Search for pair production of Higgs bosons via vector-boson fusion process in the $b\bar{b}b\bar{b}$ final state using proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

The Higgs boson ($h$) was discovered by the ATLAS and CMS collaborations in 2012, using proton-proton ($pp$) collisions at the Large Hadron Collider (LHC). The measured properties have so far been found to be in agreement with the Standard Model (SM) predictions. However, there is a "fine-tuning" problem that means a quite large radiative correction is needed to explain the difference between the observed Higgs mass (125 GeV) and the bare Higgs mass in the SM. The hypothesis of Two Higgs Doublet Model (2HDM) is a candidate to solve that problem. The production of a pair of Higgs bosons ($hh$) is a rare process in the SM, but various models beyond the SM predict cross-sections for the $hh$ production that are significantly higher than those of the SM prediction. The heavy scalar boson that decay into Higgs boson pairs appear in exotic scenarios of the 2HDM. Enhanced non-resonant Higgs boson pair production is also predicted by many models. Previous searches for Higgs boson pair production in the $b\bar{b}b\bar{b}$ channel were carried out in the gluon-gluon fusion (ggF) production mode by the ATLAS and CMS collaborations and limits were set for resonant and non-resonant productions. This thesis report a search for a Higgs boson pair ($hh$) produced via Vector Boson Fusion (VBF) and decaying into the dominant $b\bar{b}b\bar{b}$ final state. This study provides a completely new signature in the Higgs sector. This search has complementary sensitivity to the production of an additional heavy scalar boson, that may decay into a Higgs boson pair, compared to past direct searches. Additionally, this search can place constraints on the parameters of the Higgs coupling with vector bosons, especially the quadruple coupling of $VVhh$, using the non-resonant signature. This analysis uses the Run-2 dataset collected by ATLAS at $\sqrt{s}=13$ TeV, corresponding to 126.0 fb$^{-1}$ taken in 2016-2018. In this research, the following items are achieved: The correction on the $b$-jet energy has been implemented to improve the resolution of the reconstructed mass of the Higgs boson candidates. The event selections that are specific to the VBF signal are defined and optimized. The unique procedure of the estimation of QCD multi-jet background and $t\bar{t}$ background is established. The background estimation is evaluated to be well-established. As a result, unfortunately, no significant excess was observed, but I have worked out two important results. The first one is that the limits on the cross-section of heavy resonant signals have been set. The observed excluded region with 95% C.L. corresponding to $m_{H}$ > 666.9 GeV for the parameters of $\tan$$\beta$ = 2.0 and sin($\beta$ - $\alpha$) = 0.6 in the Type-II 2HDM. The second one is that the limits on the cross-section of non-resonant signals with various $VVhh$ coupling strength, $\kappa$$_{2V}$, are set. The observed 95% C.L. limits on the cross-section of SM non-resonant $HH$ production via VBF is given as 1450 fb. The parameter regions $\kappa$$_{2V}$ is $\kappa$$_{2V}$ 2.89 are excluded at 95% C.L. This constraint on $\kappa$$_{2V}$ is provided for the first time in the world. We can also explore the VBF production using the final states of $hh$ $\rightarrow$ $b$$\bar{b}$$\gamma$$\gamma$, $b$$\bar{b}$$\tau$$\tau$ and so on. This first research of $hh$ $\rightarrow$ $b\bar{b}b\bar{b}$ in VBF production opened up new parameter spaces, to perform a measurement of the $VVhh$ coupling and to search for new physics in specific models