CERN Accelerating science

Symmetry and conservation are elementary parts in the physics. The charge conjugation parity symmetry ($\mathcal{CP}$-symmetry) is related to the conservation of matter and antimatter. Currently, the most successful and validated theory of depicting matter and its interaction is the Standard Model (SM) in particle physics. In the universe, there exists an imbalance between matter and antimatter and it is explained by $\mathcal{CP}$ violation (CPV) by introducing the Kobayashi-Maskawa (KM) mechanism in SM. However, the theoretical calculated results by the KM mechanism are not sufficient to explain the magnitude of the matter-antimatter asymmetry. Thus, a new source of the CPV is crucial in particle physics. Although the discovery of the Higgs boson at the Large Hadron Collider (LHC) in 2012 meant that SM particles have been discovered completely, there are still some questions remained to be solved such as matter-antimatter asymmetry. Therefore, we want to measure the properties of the Higgs boson precisely, not only for further validation of the SM but also we want to find some hints of beyond Standard Model (BSM) physics like a new source of CPV in the Higgs sector for new physics. In SM, the Higgs boson can interact with weak gauge bosons by electroweak interaction, and with fermions by Yukawa coupling. In this thesis, a rigorous study of $\mathcal{CP}$ property of the Higgs boson is presented in Higgs $\tau$-lepton Yukawa coupling vertices. By analyzing data recorded by the ATLAS experiment at LHC in the center-of-mass of 13 TeV with an integrated luminosity of 139 $\text{fb}^{-1}$, we probed $\mathcal{CP}$ property of the Higgs boson in H-$\tau$ Yukawa coupling vertex in $H \rightarrow \tau\tau$ decay channel. In the $H \rightarrow \tau\tau$ decay analysis, the Higgs boson $\mathcal{CP}$ property in interaction with $\tau$ lepton parameterized by the $\mathcal{CP}$ mixing angle $\phi_{\tau}$ is measured by the distribution of the acoplanarity angle between di-$\tau$ decay planes. One leptonically decayed $\tau$ and the other hadronically decayed $\tau$ (marked as $\tau_{\text{lep}}\tau_{\text{had}}$) channel and both hadronically decayed $\tau$ (marked as $\tau_{\text{had}}\tau_{\text{had}}$) channels are considered with all main Higgs production modes in this analysis for sensitivity. After the reconstruction of two $\tau$ decay planes, an observable $\varphi^{*}_{\mathrm{CP}}$ is calculated in $\text{di-}\tau_{\text{vis}}$ zero-momentum-frame (ZMF). With statistic analysis, the mixing angle $\phi_{\tau}$ is measured to be $9 \pm 16^{\circ}$ ($0 \pm 28^{\circ}$) as observed (expected) value at 68\% confidence level (CL). And the pure $\mathcal{CP}$-odd Higgs hypothesis is excluded at 3.4$\sigma$ (2.1$\sigma$) level as observed (expected) value. The results are consistent with the Standard Model prediction considering the uncertainties. This is the first measurement of the $\mathcal{CP}$ property in the Higgs-lepton Yukawa coupling vertices in the ATLAS experiment.