Search for New Physics through Higgs-Boson-Pair Production at the LHC and Beyond

This thesis presents a search for resonant production of highly energetic Higgs boson pairs, with each Higgs boson decaying to a $b$-quark pair, with the ATLAS detector. This analysis uses the complete ATLAS run 2 dataset of 139.0 $\text{fb}^{-1}$ of proton-proton collisions at a centre-of-mass energy of $\sqrt{s}= 13$ TeV. The expanded dataset, new flavour-tagging techniques, and novel subjet reconstruction algorithms provide better sensitivity than previous studies of the process. Two beyond-the-Standard-Model resonances are chosen as benchmarks for the result: a two-Higgs-doublet model scalar $S$ and Kaluza-Klein (KK) gravitons $G_{kk}^*$ predicted in the bulk Randall-Sundrum (RS) model. No significant deviations from Standard Model predictions are found, and upper limits are set on the production cross section of these resonances. A phenomenology study on the analysis strategy of this search in conditions of the future High Luminosity Large Hadron Collider is presented as well. This study shows proof-of-concept improvements in sensitivity by using a deep-learning approach to separate the $hh \to 4b$ signal, and discusses the optimization of the search to constrain the Higgs boson self-coupling parameter $\lambda_{hhh}$.