Linearly polarized small-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math> gluons in forward heavy-quark pair production

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\"acker-Williams gluon distribution, the adjoint-dipole gluon distribution, and an additional one. When quark masses are kept nonzero, 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 toward smaller values of $x$ using a numerical implementation of Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution.