Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel

TL;DR

This paper investigates the nonperturbative aspects of TMD parton densities and proposes a new parameterization for the evolution kernel to reconcile conflicting experimental data and theoretical models.

Contribution

The authors introduce a scheme- and scale-independent function A(b_T) to compare TMD evolution proposals and suggest a new parameterization for the nonperturbative evolution kernel.

Findings

Proposed a unified framework for TMD evolution analysis.

Reconciled conflicting experimental and theoretical data.

Highlighted the importance of A(b_T) in phenomenological studies.

Abstract

There is considerable controversy about the size and importance of nonperturbative contributions to the evolution of transverse-momentum-dependent (TMD) parton distribution functions. Standard fits to relatively high-energy Drell-Yan data give evolution that when taken to lower Q is too rapid to be consistent with recent data in semi-inclusive deeply inelastic scattering. Some authors provide very different forms for TMD evolution, even arguing that nonperturbative contributions at large transverse distance b_T are not needed or are irrelevant. Here, we systematically analyze the issues, both perturbative and nonperturbative. We make a motivated proposal for the parameterization of the nonperturbative part of the TMD evolution kernel that could give consistency: with the variety of apparently conflicting data, with theoretical perturbative calculations where they are applicable, and with general theoretical nonperturbative constraints on correlation functions at large distances. We propose and use a scheme- and scale-independent function A(b_T) that gives a tool to compare and diagnose different proposals for TMD evolution. We also advocate for phenomenological studies of A(b_T) as a probe of TMD evolution. The results are important generally for applications of TMD factorization. In particular, they are important to making predictions for proposed polarized Drell-Yan experiments to measure the Sivers function.