 与...的幂成正比 $\overline{\mu }$; ii）${\kappa }_4$ 保持恒定并且iii） $\overline{\mu }$保持不变。我们发现，前两种选择会导致一个场景，其中小x动作会演变为以大的非高斯波动为主导的理论，而与系统大小无关，而最后一个则允许控制与MV模型的偏差。