The thesis investigates the role of quantum chromodynamics (QCD) in scattering cross sections at particle accelerators, in cases which include information on the transverse momentum of outgoing particles, with respect to the beam axis. More specifically, I focus on two processes: semi-inclusive Deep Inelastic Scattering (SIDIS) and Drell-Yan. These are key processes for the extraction of the Transverse Momentum Distribution (TMD) of quarks.
In Chapt. 2 I summarise the basic aspects of these cross sections and their description in QCD, while in Chapt. 3 I introduce the theory of TMDs, delineating the theoretical framework for Chapt. 4, where I present separate phenomenological studies for SIDIS and Drell-Yan, concentrated on the low transverse-momentum part of the measured spectrum. I discuss for the first time the description of SIDIS data beyond leading order in QCD, which reveals important discrepancies. I present a theoretical argument for the explanation of these discrepancies, related to the separation of TMD and collinear factorisation regimes in transverse momentum observables, and supported by a numerical study. For Drell-Yan, I present a TMD fit of the newest data at the highest available perturbative accuracy. The possible role of non-perturbative transverse momentum at LHC is investigated, by analysing high precision measurements from ATLAS, CMS and LHCb, and a non-perturbative function such to describe, simultaneously, collider and fixed-target data from different experiments is provided.
In Chapt. 5 I discuss Drell-Yan in the regime of fixed-target (and low-energy collider) experiments. While different TMD studies in the literature have considered the low transverse momentum region, where TMD factorisation is well established, there have been no studies to date of the high end of the transverse momentum spectrum, where a transition to collinear factorisation is expected. Similar to what was recently observed for SIDIS, I show that predictions from collinear factorisation largely underestimate data. In addiction, I explore possible explanations of the discrepancy, of both perturbative and non-perturbative nature.
In Chapt. 6 I present the calculation in perturbative QCD of a single-spin asymmetry in SIDIS, more precisely for the case of a nucleon target polarised along the direction of the exchanged vector boson. This observable has been previously analysed in the low transverse momentum framework of TMDs, but an analysis in the framework of collinear factorisation was lacking. After calculating at 1-loop level the relevant Feynman diagrams, I show numerical results for modulations in the angular distribution of the final hadron, comparing to data from the HERMES experiment, and making predictions for a future Electron-Ion Collider
