Searches for direct pair production of scalar tau leptons in events with two hadronically decaying tau leptons with the ATLAS detector in LHC run 2

The Standard Model of particle physics has so far not been contradicted by evidence from experiments. There are, however, several indications that a more fundamental underlying theory is necessary at higher energy scales. At the Large Hadron Collider the possible presence of new physics can be probed in proton-proton collisions at an unprecedented center-of-mass energy of $13\,\text{TeV}$. Some of the most promising extensions to the Standard Model are suggested by supersymmetric models, which predict an entirely new particle spectrum connected to the Standard Model particle content via a fermion-boson symmetry. In this thesis, two approaches for the search for the supersymmetric partner particle to the Standard Model $\tau$-lepton (stau or $\tilde{\tau}$) with $139\,\text{fb}^{-1}$ of data taken by the ATLAS detector at the LHC are presented. The considered collision events should contain two hadronically decaying $\tau$-leptons and missing transverse momentum. The first approach is an analysis based on cuts on kinematic variables, which $-$ in the absence of a supersymmetric signal in data $-$ could exclude stau masses between $120\,\text{GeV}$ and $390\,\text{GeV}$ at 95$\%$ CL for a nearly massless lightest supersymmetric particle (LSP). It was also possible to exclude pair production of the supersymmetric partner of the left-handed $\tau$-lepton ($\tilde{\tau}_{L}$) for stau masses between $155\,\text{GeV}$ and $310\,\text{GeV}$ at 95$\%$ CL. For the supersymmetric partner of the right-handed $\tau$-lepton it was not possible to reach exclusion sensitivity separately from $\tilde{\tau}_{L}$ production. The second search aims to improve the sensitivity of the first iteration of the analysis by using boosted decision trees and a shape fit. The expected exclusion sensitivity ranges from stau masses of $80\,\text{GeV}$ to $430\,\text{GeV}$ for the combined scenarios of $\tilde{\tau}_{L}$ and $\tilde{\tau}_{R}$ production. For the separate $\tilde{\tau}_{L}$ pair production, the expected exclusion range covers stau masses from $100\,\text{GeV}$ to $350\,\text{GeV}$. Furthermore, for a range of stau masses between $120\,\text{GeV}$ and $230\,\text{GeV}$ exclusion sensitivity could also be achieved for separate $\tilde{\tau}_{R}$ pair production.