20 pagesInternational audienceWe provide a concise overview on transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q_T spectra of Higgs and vector bosons for low q_T, and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present an application of a new tool, TMDlib, to parton density fits and parameterizations

We present an extraction of unpolarized partonic transverse momentum distributions (TMDs) from a simultaneous fit of available data measured in semi-inclusive deep-inelastic scattering, Drell-Yan and Z boson production. To connect data at different scales, we use TMD evolution at next-to-leading logarithmic accuracy. The analysis is restricted to the low-transverse-momentum region, with no matching to fixed-order calculations at high transverse momentum. We introduce specific choices to deal with TMD evolution at low scales, of the order of 1 GeV 2 . This could be considered as a first attempt at a global fit of TMDs.

Recent experimental data on semi-inclusive deep-inelastic scattering from the Hermes collaboration allow us to discuss for the first time the flavor dependence of unpolarized transverse-momentum dependent distribution and fragmentation functions. We find convincing indications that favored fragmentation functions into pions have smaller average transverse momentum than unfavored functions and fragmentation functions into kaons. We find weaker indications of flavor dependence in the distribution functions.

In this paper we consider the parametrizations of gluon transverse momentum dependent (TMD) correlators in terms of TMD parton distribution functions (PDFs). These functions, referred to as TMDs, are defined as the Fourier transforms of hadronic matrix elements of nonlocal combinations of gluon fields. The nonlocality is bridged by gauge links, which have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. For gluons, the specific correlator with one future and one past pointing gauge link is, in the limit of small x, related to a correlator of a single Wilson loop. We present the parametrization of Wilson loop correlators in terms of Wilson loop TMDs and discuss the relation between these functions and the small-x 'dipole' gluon TMDs. This analysis shows which gluon TMDs are leading or suppressed in the smallx limit. We discuss hadronic targets that are unpolarized, vector polarized (relevant for spin-1/2 and spin-1 hadrons), and tensor polarized (relevant for spin-1 hadrons). The latter are of interest for studies with a future Electron-Ion Collider with polarized deuterons.