Abstract
The Standard Model of particle physics has achieved great success in predicting the existence and property of SM particles in collider experiments. The discovery of the Higgs boson in 2012 marks that the final piece of lego bricks was found in SM. Despite such great success, many questions are unanswered in SM while Higgs serves as a portal to new physics. Therefore dedicated data analysis strategies of collider events is needed to decipher underlying physics. In this thesis, we focus on addressing the limitation of jets for collider events. We first introduce persistent homology to characterize topological structure of jets in relation to study jet substructures. These topological invariants measure multiplicity and connectivity of jet branches at a given scale threshold, while their persistence records the evolution of each topological feature as this threshold varies. With this knowledge, we are able to reconstruct the topological phylogenetic tree for each jet. We then introduce CMB-like observable scheme at future e+e− colliders in relation to addressing the information deformation and loss in jet clustering for precisely measuring hadronic events. In this scheme the event-level kinematics is encoded as Fox-Wolfram (FW) moments at leading order and multi-spectra of spherical harmonics at higher orders. We show that this difficulty can be well-addressed by synergizing the event-level information into the data analysis, with the techniques of deep neutral network.