Transformation of transverse momentum distributions from Parton Branching to Collins-Soper-Sterman framework

TL;DR

This paper presents the first transformation method converting TMD parton distributions from the Parton Branching framework to the Collins-Soper-Sterman formalism, facilitating comparisons and unified analyses of transverse momentum dependent distributions.

Contribution

It introduces a novel transformation technique from PB-TMDs to CSS formalism, enabling consistent evolution and comparison of TMDs across frameworks.

Findings

The transformation aligns PB-TMDs with CSS evolution in $b$-space.

Comparison shows good agreement with ART23 TMD distribution.

First demonstration of converting between these two TMD frameworks.

Abstract

Two main frameworks for defining transverse momentum dependent (TMD) parton densities are the Collins-Soper-Sterman (CSS) formalism, and the Parton Branching (PB) approach. While PB-TMDs have an explicit dependence on a single scale which is used to evolve PB-TMDs in momentum space, TMDs defined in CSS formalism present a double-scale evolution in renormalization and rapidity scales, via a pair of coupled evolution equations. In this letter I leverage the Collins-Soper kernel determined from simulated Drell Yan transverse momentum spectra using PB-TMDs, and provide, for the first time, the transformation of TMD parton distributions from the PB framework to the CSS formalism. The evolved PB-TMDs in $b$-space are compared to the recently released, unpolarized TMD distribution ART23.