Definition and Evolution of Transverse Momentum Dependent Parton Distribution Functions

I will consider the qT-dependent spectrum of Drell-Yan lepton pair production as a prototype of qT-dependent process. In this kind of processes the relevant modes, collinear and soft, can only be distinguished by their relative rapidities. This fact and a novel feature of the soft function involved will allow us to define the TMDPDF properly, solving a puzzle of 30 years. Then I will show some of its properties, as its universality, the possibility to recover the PDF by integrating over the transverse momentum and the its evolution. I will focus on this last one, since we have devised a new method to evolve TMD distributions, which is model-independent as compared to the standard CSS approach, and illustrate its effect by applying it to the unpolarized TMDPDF and the Sivers function.