Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions

TL;DR

This paper develops a scheme-independent definition of transverse momentum dependent parton distribution functions by analyzing soft and collinear factorization in Drell-Yan processes, comparing with Collins' approach.

Contribution

It introduces a method to define TMD PDFs that is independent of regularization schemes by splitting soft functions into boost-invariant parts and combining them with collinear contributions.

Findings

Well-defined TMD distributions emerge from the proposed soft and collinear splitting.

Comparison with Collins' definition highlights differences and similarities.

The approach ensures scheme independence in TMD PDF definitions.

Abstract

In this work we consider how a parton distribution function, with an explicit transverse momentum dependence can be properly defined in a regularization-scheme independent manner. We argue that by considering a factorized form of the transverse momentum dependent spectrum for the production of a heavy lepton pair in Drell-Yan reaction, one should first split the relevant soft function into two boost invariant contributions. When those soft contributions are added to the pure collinear contributions, well-defined hadronic matrix elements emerge, i.e., the transverse momentum dependent distributions. We also perform a comparison with Collins' definition.