Test of Standard Model and search for new physics with Vector Boson Scattering and Fusion processes in electroweak boson and Di-Higgs final states at ATLAS

This dissertation explores three pivotal aspects of particle physics, examining electroweak interactions within the Standard Model(SM) theory, search for new physics beyond the SM, and chances for new physics search in future lepton colliders. First, we report the observation of electroweak production of a \( W \) boson and a photon in association with two jets, using \( pp \) collision data from the ATLAS experiment at the LHC with a center of mass energy of \( \sqrt{s} = 13 \) TeV. This is the first observation by the ATLAS experiment. The process tests the electroweak gauge symmetry breaking mechanism of the Standard Model. With an integrated luminosity of 140 fb\(^{-1}\), the observed significance exceeds six standard deviations, closely matching the expected significance. Measurements of fiducial and differential cross sections align well with Standard Model predictions, and constraints on new physics effects are derived. Second, a search for Higgs boson pair production via vector-boson fusion was conducted in the Lorentz-boosted regime using 140 fb\(^{-1}\) of data. Focusing on Higgs decays into bottom quark pairs, the study constrains the quartic coupling \( \kappa_{2V} \) to 0.55 < \( \kappa_{2V} \) < 1.49 at 95\% confidence level, excluding \( \kappa_{2V} = 0 \) with a significance of 3.8 standard deviations. Additionally, limits on new heavy spin-0 resonances mediating Higgs pair production were established, showing no significant deviations from the Standard Model. Third, this thesis investigates a strong first-order electroweak phase transition driven by a light scalar \( s \) with a mass between 15 and 60 GeV. The study involves a search for exotic Higgs decays into a pair of spin-zero particles (\( h \rightarrow ss \)), with each \( s \)-boson decaying into \( b \)-quarks. Using simulated data from the CEPC, the analysis sets upper limits on the cross-section times branching ratio for \( h \rightarrow ss \), with sensitivity significantly higher than achievable at the LHC. These studies provide crucial insights into electroweak interactions, search for new physics beyond the SM, and potential new physics with future lepton colliders, offering stringent tests and constraints that advance our understanding of fundamental forces.