Transverse Momentum Dependent Quasi-Parton-Distributions

TL;DR

This paper develops a framework for calculating transverse momentum dependent parton distributions (TMDs) using quasi-distributions, resolving longstanding singularities and establishing a clear connection to standard TMDs.

Contribution

It introduces a method to handle pinch pole singularities in quasi-TMDs and demonstrates the energy evolution depends solely on hadron momentum, enabling precise matching.

Findings

Resolved pinch pole singularity with finite gauge link length.

Quasi-TMDs are free of linear divergence after soft factor subtraction.

Established a direct matching between quasi-TMDs and standard TMDs.

Abstract

We investigate the transverse momentum dependent parton distributions (TMDs) in the quasi-parton-distribution framework. The long standing hurdle of the so-called pinch pole singularity from the space-like gauge links in the TMD definitions can be resolved by the finite length of the gauge link along the hadron moving direction. In addition, with the soft factor subtraction, the quasi-TMD is free of linear divergence. We further demonstrate that the energy evolution equation of the quasi-TMD a.k.a. the Collins-Soper evolution, only depends on the hadron momentum. This leads to a clear matching between the quasi-TMD and the standard TMDs.