Universality of TMD correlators

TL;DR

This paper demonstrates that despite process-dependent Wilson lines, a finite set of universal TMDs can be used across different high-energy scattering processes, ensuring a generalized form of universality.

Contribution

It shows that TMDs, though process-dependent in their gauge link structures, can be expressed as finite universal functions combined differently for each process.

Findings

Only a finite number of universal TMDs are needed.

Different processes correspond to different linear combinations of these TMDs.

For quarks, three Pretzelocity functions are identified; gluons have a richer structure.

Abstract

In a high-energy scattering process with hadrons in the initial state, color is involved. Transverse momentum dependent distribution functions (TMDs) describe the quark and gluon distributions in these hadrons in momentum space with the inclusion of transverse directions. Apart from the (anti)-quarks and gluons that are involved in the hard scattering process, additional gluon emissions by the hadrons have to be taken into account as well, giving rise to Wilson lines or gauge links. The TMDs involved are sensitive to the process under consideration and hence potentially nonuniversal due to these Wilson line interactions with the hard process; different hard processes give rise to different Wilson line structures. We will show that in practice only a finite number of universal TMDs have to be considered, which come in different linear combinations depending on the hard process under consideration, ensuring a generalized universality. For quarks this gives rise to three Pretzelocity functions, whereas for gluons a richer structure of functions arises.