UCLA

Scientific investigations show that nucleons are the building blocks of atomic nuclei, which constitute nearly all the mass of visible matter in the universe. Unlike electrons, which are fundamental particles, nucleons have an internal structure composed of quarks and gluons. While much has been learned about nucleon structure, many details remain to be understood. There is broad consensus that understanding the fundamental properties of matter requires understanding the nucleon’s internal structure in terms of its constituents. In Quantum Chromodynamics (QCD), the theory of strong interactions, the nucleon is described as a relativistic bound state of quarks and gluons, interacting strongly through the exchange of gluons. These partons are permanently confined within hadrons due to the property of color confinement, which prevents their direct isolation but still allows their dynamics to be studied through high-energy scattering experiments. However, at sufficiently small distance scales, QCD exhibits the property of asymptotic freedom \cite{PhysRevLett.30.1343,PhysRevLett.30.1346}, where the strong coupling becomes significantly weaker. This allows QCD factorization to be used in perturbative calculations, enabling the study of nucleon structure \cite{Accardi2016}.

One of the key challenges in QCD is the full understanding the spin structure of the nucleon in terms of its constituents. A nucleon is known to be a fermion with a spin of $1/2$, and while we understand how to distribute the nucleon's spin between the orbital angular momentum and the spins of quarks and gluons, the exact numerical values of each contribution remain uncertain, especially when it comes to the orbital angular momentum. In this context, three-dimensional distributions of quarks and gluons in momentum space are crucial tools, as they capture all possible spin-orbit and spin-spin interactions between the proton and its constituents. A thorough understanding of these distributions can offer valuable insights into the roles of quarks and gluons in determining the nucleon's spin. The early studies focused on processes involving collinear functions to understand the nucleon spin structure. While these functions offer valuable insight into the internal composition of nucleons, it was quickly realized that they were not sufficient since they only provide a one-dimensional and, therefore, partial perspective on the complex structure of the nucleon.

The search for alternative methods beyond collinear factorization to fully describe the nucleon internal structure has led to the development of a robust transverse momentum dependent (TMD) factorization framework. This framework allows to acquire the three-dimensional (3D) dynamics of quarks and gluons within a colliding nucleon.These new and precise data provide the means to determine transverse momentum dependent parton distributions, often referred to as TMDs. In this dissertation, we develop TMD formalisms to perform simultaneous global analysis of Sivers asymmetries and Collins asymmetries. The TMD Sivers formalism allows us to extract simultaneously the Sivers function from semi-inclusive deep inelastic scattering, Drell-Yan production, and jet production in proton-proton collisions. The TMD Collins formalism allows us to extract simultaneously the Collins fragmentation function from semi-inclusive deep inelastic scattering, $e^{+}e^{-}$ annihilation, and hadron production inside jets in proton-proton collisions.