Universality of TMD distribution functions of definite rank

TL;DR

This paper demonstrates that by expanding TMD distribution functions into irreducible tensors, one can define a universal set of correlators of definite rank, clarifying their process dependence and universality.

Contribution

It introduces a method to define universal TMD correlators of definite rank by expanding into irreducible tensors, clarifying process dependence.

Findings

Universal TMD correlators of definite rank are defined.

Process dependence is traced back to gauge link paths.

Operator structure of TMD functions is clarified.

Abstract

Transverse momentum dependent (TMD) distribution and fragmentation functions are described as Fourier transforms of matrix elementscontaining nonlocal combinations of quark and gluon fields. These matrix elements also contain a gauge link operator with a process dependent path, of which the process dependence that can be traced back to the color flow in the process. Expanding into irreducible tensors built from the transverse momenta $p_\st$, we can define a universal set of TMD correlators of definite rank with a well-defined operator structure.