A high-resolution imaging of the collinear substructure of the proton

This thesis investigates some fundamental questions about the proton, the most abundant object we experience in our world. Protons are indeed complex systems made of tightly bound elementary particles: quarks and gluons. Their interaction is among the strongest forces in nature, making the proton a stable object of which we are all composed. Understanding how these smaller components interact and distribute their energy within the proton is crucial for advancing our knowledge of particle physics. In particular, the proton’s substructure becomes relevant during high-energy collisions, such as those at the Large Hadron Collider (LHC). This inner structure is described by Parton Distribution Functions (PDFs), which are the main tool adopted in our research. PDFs describe how the proton’s energy is probabilistically distributed among quarks and gluons. PDFs are thus essential for interpreting data from LHC experiments and making predictions about the behavior of particles under extreme conditions. Like any physical quantity, PDFs are subject to uncertainties, which can affect our ability to identify new particles or verify existing theories, such as the Standard Model of particle physics. The main goal of this thesis is thus to improve the current estimate of PDFs by adopting state-of-the-art of theoretical calculations combined with machine learning techniques and a vast amount of high energy data collected from various experiments. Our key findings are presented in Chapters 3 to 5 and include: Approximate N3LO QCD PDFs: we incorporate the current known next-to-next-to-next-to-leading-order (N3LO) QCD corrections relevant for PDF evolution and Deep Inelastic Scattering, within the NNPDF framework. This allows us to refine our knowledge of PDFs accounting for suppressed effects and theoretical errors, which are usually neglected but can be relevant in current and forthcoming LHC analyses. Intrinsic Charm: we provide a first evidence of a non-vanishing intrinsic charm contribution to the proton structure. This is a phenomenon where virtual charm quarks are present also in low energy protons and are not only generated by high energy splitting. This evidence is supported by a comparison with the most up-to-date LHCb data and could be further probed in the upcoming Electron-Ion Collider. Polarized PDFs and proton spin: we revise the determination of spin-dependent PDFs by including next-to-next-to-leading-order (NNLO) QCD corrections together with a large number of data from proton-proton scattering not included in previous analyses. Our study further suggests that quarks carry only a fraction of the total proton spin but remains uncertain regarding the gluon contribution. In this respect, our study will be beneficial for upcoming experiments form the EIC which are predicted to definitely shade light on proton spin puzzle. By addressing both the theoretical challenges and practical applications of PDFs, this research strengthens our knowledge of the proton behavior during high energy collisions. Hopefully, our contribution could pave the way for a more precise interpretation of complex experimental measurements, ultimately giving us a better understanding of the interaction between elementary particles.