Novel Approaches to the Fast Simulation of the ATLAS Calorimeter and Performance Studies of Track-Assisted Reclustered Jets for Searches for Resonant $X \rightarrow S H \rightarrow b \bar{b} W W^*$ Production with the ATLAS Detector

One of the most essential tools for all measurements and searches at the LHC experiments is the Monte Carlo (MC) simulation of proton-proton collisions. The generation of MC events, in particular the simulation of the detector response, is a very CPU-intensive process. Presently, the limited availability of MC statistics ranks among the most significant sources of systematic uncertainties in numerous ATLAS physics analyses. The primary bottleneck of the detector simulation is the detailed simulation of electromagnetic and hadronic showers in the ATLAS calorimeter system using Geant4. To increase the number of available MC events, ATLAS has successfully employed a fast calorimeter simulation FastCaloSim during Run 1 and Run 2 of the LHC that reduces the simulation time by almost an order of magnitude. FastCaloSim parametrizes the energy response of particles in the calorimeter cells, taking into account the lateral shower profile and the correlation between the energy depositions in the various layers of the calorimeter. $\\~\\$ This thesis presents a significantly improved version of FastCaloSim, which makes use of machine learning techniques such as principal component analysis. The new fast calorimeter package is named FastCaloSimV2 and is embedded in the state-of-the-art fast simulation software suite AtIFast3, which was used to simulate about 7 billion events during the Run 2 MC reprocessing campaign in ATLAS. New developments for fast calorimeter simulation in ATLAS for Run 3 and the high-luminosity era of the LHC are also discussed. Among other aspects, new models for a precise data-driven fast simulation of electromagnetic showers are presented, as well as first efforts towards a major structural refactoring of the ATLAS simulation infrastructure, which is anticipated to greatly streamline the overall ATLAS simulation workflow in the coming years. $\\~\\$ The second part of this work presents performance studies of Track-Assisted Reclustered (TAR) jets employed in searches for resonant Higgs boson pair production with the ATLAS detector. Many beyond the Standard Model extensions predict an additional massive scalar boson $X$ that subsequently decays into two SM-like Higgs bosons $(X \rightarrow H H)$ or into another spin-0 particle $S$ in conjunction with a SM-like Higgs boson $(X \rightarrow S H)$. The products of the subsequent scalar decays are heavily boosted and therefore cannot be resolved individually. Instead, the decay products are reconstructed as single large jets and information about their substructure is used to identify their origin. Traditional jet reconstruction algorithms rely solely on topological calorimeter clusters, which limits the resolution of jet substructure variables. TAR jets effectively overcome this limitation by exploiting angular information from the Inner Detector, and allow for a flexible choice of the reconstruction algorithm and jet size. This thesis presents performance studies targeting the $b \bar{b} W W^*$ decay mode that aim to find the optimal TAR jet configuration for two $H H$ searches in the boosted $0 \ell$ and $1 \ell$ final states, and a $S H$ search in the split-boosted $0 \ell$ final state.