Precision measurements in neutral current Drell-Yan production at ATLAS

The Large Hadron Collider (LHC) at CERN is a powerful machine to facilitate collisions of hadrons such as protons. Its high instantaneous luminosity allows to collect large datasets of proton-proton collisions. In this thesis the data taken at the ATLAS experiment from 2015-2018 at $\sqrt{s}=13 \textrm{TeV}$, amounting to ${139} \textrm{fb}^{-1}$ is analysed in the context of the Drell-Yan process. In particular, for the first time the full set of eight so-called \textit{angular coefficients} of the $Z/\gamma^*$ boson using electron/positron and muon/anti-muon pairs are extracted from this data differentially in dilepton rapidity and transverse momentum. In addition, the differential cross section of the Drell-Yan process is determined. Results of the template fits using electrons/positrons and muons/anti-muons are predominantly consistent with each other. Additionally, previous measurements, in particular non-zero angular coefficients $A_5$, $A_6$ and $A_7$ as well as the breaking of the Lam-Tung relation are supported by the results presented. \\ The angular coefficient $A_4$ is closely connected to the weak mixing angle. For this reason, in the second part of this dissertation, $A_4$ is studied in simulation to assess its expected sensitivity on the effective leptonic weak mixing angle emulating the statistical accuracy and uncertainties of the data. The study is focussed on electron/positron and muon/anti-muon pairs in the so-called central region of the ATLAS detector. The resulting expected sensitivity improves the previous ATLAS measurement of the weak mixing angle using this method in these decay channels by about 26\%. The sensitivity of such a measurement benefits from the addition of electrons or positrons from the so-called forward region of ATLAS. \\ For this reason, in the final part of this thesis different options for algorithms to trigger on electrons, positrons or photons are evaluated using the so-called \textit{forward feature extractor} module as part of the planned Phase-II upgrade of ATLAS for the High-Luminosity LHC era. It is shown that exploiting information about particle shower shapes in neural networks provides the best performance in identifying signal objects and rejecting backgrounds, the majority of which are jets, and proves to be superior to simpler approaches that rely on fixed selection criteria.