SUBSTRUCTURE AT COLLIDERS

In this PhD thesis we investigate several aspects of parton distribution functions (PDFs) and jets as applicable to the physics underpinning the Large Hadron Collider (LHC) as well as future colliders. We first discuss jet observables at the LHC, focusing on the single-jet inclusive cross section. We introduce possible alternative definitions, which weigh the individual contributions coming from each jet in the event and are thus unitary by construction. We also clarify the origin of some problematic aspects of the standard definition. Secondly, within the hadronic PDF fitting framework of the NNPDF collaboration, we investigate the inclusion of single-jet inclusive and dijet measurements into a global PDF fit, using QCD next-to-next-to-leading order predictions for jet processes. We field-test which observables lead to better perturbative stability, better PDF compatibility with other data, better fit quality, and more stringent constraints on the PDFs. Thirdly, we focus on an analytical understanding of machine learning techniques used for quark versus gluon discrimination, a hot topic in jet substructure studies. We construct a new version of the widely used N -subjettiness variable, which features a simpler theoretical behaviour than the original one, while maintaining, if not exceeding, the discriminating power. We input these new observables to the simplest possible neural network, with only one neuron, and we study analytically the network behaviour at leading logarithmic accuracy. We also compare our analytic findings to a more realistic neural network trained with Monte Carlo pseudo-data. Fourthly, we compute the unpolarised electron, positron, and photon PDFs at next- to-leading logarithmic accuracy in QED, which are crucial for high-precision predictions needed for future e + e 12 colliders. We present both numerical and analytical results. The analytical predictions, defined by means of a specific additive formula, provide a large-z analytical solution that includes all orders in the QED coupling constant \u3b1, with a small- and intermediate-z solution that includes terms up to O(\u3b1 3 ). The content of this thesis is based on arXiv:1906.11850, arXiv:1911.12040, arXiv:2005.11327, and arXiv:2007.04319