小-x TMD分布：JIMWLK演化与高斯截断
Small-x TMD distributions: JIMWLK evolution and the Gaussian truncation
- Institute of Theoretical Physics, Jagiellonian University（雅盖隆大学理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究扩展小-x TMD分布的系统研究，采用JIMWLK演化方程结合McLerran-Venugopalan模型初始条件，对比高斯截断结果以分析其适用性，为理解大-$N_c$极限与演化方程的相互作用提供基础。
AI中文摘要：
我们扩展了文献[Cougoulic:2026drr]中启动的小-x横向动量依赖（TMD）分布的系统研究，纳入了能量演化。我们采用JIMWLK演化方程研究夸克-胶子领域的3种分布（$\boldsymbol{\textit{F}}_{qg}$）和胶子-胶子领域的7种分布（$\boldsymbol{\textit{F}}_{gg}$）的能量依赖关系，初始条件由McLerran-Venugopalan模型提供。我们在位置空间且固定$N_c=3$的条件下研究这些TMD分布，随后将结果与Balitsky层次的高斯截断进行比较。尽管高斯截断在初始条件下的TMD分布中表现良好，但我们发现部分情况下其能给出合理的描述，不过在多数情况下无法完全重现数值数据。利用固定表示构建块$\boldsymbol{\textit{\textOmega}}_{ag}^\boldsymbol{\textit{\textomega}}$，我们能够部分解释上述结果。本研究是理解大-$N_c$极限与高斯截断、以及BK/JIMWLK演化方程之间相互作用的下一步，相关研究针对具有唯象意义的可观测量。
英文摘要：
We extend the systematic study of small-$x$ Transverse Momentum Dependent (TMD) distributions, initiated in [Cougoulic:2026drr], by including the energy evolution. We use the JIMWLK evolution equation to study the energy dependence of three distributions in the quark-gluon sector, $\mathcal{F}_{qg}$, and seven distributions in the gluon-gluon sector, $\mathcal{F}_{gg}$. The initial conditions are provided by the McLerran-Venugopalan model. We study these TMD distributions in position space and with $N_c = 3$ fixed. We then compare these results to the Gaussian truncation of the Balitsky hierarchy. Although the Gaussian truncation worked very well for the TMD distributions at the initial condition, now we identify some cases where the Gaussian truncation provides a reasonably good description, but in the majority of cases it fails to fully reproduce numerical data. Using the fixed representation building blocks, $Ω_{ag}^ω$, we are able to partially explain the outcomes. This work constitutes the next step with the goal of understanding the interplays between the large-$N_c$ limit and Gaussian truncation as well as the BK/JIMWLK evolution equations for phenomenologically relevant observables.
