First measurement of the $Z/\gamma^{\ast} \rightarrow \tau\tau$ cross section in proton-proton collisions at $\sqrt{s} = 7$\,TeV with the ATLAS experiment at the LHC

The re-discovery of the $W$ and $Z$ bosons and the measurement of their production cross sections at the LHC are important steps towards new physics discoveries. In this thesis a first measurement of the production cross section of the process $pp \rightarrow Z/ \gamma^{\ast} \rightarrow \tau \tau$ with the ATLAS experiment at a centre-of-mass energy of $\sqrt{s}=7$\,TeV has been performed. The $Z/\gamma^{\ast} \rightarrow \tau \tau $ production cross section is measured using all data collected in 2010 corresponding to an integrated luminosity of 36\,$\mathrm{pb}^{-1}$. The $\tau$ leptons can either decay hadronically ($\tau_\mathrm{h}$) or leptonically ($\tau_\mathrm{\ell}$) to muons or electrons. The $Z/\gamma^{\ast} \rightarrow \tau \tau$ process is an important reference process since $\tau$ leptons play a major role in searches for the Higgs boson. The selection and cross section measurement of the $Z/\gamma^{\ast} \rightarrow \tau \tau \rightarrow \ell \nu \nu \, \tau_\mathrm{h} \nu $ final states comprises the main part of this thesis. Together with the $Z/\gamma^{\ast} \rightarrow \tau\tau \rightarrow \ell \nu \nu \, \ell \nu \nu$ final states, a combined measurement of the $Z/\gamma^{\ast}$ cross section times branching fraction to two $\tau$ leptons in an invariant $\tau\tau$ mass range (denoted as $m_{\mathrm{inv}}$) of $66<m_{\mathrm{inv}}<116\,\mathrm{GeV}$ is achieved. The combined result takes into account correlations between the uncertainties in the various final states and is $$ \sigma(Z/\gamma^{\ast} \rightarrow \tau\tau ,~66<m_{\mathrm{inv}}<116\,\mathrm{GeV}) = (0.97 \pm 0.07\textrm{(stat)} \pm 0.06\textrm{(syst)} \pm 0.03\textrm{(lumi)}) \textrm{ nb}.$$ This value is in very good agreement with the theoretical predicted cross section of $0.96 \pm 0.05$\,nb calculated at next-to-next-to-leading order. It allows a test of the lepton universality by comparing with cross section results in $Z/\gamma^{\ast} \rightarrow ee$ and $Z/\gamma^{\ast} \rightarrow \mu \mu$ final states. In a second part of this thesis silicon strip detectors are investigated for an upgrade of the ATLAS silicon strip detector. After several years of running the LHC, an increase of the instantaneous luminosity by a factor of ten is foreseen at a centre-of-mass energy of 14\,TeV. Because of radiation damage the current silicon detectors in the ATLAS experiment cannot withstand fluences of up to $1\times 10^{15}$\,1-MeV-equivalent neutrons (Neq)/cm$^2$ which are expected in the strip detector regions at the upgraded LHC. In this thesis one candidate sensor technology is investigated for the tracker upgrade of the ATLAS experiment: 3D Single Type Column strip detectors. Measurements of the characteristics of these sensors and a comparison of the results before and after irradiation to fluences expected at the upgraded LHC make it possible to quantify the radiation-induced performance degradation.