Universality of TMD distribution functions

TL;DR

This paper develops a framework for gluon transverse momentum dependent distribution functions (TMDs) with definite rank, clarifying their universal structure and process dependence through gauge links and gluonic pole factors.

Contribution

It introduces a finite set of universal gluon TMDs of definite rank, explicitly incorporating gauge link dependence and process dependence via gluonic pole factors.

Findings

Defines TMDs with definite rank based on azimuthal dependence.

Expresses process dependence through gauge links and gluonic pole factors.

Provides a universal set of gluon TMDs separating process dependence.

Abstract

We introduce transverse momentum dependent parton distribution functions (TMDs) for gluons with definite rank. The rank refers to the azimuthal dependence corresponding to the tensorial structure in transverse momenta multiplying universal functions only depending on $x$ and $p_T^2$. In this way only a finite number of functions of definite rank remains for a target with the maximal rank depending on its spin. Gauge links, required for color gauge invariance, enter in the explicit description of the matrix elements corresponding to these TMDs and account for their process dependence. In this way a general gauge link dependent function is expressed in the universal set, where all process (i.e. gauge link) dependence is isolated in gluonic pole factors multiplying the universal TMDs of definite rank.