Many apparently contradictory approaches to TMD factorization and its non-perturbative content exist. This talk evaluated the different methods and proposed tools for resolving the contradictions and experimentally adjudicating the results.
In the original Collins-Soper-Sterman (CSS) presentation of the results of transverse-momentum-dependent (TMD) factorization for the Drell-Yan process, results for perturbative coefficients can be obtained from calculations for collinear factorizatio
n. Here we show how to use these results, plus known results for the quark form factor, to obtain coefficients for TMD factorization in more recent formulations, e.g., that due to Collins, and apply them to known results at order $alpha_s^2$ and $alpha_s^3$. We also show that the non-perturbative functions as obtained from fits to data are equal in the two schemes. We compile the higher-order perturbative inputs needed for the updated CSS scheme by appealing to results obtained in a variety of different formalisms. In addition, we derive the connection between bo
We give an overview of the current status of perturbative QCD factorization theorems in processes that involve transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FF). We enumerate those cases where T
MD-factorization is well-established, and mention cases where it is likely to fail. We discuss recent progress in the implementation of specific TMD-factorization calculations, including the implementation of evolution. We also give examples of hard part calculations. We end by discussing future strategies for the implementation of TMD-factorization in phenomenological applications.
We summarize some of our recent work on non-perturbative transverse momentum dependent (TMD) evolution, emphasizing aspects that are necessary for dealing with moderately low scale processes like semi-inclusive deep inelastic scattering.
The theoretical description of the physics of multi-jets in hadronic collisions at high energies is based on merging methods, which combine short-timescale production of jets with long-timescale evolution of partonic showers. We point out potential i
mplications of the evolution of transverse momentum dependent (TMD) distributions on the structure of multi-jet states at high energies, and in particular on the theoretical systematics associated with multi-jet merging. To analyze this, we propose a new merging methodology, and illustrate its impact by comparing our theoretical results with experimental measurements for Z-boson + jets production at the Large Hadron Collider (LHC).