Measurement of the Higgs-Boson Production Cross-Section and Test of CP Invariance in Vector-Boson Fusion Production with $H\rightarrow\tau^+\tau^-$ Decays in the Fully-Leptonic Final State with the ATLAS Detector at the LHC

This thesis presents the measurement of the Higgs-boson production cross-section in the $H\rightarrow\tau\tau$ fully-leptonic final state based on data taken with the ATLAS detector at $\sqrt{s}=13\,$TeV with an integrated luminosity of $36.1\,\text{fb}^{-1}$. The analysis is based on the classification of events into categories, which target the dominant Higgs-boson production modes in gluon-fusion (ggF) and vector-boson fusion (VBF). The $H\rightarrow\tau\tau$ signal is extracted by performing a maximum likelihood fit in the reconstructed di-$\tau$ mass. In the fully-leptonic final state, an excess of $H\rightarrow\tau\tau$ signal events over the background-only hypothesis is observed with a significance of $2.2$ standard deviations, while $1.2$ standard deviations are expected. The obtained Higgs-boson production cross-section times branching ratio is $6.76^{+2.80}_{-2.78}\,$pb, which is consistent with the SM prediction within two standard deviations. The combined analysis with the semi-leptonic and fully-hadronic final states yields a Higgs-boson production cross-section times branching ratio of $3.77^{+1.06}_{-0.95}\,$pb. This result is consistent with the SM prediction within the uncertainties. The observed signal excess over the background-only hypothesis corresponds to a significance of $4.4$ standard deviations, while $4.14$ standard deviations are expected. In combination with the analysis of the data taken at $7\,$TeV and $8\,$TeV with integrated luminosities of $4.5\,\text{fb}^{-1}$ and $20.3\,\text{fb}^{-1}$, respectively, the observed significance amounts to $6.4$ standard deviations, while $5.4$ standard deviations are expected. This result allows to establish the discovery of $H\rightarrow\tau\tau$ decays with the ATLAS experiment. Furthermore, this thesis presents a search for CP-violating interactions of the Higgs boson with weak gauge-bosons HVV in the VBF production mode with subsequent $H\rightarrow\tau\tau$ decays. Additional CP-odd contributions to the CP-even HVV coupling stucture are described by the parameter $\tilde{d}$ in the framework of an effective field theory with $\tilde{d}=0$ corresponding to the SM prediction. The VBF Higgs-boson signal is separated from the background processes, where no CP violation is expected, by exploiting a multivariate approach. The CP-odd Optimal Observable is used in order to determine the $\tilde{d}$-parameter and construct its central confidence level (CL) intervals. In the fully-leptonic final state, the obtained $\tilde{d}$-parameter is $-0.03$ and no CL intervals for dtilde can be derived. The combined analysis with the semi-leptonic and fully-hadronic final states measures $\tilde{d}$ to be $-0.01$ and obtains a $68\,\%$ CL interval of $[-0.090,0.035]$ compared to the expected $68\,\%$ CL interval for the SM hypothesis of $[-0.035,0.033]$. No $95\,\%$ CL interval for $\tilde{d}$ is observed, while the expected $95\,\%$ CL interval for the SM hypothesis is $[-0.21,0.15]$. These results are consistent with the SM prediction of a CP-even Higgs boson and show no sign of CP-violating HVV interactions.