  We assess the current phenomenological status of transverse momentum
dependent (TMD) parton distribution functions (PDFs) and fragmentation
functions (FFs) and study the effect of consistently including perturbative QCD
(pQCD) evolution. Our goal is to initiate the process of establishing reliable,
QCD-evolved parametrizations for the TMD PDFs and TMD FFs that can be used both
to test TMD-factorization and to search for evidence of the breakdown of
TMD-factorization that is expected for certain processes. In this article, we
focus on spin-independent processes because they provide the simplest
illustration of the basic steps and can already be used in direct tests of
TMD-factorization. Our calculations are based on the Collins-Soper-Sterman
(CSS) formalism, supplemented by recent theoretical developments which have
clarified the precise definitions of the TMD PDFs and TMD FFs needed for a
valid TMD-factorization theorem. Starting with these definitions, we
numerically generate evolved TMD PDFs and TMD FFs using as input existing
parametrizations for the collinear PDFs, collinear FFs, non-perturbative
factors in the CSS factorization formalism, and recent fixed-scale fits. We
confirm that evolution has important consequences, both qualitatively and
quantitatively, and argue that it should be included in future phenomenological
studies of TMD functions. Our analysis is also suggestive of extensions to
processes that involve spin-dependent functions such as the Boer-Mulders,
Sivers, or Collins functions, which we intend to pursue in future publications.
At our website we have made available the tables and calculations needed to
obtain the TMD parametrizations presented herein.
