One of the main goals of nuclear physics is to understand the internal structure of hadrons. For many decades, it has been known that hadrons are complicated objects composed of quarks and gluons, collectively called partons, that are held together by the strong nuclear force and whose interactions are described by Quantum Chromodynamics (QCD). The longitudinal motion of partons inside high-energy hadrons, encoded by collinear parton distribution functions (PDFs) and fragmentation functions (FFs), is fairly well known. However, there are still outstanding issues in our understanding of the “intrinsic” transverse motion of partons, encoded by transverse momentum dependent (TMD) PDFs and FFs (or TMDs for short). TMDs are of particular importance because they allow one to perform a 3-dimensional momentum-space tomography of hadrons.

The last 25 years, driven by intense theoretical, phenomenological, and experimental work, have seen great progress and success in attempts to model and extract TMDs. However, in recent years, motivated by the various reactions and energy ranges measured by ongoing and future experiments, the need has arisen to more rigorously study TMDs within QCD. Such issues currently being addressed include factorization, evolution, and operator definitions of TMDs and how they influence phenomenological and lattice QCD studies. These problems are especially important in order to achieve a global fit of TMDs using experimental data over all energy ranges, and some progress has been made towards this goal. Such a feat would be a true milestone in the field.

Therefore, the aim of this special issue is to further the effort of understanding TMDs, in particular, given the challenges that arise when one attempts to describe experimental data across a wide energy range and for different observables. We especially welcome papers related to TMD factorization, evolution, and global analyses. Such studies are required in order to meet the demands of ongoing and future measurements. We also hope to attract review articles that synthesize and elucidate the state of the art theoretical, phenomenological, and lattice QCD frameworks of TMDs and TMD observables.

Potential topics include but are not limited to the following:

• Analyses of the kinematical limits of TMD factorization, including how applying such criteria to experimental data impacts phenomenological extractions of TMDs
• Generalizations of TMD factorization to include central and target fragmentation regions
• Studies on the proper implementation of TMD evolution, including matching of the low to high transverse momentum regions
• Connections of TMDs and TMD observables to collinear functions and reactions, especially those involving polarization
• Progress on global analyses of TMDs in both unpolarized and polarized reactions
• Lattice QCD calculations of TMDs and related theoretical issues
• Studies of high transverse momentum LHC data within soft collinear effective theory (SCET) and its connections to low energy TMD physics