Exploring the Boundary of Perturbative Quantum Chromodynamics - Resummation of Non-Global Logarithms and Soft Superstructure of Jets

This thesis arises in the context of the precision era of Higgs physics from the recent high accuracy data at the Large Hadron Collider (LHC). With the data of an unprecedented level of precision, the theoretical error is now lagging behind. In addition, the accurate theoretical prediction of Standard Model (SM) processes can also lead a path to the discovery of new physics, which thus far has proven so elusive. Indeed, careful analyses of the QCD radiation pattern are crucial to distinguish Standard Model physics from possible new physics signals. In this context, studies of the internal structure of jets, i.e. jet substructure, have proved a valuable addition to LHC phenomenology. Furthermore, in order to obtain precise predictions, the jet substructure calculations usually involve resummation of the perturbative series, where large logarithms arise from the multi-scale hierarchy. The aim of this thesis is to explore novel approaches to probe colour flow and soft substructure of jets, which is beyond the traditional boundaries of Perturbative Quantum Chromodynamics (pQCD), namely globalness and infrared & collinear (IRC) safety. In this thesis, the impact of non-global logarithms (NGLs) and IRC unsafe observables are studied in detail. In particular, for the non-global case, a novel approach to solving differential equations using artificial neural networks is presented, and we compare the results with the other methods in the literature. In the context of IRC unsafety, the first-principle calculation in resummed perturbation theory for the jet pull angle is performed, along with the resummation formalism is reviewed and improved. As phenomenological applications, each ingredient is studied independently. Moreover, because of the large theoretical uncertainty of IRC unsafe observable, the result is improved by introducing IRC safety projection for the jet pull vector. Additionally, with the purpose of assessing sub-leading colour correlations, the novel azimuthal asymmetry distribution is introduced and studied in some detail.