Transverse-momentum-dependent gluon distributions from JIMWLK evolution

TL;DR

This paper investigates the operator definitions of TMD gluon distributions at small x, demonstrating their relation to CGC correlators, and explores their behavior through numerical solutions of the JIMWLK equation, revealing saturation effects and geometric scaling.

Contribution

It establishes the equivalence of TMD and CGC approaches for di-jet production at small x and expresses TMD gluon distributions in terms of Wilson line correlators, solved via JIMWLK evolution.

Findings

TMD and CGC descriptions coincide for di-jet cross sections.

At large transverse momentum, process dependence diminishes.

Saturation effects significantly influence TMD distributions at small transverse momentum.

Abstract

Transverse-momentum-dependent (TMD) gluon distributions have different operator definitions, depending on the process under consideration. We study that aspect of TMD factorization in the small-x limit, for the various unpolarized TMD gluon distributions encountered in the literature. To do this, we consider di-jet production in hadronic collisions, since this process allows to be exhaustive with respect to the possible operator definitions, and is suitable to be investigated at small x. Indeed, for forward and nearly back-to-back jets, one can apply both the TMD factorization and Color Glass Condensate (CGC) approaches to compute the di-jet cross-section, and compare the results. Doing so, we show that both descriptions coincide, and we show how to express the various TMD gluon distributions in terms of CGC correlators of Wilson lines, while keeping Nc finite. We then proceed to evaluate them by solving the JIMWLK equation numerically. We obtain that at large transverse momentum, the process dependence essentially disappears, while at small transverse momentum, non-linear saturation effects impact the various TMD gluon distributions in very different ways. We notice the presence of a geometric scaling regime for all the TMD gluon distributions studied: the "dipole" one, the Weizs\"acker-Williams one, and the six others involved in forward di-jet production.