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 derive the scattering amplitude N (r) for a QCD dipole on a dense target in the semi-classical approximation. We include the first subleading correction in the target thickness arising from ∼ ρ 4 operators in the effective action for the large-x valence charges. Our result for N (r) can be matched to a phenomenological proton fit by Albacete et al. over a broad range of dipole sizes r and provides a definite prediction for the A-dependence for heavy-ion targets. We find a suppression of N (r) for finite A for dipole sizes a few times smaller than the inverse saturation scale, corresponding to a suppression of the classical bremsstrahlung tail.

We study forward dijet production in dilute-dense hadronic collisions. By considering the appropriate limits, we show that both the transverse-momentum-dependent (TMD) and the high-energy factorization formulas can be derived from the Color Glass Condensate framework. Respectively, this happens when the transverse momentum imbalance of the dijet system, k t , is of the order of either the saturation scale, or the hard jet momenta, the former being always much smaller than the latter. We propose a new formula for forward dijets that encompasses both situations and is therefore applicable regardless of the magnitude of k t . That involves generalizing the TMD factorization formula for dijet production to the case where the incoming small-x gluon is off-shell. The derivation is performed in two independent ways, using either Feynman diagram techniques, or color-ordered amplitudes.