Photoproduction of three jets in the CGC: gluon TMDs and dilute limit

TL;DR

This paper analyzes three-jet photoproduction in the CGC framework, deriving simplified expressions in specific kinematic limits and exploring the evolution of gluon TMDs through numerical simulations.

Contribution

It provides a detailed derivation of the cross section in the correlation and dilute limits within the CGC, linking to gluon TMDs and their evolution.

Findings

Cross section simplifies in the correlation limit, revealing sensitivity to gluon TMDs.

In the dilute limit, the cross section reduces to a linear regime involving a single gluon distribution.

Numerical simulations show the rapidity dependence of the cross section in the correlation limit.

Abstract

We study the process $\gamma A \to q \bar{q} g+X$ in the Color Glass Condensate (CGC) effective theory. After obtaining the cross section, we consider two kinematic limits which are encompassed in our result. In the so-called correlation limit, the vector sum of the transverse momenta of the three outgoing particles is small with respect to the individual transverse momenta; the cross section then simplifies considerably and can be written in a factorized form, sensitive to both the unpolarized and linearly-polarized Weizs\"acker-Williams transverse momentum dependent gluon distribution function (gluon TMD). The second limit of the CGC cross section that we consider is the dilute limit, which we obtain after performing a weak-field expansion; we recover a typical linear-regime expression, involving a single unintegrated gluon distribution function. Using numerical simulations of the small-$x$ QCD evolution of the TMDs, we investigate the rapidity dependence of the cross section in the correlation limit.