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There is considerable controversy about the size and importance ofnonperturbative contributions to the evolution of transverse-momentum-dependent(TMD) parton distribution functions. Standard fits to relatively high-energyDrell-Yan data give evolution that when taken to lower Q is too rapid to beconsistent with recent data in semi-inclusive deeply inelastic scattering. Someauthors provide very different forms for TMD evolution, even arguing thatnonperturbative contributions at large transverse distance b_T are not neededor are irrelevant. Here, we systematically analyze the issues, bothperturbative and nonperturbative. We make a motivated proposal for theparameterization of the nonperturbative part of the TMD evolution kernel thatcould give consistency: with the variety of apparently conflicting data, withtheoretical perturbative calculations where they are applicable, and withgeneral theoretical nonperturbative constraints on correlation functions atlarge distances. We propose and use a scheme- and scale-independent functionA(b_T) that gives a tool to compare and diagnose different proposals for TMDevolution. We also advocate for phenomenological studies of A(b_T) as a probeof TMD evolution. The results are important generally for applications of TMDfactorization. In particular, they are important to making predictions forproposed polarized Drell-Yan experiments to measure the Sivers function.

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