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

International audienceWe 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 Weizsäcker-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