Definition and Evolution of Transverse Momentum Distributions

TL;DR

This paper clarifies the definition and evolution of unpolarized transverse-momentum-dependent parton distribution functions on-the-light-cone, providing a regulator-independent approach and an alternative resummation method to Collins-Soper evolution.

Contribution

It introduces a consistent, regulator-agnostic definition of TMD PDFs on-the-light-cone and discusses their evolution, offering an alternative to the Collins-Soper equation.

Findings

Compatible with generic factorization theorems including soft functions

Provides a regulator-independent framework for TMD PDFs

Proposes an alternative resummation method for large logarithms

Abstract

We consider the definition of unpolarized transverse-momentum-dependent parton distribution functions while staying on-the-light-cone. By imposing a requirement of identical treatment of two collinear sectors, our approach, compatible with a generic factorization theorem with the soft function included, is valid for all non-ultra-violet regulators (as it should), an issue which causes much confusion in the whole field. We explain how large logarithms can be resummed in a way which can be considered as an alternative to the use of Collins-Soper evolution equation. The evolution properties are also discussed and the gauge-invariance, in both classes of gauges, regular and singular, is emphasized.