Phenomenological analysis of unpolarized partonic Transverse Momentum Distributions and Sivers Function

Parton distribution functions describe the internal structure of the nucleon in terms of its elementary constituents (quarks and gluons). They cannot be easily computed from first principles, because they require the ability to carry out Quantum Chromodynamics (QCD) calculations in its nonperturbative regime. Many experimental observables in hard scattering experiments involving hadrons are related to parton distribution functions (PDFs) and fragmentation functions (FFs), in a way that is specified by factorization theorems. Collinear PDFs describe the distribution of partons integrated over all components of partonic momentum except the one collinear to the parent hadron, while TMD PDFs include also the dependence on the transverse momentum k⊥. They can be interpreted as three-dimensional generalizations of collinear PDFs. Availability of measurements of different processes in different experiments makes it possible to extract PDFs and FFs through so-called global fits. In this thesis we present a first attempt at the extraction of unpolarized TMDs parton distribution and fragmentation functions from a wide set of data, covering a large kinematic region and including measurements taken from semi-inclusive deep-inelastic scattering, Drell-Yan and Z boson production. In the second part of the thesis we analyze a polarized TMDs, the so-called Sivers distribution function, which describes the density of unpolarized partons inside a polarized nucleons. The extraction of the Sivers function is directly connected with the first part of our study, as it requires the knowledge of the unpolarized TMDs. The work is organized in the following way. In Ch. 2, the theory for transverse momentum dependent parton distribution and fragmentation function is shown, focusing on the unpolarized and on the Sivers distribution. We discuss the relation between the experimental observables and the TMDs and how the latter evolve with respect to their characteristic scales. In Ch. 3 the general formalism for TMDs in SIDIS, DY processes, and Z production is briefly outlined, including a description of the assumptions and approximations in the phenomenological implementation of TMD evolution equations. We present the data included in the global fit and the criteria for selecting the data analyzed. In the last part we show the results of our analysis and discuss their stability in relation to different choices for the parametrization of our functional form. In Ch. 4 we discuss our extraction of the Sivers function from SIDIS data on the Sivers asymmetry, coming from Hermes Compass and JLab experiments. In the first part the parametrization and choices for the parametrization and evolution of the Sivers are discussed. Subsequently, the criteria for selecting the data analysed in the fit are summarized and commented. Finally, the results of our global fit are presented and the agreement between our theoretical prediction and the experimental measurements for the Sivers asymmetry is discussed. In the final section, we summarize the results and present an outlook for future improvements