The multidimensional distribution of quarks and its flavor dependence

One of the primary goals of hadronic physics is to describe the internal structure of the nucleon in terms of its constituents, quarks and gluons (collectively referred to as partons). Over the past forty years, substantial information has been gathered regarding the one-dimensional distribution of partons, encoded in the well-established collinear Parton Distribution Functions (PDFs). Recently, research has been extended to explore the three-dimensional momentum space distribution of partons, described by the so-called Transverse Momentum Dependent Distributions (TMDs). This thesis focuses on the phenomenology of TMDs, with a particular emphasis on their flavor and spin dependence. The thesis begins by reviewing the theoretical framework necessary for the extraction of TMDs in two types of scattering processes: the Drell–Yan process $ h_A + h_B\rightarrow \ell^+ + \ell^- + X$ and Semi-Inclusive Deep Inelastic Scattering $\ell + N \rightarrow \ell + h + X$, along with the relevant theoretical background on TMDs. It then presents the first global extraction of unpolarized quark TMDs in the proton, using a flavor-dependent approach at the highest level of accuracy, Next-to-Next-to-Next-to-Leading Logarithm (N$^3$LL). This result marks a milestone, as it demonstrates the distinct transverse momentum behavior of different quark flavors within the proton. Subsequently a similar study is conducted for unpolarized TMDs in the pion, achieving the highest available accuracy (N$^3$LL) and providing an excellent fit to the experimental data, which indicates a potential distinction in the transverse momentum behavior between sea and valence quarks in pions. The thesis also reports the first-ever extraction of helicity quark TMDs in the proton, performed at all orders of accuracy possible. This analysis reveals non-trivial differences compared to unpolarized distributions and exhibits partial agreement with lattice QCD calculations. Finally, the thesis addresses the evolution equations for twist-3 PDFs, which are a crucial component for studying polarized TMDs, and introduces a numerical framework developed to solve these evolution equations computationally.