Equality of Two Definitions for Transverse Momentum Dependent Parton Distribution Functions

TL;DR

This paper demonstrates that two recent approaches to TMD-factorization are fundamentally equivalent, differing only in their renormalization scheme definitions, clarifying the theoretical understanding of transverse momentum dependent parton distribution functions.

Contribution

It shows the equivalence of two prominent TMD-factorization formalisms, resolving apparent differences and unifying the theoretical framework.

Findings

The two approaches are mathematically equivalent.

Differences are due to renormalization scheme definitions.

Clarifies the theoretical basis of TMD PDFs.

Abstract

We compare recent, seemingly different, approaches to TMD-factorization (due to Echevarria, Idilbi, and Scimemi and to Collins), and show that they are the same, apart from an apparent difference in their definition of the \MSbar{} renormalization scheme.