Small-x TMD distributions: JIMWLK evolution and the Gaussian truncation

Abstract

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.