Mass reconstruction techniques and cross section measurement for $Z\to \tau\tau \to e\mu+4\nu$ with the ATLAS experiment

A central aspect of modern particle physics is the search for the Higgs boson. First, the Higgs boson remains the only particle of the Standard Model not being proven experimentally. Secondly, its possible observation may improve our understanding of new physics. With the start of operation of the LHC at the European Organization for Nuclear Research (CERN), proton-proton collisions with a centre of mass energy being as high as ${\sqrt{s}=7}$ TeV and ${\sqrt{s}=8}$ TeV could be achieved.\\ This work measures the cross section of the process ${pp\to Z^{0}/\gamma^{*} \rightarrow \tau^{+}\tau^{-}}$ in the mixed leptonic final state with data of the ATLAS detector. The decay of the coherent sum of the photon, $\gamma^{*}$, and the $Z^{0}$ boson is an irreducible background for Higgs boson decays into two $\tau$-leptons. For the Higgs boson search a precise knowledge of its mass spectrum and its normalisation is essential. The data used are equal to an integrated luminosity of L = 35.51 pb$^{-1}$ with a centre of mass energy of ${\sqrt{s}=7}$ TeV. A cross section of ${\sigma^{\mathrm{tot.}}_{Z/\gamma^*} \times \mathrm{BR}(Z \rightarrow \tau\tau)=(1041 \pm 143 \pm 74 \pm 35)}$ pb is yielded, with its statistical and systematic uncertainties as well as uncertainties from luminosity determination. The result is compatible with the results from theoretical calculations and that from other experiments within their uncertainties.\\ The second part of this work examines mass reconstruction methods of decays into two $\tau$-leptons. The analysis concentrates on Higgs bosons, $\phi$, of the minimal supersymmetric extension of the Standard Model, the MSSM. In particular, the decay of Higgs bosons to two $\tau$-leptons and further into an electron, a muon and four neutrinos is examined, $\phi\to\tau^+\tau^-\to e\mu+4\nu$. The appropriate mass reconstruction techniques being investigated are the visible mass, the effective mass and the early and late projected transverse mass. Furthermore, a dependency of the mass distributions on the transverse momentum of the leptons and on the missing transverse energy is observed. However, a dependency on the transverse momentum of the highest $p_{T}$ jet was not found. The elimination of the variable dependencies leads to a worse separation power between the signal and background processes as well as a worse resolution between different Higgs boson masses. The work concludes with a calibration of the masses calculated with the analysed mass reconstruction techniques.