Applying Field Theories: From Polarised Parton Distribution Functions to Neural Networks

Abstract

This thesis explores two areas of theoretical physics: contributing to the refinement of polarised Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs), and applying an Effective Field Theory (EFT) to neural networks (NNs). For the polarised PDFs, as a novel addition to the NNPDFpol2.0 fit, the inclusion of the Drell-Yan (DY) process up to next-to-next-to-leading-order (NNLO) significantly constrains and improves the polarised PDF fit with respect to the difference between anti- and quarks. For FFs, the inclusion of polarised and unpolarised Semi-Inclusive Deep Inelastic Scattering (SIDIS) structure function coefficients up to NNLO to a soon-to-be-released library (tentatively) named virtual hadron factory (vhf), will facilitate the calculation of FF observables and their fitting. When showcasing the abilities of vhf by comparing different FFs, we find surprising results, particularly regarding assumptions related to charge conjugation symmetry. These advancements aid in addressing questions like the protonspin puzzle. The second focus applies EFT to transformers, a NN architecture. This EFT approach has been successfully applied to multi-layer perceptrons (MLP). In this thesis we examine the multi-head selfattention (MHSA) block and derive a LO description of the MHSA at initialisation, i.e. without training. We use this result to compare theoretical predictions with numerical results. We find that variance predictions of the EFT align quite well with the numerical results. However, discrepancies between the measured and predicted distributions challenge the applicability of the EFT to MHSA NNs (at limited sizes). This thesis bridges particle physics and NNs in both directions, advancing the understanding of PDFs and working on the theoretical understanding of NNs.