论文标题
从非高斯小型$ x $ ACTION的平均颜色充电和多点相关器的非扰动重新归一化
Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-$x$ action
论文作者
论文摘要
McLerran-Venugopalan（MV）模型是高斯有效的有效的颜色电荷波动理论，该理论在较小的价电荷密度的极限下，{\ it I}。{\ it e}。在这项工作中，我们探讨了第一个非平地（甚至c- parity）非高斯校正对SU（2）和SU（2）和SU（3）颜色组中MV模型（“四重奏”术语）对颜色电荷密度（“四重奏”术语）的影响。我们将（数值）非扰动结果与（分析）扰动的结果进行比较，该结果在大小非高斯波动的极限下进行了比较。非高斯动作中的耦合，二次的$ \barμ$，四分之一术语的$κ_4$，需要重新归一化，以匹配高斯理论中的两点函数。我们研究了这些耦合重新归一化的三种不同选择：i）$κ_{4} $与$ \barμ$的功率成正比； ii）$κ_4$保持恒定，iii）$ \barμ$保持恒定。我们发现，前两种选择导致了一种场景，小$ x $动作朝着由大型非高斯波动主导的理论演变而成，而不论系统大小如何，而最后一个则允许控制与MV模型的偏差。
The McLerran-Venugopalan (MV) model is a Gaussian effective theory of color charge fluctuations at small-$x$ in the limit of large valence charge density, {\it i}.{\it 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, $\barμ$ for the quadratic and $κ_4$ 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) $κ_{4}$ is proportional to a power of $\barμ$; ii) $κ_4$ is kept constant and iii) $\barμ$ 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.
