Linearly-polarized small-x gluons in forward heavy-quark pair production

TL;DR

This paper investigates the role of linearly-polarized small-x gluons in forward heavy-quark pair production using the CGC framework, revealing new gluon TMDs and their evolution with x.

Contribution

It introduces six gluon TMDs related to linearly-polarized gluons in unpolarized small-x targets and derives their expressions from the CGC framework.

Findings

Derived analytical expressions for gluon TMDs in the MV model

Identified three new gluon TMDs associated with quark mass effects

Numerically evolved gluon TMDs using JIMWLK equations

Abstract

We use the Color Glass Condensate (CGC) framework to study the production of forward heavy quark-antiquark pairs in unpolarized proton-nucleus or proton-proton collisions in the small-x regime. In the limit of nearly back-to-back jets, the CGC result simplifies into the transverse-momentum dependent (TMD) factorization approach. For massless quarks, the TMD factorization formula involves three unpolarized gluon TMDs: the Weizs\"{a}cker-Williams gluon distribution, the adjoint-dipole gluon distribution, and an additional one. When quark masses are kept non-zero, three new gluon TMDs appear -- each partnered to one of the aforementioned distributions -- which describe the distribution of linearly-polarized gluons in the unpolarized small-x target. We show how these six gluon TMDs emerge from the CGC formulation and we determine their expressions in terms of Wilson line correlators. We calculate them analytically in the McLerran-Venugopalan model, and further evolve them towards smaller values of x using a numerical implementation of JIMWLK evolution.