Measurement of Higgs-boson production cross-sections and test of CP invariance in vector-boson fusion production in the $H \rightarrow \tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ decay mode with the ATLAS detector

This thesis presents a measurement of the Higgs-boson production cross-section and a test of CP invariance in vector-boson fusion production in the semileptonic final state of the $H\rightarrow\tau\tau$ decay channel. Both analyses use proton-proton collision data corresponding to an integrated luminosity of $36.1\,\mathrm{fb}^{-1}$ recorded with the ATLAS detector at a center-of-mass energy of $13\,\mathrm{TeV}$. The events are divided into categories that target the specific kinematics of the gluon fusion- and the vector-boson fusion production processes of the Higgs boson. A maximum-likelihood fit in the reconstructed di-$\tau$ mass is performed to extract the $H\rightarrow\tau\tau$ cross-section. A signal excess with an observed significance of $2.4$ standard deviations is found under the background-only hypothesis, whereas the expected significance is $2.6$ standard deviations. The resulting $H\rightarrow\tau\tau$ cross-section is $3.13^{+1.53}_{-1.33}\,\mathrm{pb}$, which is in agreement with the prediction by the Standard Model. In combination with the fully leptonic- and fully hadronic final states of the $H\rightarrow\tau\tau$ decay channel, the resulting cross-section is $3.77^{+1.06}_{-0.95}\,\mathrm{pb}$, which is again consistent with the prediction by the Standard Model. The obtained observed significance is $4.4$ standard deviations with an expected significance of $4.1$ standard deviations. Further combination with the result of the search for the $H\rightarrow\tau\tau$ decay with data recorded at center-of-mass energies of $7$ and $8\,\mathrm{TeV}$ yields an observed significance of $6.4$ standard deviation with an expected significance of $5.4$ standard deviations. To test CP invariance in the coupling between the Higgs boson and the electroweak gauge bosons, the production of the Higgs boson via vector-boson fusion is studied. This production process is separated from other processes by using a machine learning approach in form of Boosted Decision Trees. An Effective Field Theory approach is used to expand the Lagrangian of the Standard Model with additional CP-odd terms, quantified by the parameter $\tilde{d}$. Maximum-likelihood fits are performed in the CP-odd Optimal Observable to set constraints on $\tilde{d}$. The observed confidence interval at $68.3\,\%$ confidence level is $[-0.006,0.089]$, whereas the expected confidence interval is $[-0.064,0.065]$. The combination with the fully leptonic- and fully hadronic final states of the $H\rightarrow\tau\tau$ decay channel yields an observed $68.3\,\%$ confidence interval of $[-0.090,0.035]$ with an expected confidence interval of $[-0.035,0.033]$. In the combination, also an expected confidence interval at $95\,\%$ confidence level of $[-0.21,015]$ is obtained. All the results are in agreement with $\tilde{d}=0$ as predicted by the Standard Model.