On the linearly polarized gluon distributions in the color dipole model

TL;DR

This paper derives the role of linearly polarized gluon distributions in the color dipole model, showing their contribution to DIS and Drell-Yan dijet processes, and analyzes their small-x evolution at high energies.

Contribution

It provides the first full derivation of the cross sections involving linearly polarized gluons in the color dipole framework, confirming previous TMD results and exploring their small-x behavior.

Findings

Linearly polarized gluon distributions contribute to DIS dijet cross sections.

The same distributions appear in Drell-Yan dijet processes.

These distributions increase as x decreases at high energies.

Abstract

We show that the linearly polarized gluon distributions appear in the color dipole model as we derive the full cross sections of the DIS dijet production and the Drell-Yan dijet ($\gamma^*$ jet correlation) process. Together with the normal Weizs\"acker-Williams gluon distribution, the linearly polarized one will contribute to the DIS dijet production cross section as the coefficient of the $\cos(2 \Delta \phi) $ term in the correlation limit. We also derive the exact results for the cross section of the Drell-Yan dijet process, and find that the linearly polarized dipole gluon distribution which is identical to the normal dipole gluon distribution involves in the cross section. The results obtained in this paper agree with the previous transverse momentum dependent factorization study. We further derive the small-$x$ evolution of these linearly polarized gluon distributions and find that they rise as $x$ gets small at high energy.