Transverse Momentum Dependent Parton Distribution Functions through SIDIS and Drell-Yan at COMPASS

The spin structure of the nucleon has been studied at the COMPASS experiment at CERN. The Semi-Inclusive Deep Inelastic Scattering (SIDIS) measurements are a powerful tool to access the Parton Distribution Functions (PDFs) and the Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). The COMPASS polarised target gives the opportunity to measure the azimuthal modulations depending on the spin orientation and the extraction of the transverse spin asymmetries, which are convolutions of TMD PDFs of the nucleon and Fragmentation Functions (FF). The analysis of these data is done in several kinematic bins, which provides a vast input for the theoreticians to extract the TMDs and the FFs and their kinematic dependence. The TMD PDFs are also accessible through the measurement of the Drell-Yan process, in this case the transverse spin asymmetries are convolutions of two TMD PDFs, one corresponding to the annihilating quark from the beam hadron and the other to the annihilating quark from the target hadron. In COMPASS a negative pion beam and the polarised protons from ammonia target allow the measurement of the polarised DY process. In 2010 the COMPASS data taking was dedicated to the measurement of the SIDIS process, the naturally polarised positive muons scattering off a transversely polarised proton target. The detection of the scattering muon and the final state hadrons give access to the angular modulations. The three target cells are transversely polarised, the two outer ones oppositely to the inner one, and this configuration changes every two weeks. The events are combined between the two sub-periods with opposite polarisation, which allows to better control possible systematic effects. The analysis of these data in bins of Q^2, x, pT h, z, y and W is presented. The 2015 COMPASS data taking was dedicated to the polarised DY measurement. As the COMPASS experiment was designed and developed for DIS and spectroscopy measurements, it had to suffer modifications for the DY measurement. The DY process has a very low cross-section, thus a high intensity beam is mandatory. A hadron absorber has been added just downstream of the target to stop the secondary hadrons allowing only the passage of the muon pairs. This protects the detectors from possible radiation damage while keeping the combinatorial background at a reasonable level. A short DY beam test run, using a hadron absorber prototype, was performed in 2009. The analysis of these data is presented in this thesis. The 2015 DY run was preceded by a pilot run in 2014, with the majority of the 2015 setup already set up, but still with no target polarisation. The analysis of these data is also presented in this thesis, as well as the analysis of some preliminary reconstructed 2015 data. COMPASS has the opportunity to access the TMD PDFs from two independent processes and selecting the same phase space coverage. These results are very promising for the TMD PDFs community, since the theoretical prediction that the Sivers TMD must change sign when accessed through the DY or the SIDIS processes should be verified with these data.