Searches for CP Violation in the Higgs Sector with the $H \rightarrow ZZ^* \rightarrow 4l$ Decay Channel in the ATLAS Experiment at the Large Hadron Collider

Since the discovery of the Higgs boson at the Large Hadron Collider at CERN by the ATLAS and CMS experiments, measurements of its properties have been carried out. These measurements have yielded results in good agreement with the Standard Model expectation. Signs of new physics have not been discovered in the properties of the Higgs boson. The precision of these measurements is limited by the amount of data. Continuous measurements on the dataset of increasing size would be able to constrain the properties with shrinking uncertainties. This would enable experiments to detect potential deviations from the Standard Model more precisely and indicate the direction of future new physics searches. This study aims to search for the potential violation in simultaneous charge conjugation and parity inversion, known as CP violation, in the Higgs boson couplings with the 2015-2018 ATLAS data. Among different Higgs boson decay modes, the four-lepton decay mode through $Z$~bosons is a ``clean'' channel at the Large Hadron Collider, despite its moderate branching ratio. Events in this channel are well-separated from heavy multi-jet backgrounds. The electrons and muons in this final state are fully reconstructable with high reconstruction efficiency. These features make it a suitable channel to study the bosonic couplings of the Higgs boson. In addition, vector boson fusion, as the subleading Higgs boson production channel at the Large Hadron Collider, produces jets that are sensitive to CP violation. Their information is used together with the four-lepton decay information in this study to optimize sensitivity. In this study, the potential CP violation in the Higgs boson coupling to $Z$~bosons is searched through the measurement of the CP-odd couplings beyond the Standard Model. The CP-odd couplings measured are parametrized using the effective field theory framework. The measurement is based on the likelihood fit method of the normalized kinematic observable distributions of the leptons and jets in the final state. The results of this study are consistent with the Standard Model expectation within two standard deviations. The statistical fluctuations of data are the dominant source of uncertainties in this analysis. More strict constraints than the previous yield-based analysis have been set in the CP-odd effective couplings. This measurement inspires a deeper understanding of the coupling structure of the Higgs boson.