Towards next-gen parton distribution and fragmentation functions

The interest into parton distribution functions (PDFs) and fragmentation functions (FFs) in current high energy physics research is twofold. On the one hand, they are fundamental objects to conduct precision phenomenology studies, e.g. at the Large Hadron Collider (LHC), to determine the Standard Model parameters and search for new physics. On the other hand, they are also a means to understand the inner structure and dynamics of hadrons, e.g. in regards to the proton spin decomposition at the future Electron Ion Collider (EIC). In this thesis, I present several advancements in the determination of PDFs and FFs that will allow for the release of their next versions by the NNPDF collaboration. These include some crucial components that will enter these new PDF and FF sets. Concerning PDFs, I consider three aspects. First, I study the impact of the commonly used K-factor approximation against the use of exact next-to-next-to-leading order (NNLO) computations. Second, I study the compatibility of new data with existing PDFs, taking into account all sources of experimental and theoretical uncertainties (including those coming from PDFs, missing higher orders, and ). Third, I study the impact of incremental inclusion of new data in PDF fits. Specifically, I focus on data sets that are relevant for the determination of the gluon PDF, namely single-inclusive jet and di-jet production data in proton-proton collisions and in deep-inelastic scattering, and top quark pair production data in proton-proton collisions. Concerning FFs, I extend the NNPDF computational framework in three respects, each one corresponding to three different pieces of software. First, I implement time-like evolution in EKO. Second, I extend PineAPPL to handle multiple convolutions of PDFs and FFs, including the corresponding factorization scales and the polarization of the initial and final states. Third, I develop a new software, called vhf, specifically devised to compute singleinclusive annihilation (SIA) and semi-inclusive deep-inelastic scattering (SIDIS) cross sections. All of these developments are crucial to prepare the release of next-gen PDF and FF sets that will allow us to take advantage of the forthcoming LHC and EIC physics programs as much as possible.