Universality of Quark and Gluon TMD Correlators

TL;DR

This paper explores the universal structure of quark and gluon TMD correlators in QCD, establishing their relation to matrix elements and demonstrating how process-dependent TMDs can be expressed through universal functions.

Contribution

It introduces a finite set of universal TMDs of definite rank and shows how process dependence can be captured by their combinations.

Findings

Universal TMDs of definite rank are identified.

Process-dependent TMDs can be expressed as combinations of universal TMDs.

The link between TMDs and quark/gluon matrix elements is clarified.

Abstract

Transverse Momentum Dependent (TMD) parton distribution functions (PDFs), in short referred to as TMDs, also take into account the transverse momentum (pT) of the partons. Just as the pT-integrated analogues we want to link them to quark and gluon matrix elements using Operator Product Expansion methods in QCD, involving operators of definite twist. The TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Using the expression for TMDs involving nonlocal matrix elements of quark and gluon fields there is a gauge link dependence, which also introduces an inherent process dependence. Using transverse moments, which are specific pT-weightings, we can establish the link with quark and gluon fields including the higher twist ones. We introduce (a finite number of) universal TMDs of definite rank and show how the process dependent TMDs can be written as combinations of these universal functions.