Analysis of the Higgs boson decay in the $H\rightarrow\tau_\textrm{had}\tau_\textrm{had}$ channel and $CP$ properties with $\sqrt{s}=13~\mbox{TeV}$ collisions at the ATLAS detector

In 2012, the last undiscovered particle predicted by the Standard Model of particle physics (SM), the Higgs boson, was discovered by the ATLAS and CMS collaborations in a number of its bosonic decay channels. This has been an important step in understanding the nature of electroweak symmetry breaking. Subsequent studies of the Higgs boson spin, parity, and coupling properties are vital in confirming whether the discovered Higgs boson is compatible with the SM Higgs boson. The topics of this dissertation are the analyses of the Higgs decay to a pair of hadronically decaying tau leptons and the Higgs charge-parity ($\mathcal{C}\mathcal{P}$) properties in the same decay channel using datasets collected during 2015 and 2016 from proton-proton collisions at the LHC, corresponding to integrated luminosities of $3.21\textrm{ fb}^{-1}$ and ${32.9\textrm{ fb}^{-1}}$, respectively. In Higgs physics, the fermionic decay channels are important because they provide direct access to the Higgs boson Yukawa couplings. In the presented analysis of the Higgs decay to tau leptons ($H\rightarrow\tau\tau$), the signal extraction is performed by comparing the expected signal and background distributions to the observed di-tau mass distribution in data. The main background contributions come from the QCD $Z\rightarrow\tau\tau$+jets process and QCD multijet production, which are modeled using simulation and two different background methods developed in this dissertation, respectively. An excess of signal events beyond the expected background yield is measured with an observed significance of $1.52\sigma$, corresponding to a signal strength relative to the SM prediction of $\mu=0.62^{+0.25}_{-0.24}\textrm{(stat)}^{+0.36}_{-0.31}\textrm{(syst)}=0.62^{+0.44}_{-0.40}$. Subsequent studies of Higgs $\mathcal{C}\mathcal{P}~$properties are performed in the same decay channel using the $H\rightarrow\tau\tau$ analysis as the basis. While $\mathcal{C}\mathcal{P}~$measurements in the bosonic decay channels have excluded deviations from SM Higgs boson $\mathcal{C}\mathcal{P}$ quantum numbers, the fermionic decay channels provide unique $\mathcal{C}\mathcal{P}$ information. If there are signs of $\mathcal{C}\mathcal{P}~$mixing in the fermionic sector, the Higgs boson can possibly explain the matter-antimatter asymmetry in the universe. The Higgs $\mathcal{C}\mathcal{P}~$sensitivity is extracted by comparing the expected signal and background distributions to the observed data distribution constructed from experimental observables sensitive to Higgs $\mathcal{C}\mathcal{P}~$mixing. Studies are performed to validate the signal extraction with toy experiments and to identify the main hindrance of the analysis, which is the limited integrated luminosity. A $\mathcal{C}\mathcal{P}~$mixing angle of ${10}^\circ$ is measured with an uncertainty of ${18.3^\circ}$ for the case where the Higgs boson cross section is fixed to the SM prediction and an uncertainty of $27.5^\circ$ where it is fitted. It is consistent with the SM prediction of $\phi_\tau={0^\circ}$.