Abstract
We discuss transverse momentum dependent (TMD) gluon distributions within high energy factorization at next-to-leading order in the strong coupling within the framework of Lipatov's high energy effective action. We provide a detailed discussion of both rapidity divergences related to the TMD definition and its soft factor on the one hand, and rapidity divergences due to high energy factorization on the other hand, and discuss common features and differences between Collins-Soper (CS) and Balitsky-Fadin-Kuarev-Lipatov (BFKL) evolution. While we confirm earlier results which state that the unpolarized and linearly polarized gluon TMD agree in the BFKL limit at leading order, we find that both distributions differ, once next-to-leading order corrections are being included. Unlike previous results, our framework allows us to recover the complete anomalous dimension associated with the Collins-Soper-Sterman (CSS) evolution of the TMD distribution, including also single-logarithmic terms in the CSS evolution. As an additional result, we provide a definition of ${k}_{T}$ factorization, i.e., matching of off shell coefficients to collinear factorization at next-to-leading order within high energy factorization and the effective action framework. We furthermore establish a link between the QCD operator definition of the TMD gluon distribution and a previously derived off shell TMD gluon-to-gluon splitting function, which is within the present framework obtained as the real one-loop correction.
Highlights
Transverse momentum dependent (TMD) parton distribution functions (PDFs) [1,2,3] are objects of increased interest, since they allow us to provide a more precise kinematic description of partonic scattering processes already at the leading order (LO) of perturbation theory
TMD PDFs provide an important advantage over a description based on collinear parton distributions
With Q, the scale of the hard reactions, TMD PDFs are at first defined for the hierarchy Q ≫ qT ≫ ΛQCD with qT, the transverse momentum of the parton, and ΛQCD, the QCD characteristic scale of a few hundred MeV
Summary
Transverse momentum dependent (TMD) parton distribution functions (PDFs) [1,2,3] are objects of increased interest, since they allow us to provide a more precise kinematic description of partonic scattering processes already at the leading order (LO) of perturbation theory. We will further extend this framework to include asymmetric factorization scale settings as required for a matching to collinear factorization, i.e., kT factorization [8] While this framework is currently limited to the dilute regime, i.e., two (reggeized) gluon exchange at the level of the cross section, it has the great advantage that it allows us to systematically study different choices of factorization parameter and schemes, which will be of particular use for the further exploration of the relation between BFKL and Collins-Soper (CS) [4,5] evolution initiated in [20]. VI, we summarize our result and provide an outlook on future research
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