Transverse momentum dependent fragmentation functions and their role in spin-1/2 polarized hadron production

The study of transverse single-spin asymmetries (SSAs) is closely related to our understanding of strong interactions and to the exploration of the three-dimensional structure of hadrons in terms of quarks and gluons. The aim of this thesis is to study two processes that play a fundamental role in this context: the double and the single-inclusive hadron production in e+e- collisions. They allow for a clear and deep comprehension of the hadronization mechanisms and polarization effects, in terms of spin and transverse momentum dependent fragmentation functions (TMD-FFs). Within the helicity formalism it is possible to define, for a spin-1/2 hadron, eight leading-twist TMD-FFs with a straightforward partonic interpretation. These allow one to derive, and to present, the complete expressions for all azimuthal dependences and polarization observables in double-hadron production in unpolarized e+e- annihilation processes. These have been used, within a parton model picture and employing a Gaussian model for the transverse momentum dependence of TMD-FFs, to analyze the Belle data for the Λ transverse polarization, produced in e+e- → h1 h2 + X and e+e- → h1 + X. This allowed to obtain the first ever extraction of the Λ polarizing FF, giving the distribution of transversely polarized spin-1/2 hadrons in the fragmentation of unpolarized quarks. Due to the universality of the TMD-FFs, we used the polarizing FF to give estimates for the Λ transverse polarization in Semi-inclusive Deep Inelastic Scattering (SIDIS) processes, and for typical energies reachable at the future Electron-Ion Collider (EIC). Finally, we present a renewed analysis of Belle data by employing proper TMD factorization theorems and exploiting the Collins-Soper-Sterman (CSS) evolution equations both for double and single-inclusive hadron production case. A comparison between the old and new extraction is presented, along with the main differences between the functions extracted in the two frameworks.