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.
Highlights
In hadronic reactions that are governed by more than one hard momentum scale, the standard QCD framework of collinear factorization at leading twist becomes insufficient, and one needs to resort to more sophisticated factorization schemes
We show how these six gluon transverse-momentum dependent (TMD) emerge from the color glass condensate (CGC) formulation, and we determine their expressions in terms of Wilson line correlators
One of the many intricacies of TMDs is the fact that, in contrast to the usual collinear parton distribution functions (PDFs), their operator definition depends on the hard process under consideration; at first glance, universality is broken
Summary
In hadronic reactions that are governed by more than one hard momentum scale, the standard QCD framework of collinear factorization at leading twist becomes insufficient, and one needs to resort to more sophisticated factorization schemes. In the other regime: Qs ≪ kt ∼ Pt, kt, and Pt are of the same order and far above the saturation scale; high-energy factorization [34,35] is applicable In this case, only the linear small-x dynamics governed by the Balitsky-Fadin-Kuraev-Lipatov equation [36,37,38] is important, and the TMDs differ no more, implying that only one such distribution plays a role. We conclude and give an outlook for further work
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