Search for the non-resonant Vector Boson Fusion production of the Higgs boson pairs decaying to $b\overline{b}b\overline{b}$ final state using the ATLAS detector

Non-resonant Higgs boson pairs produced via Vector Boson Fusion (VBF) and decaying to $b\overline{b}b\overline{b}$ final state are searched for using 126 fb${}^{-1}$ of $\sqrt{s}$ = 13 TeV proton-proton collisions data collected by the ATLAS detector in Run 2. There is no evidence for the Standard Model production of Higgs boson pairs. The observed (expected) 95% CL exclusion limit on the Standard Model production cross-section is set at 132.3 (132.8) times the Standard Model cross-section prediction. The analysis strategy is optimised so that the previous limit set on the Standard Model HH $\to$$b\overline{b}b\overline{b}$ VBF cross-section is improved by a factor of 6. Non Standard Model couplings are tested as well, leading to the observed ${\kappa }_{2V}$ constrained interval of [0.09, 1.99]. The fully data-driven neural network QCD background estimation has a considerable impact on the improved result and is discussed in detail in this thesis. Additionally, projection studies for the future experimental scenarios: the HL-LHC and the FCC-hh, are performed using a simplified approach with Monte Carlo generated signal and background samples. The study results in a 95% CL expected limit on the Standard Model cross-section reaching 248 times the Standard Model cross-section prediction for for the HL-LHC and 18 times the Standard Model cross-section prediction for the FCC scenario.