Generalized Universality of Definite Rank Gluon Transverse Momentum Dependent Correlators

TL;DR

This paper develops a universal framework for gluon transverse momentum dependent correlators by expanding them into definite rank TMDs, accounting for process dependence through gauge link factors, and providing a finite set of universal TMDs applicable across processes.

Contribution

Introduction of gluon TMDs of definite rank with process dependence isolated in gauge link factors, enabling a universal description of gluon correlators across different hard processes.

Findings

Finite set of universal TMDs derived for gluons.

Tabulated gluonic pole factors for various gauge links.

Leading tree level results expressed in terms of process-dependent gluon correlators.

Abstract

Transverse momentum dependent (TMD) parton correlators describing the partonic structure of hadrons contain gauge links, required by color gauge invariance. The required gauge links enter in the matrix elements that contain the parton fields and depend on the color flow in the hard process. The correlators are expanded in terms of transverse momentum dependent parton distribution functions, referred to as TMD PDFs, or in short TMDs. In this paper, we introduce gluon TMDs of definite rank, by making an expansion of the TMD gluon correlator with the help of irreducible tensors built from the transverse momenta. The process dependence is isolated in gauge link dependent gluonic pole factors multiplying the TMDs. It is important to account for the different possibilities in the color structure within the matrix elements, leading to multiple TMDs at a given rank. In this way we are able to write the leading tree level result for a hard process in terms of process dependent gluon correlators which are expressed in a finite set of universal TMDs. We tabulate the gluonic pole factors for various gauge links, among them those that are relevant for 2 to 2 processes.