Legacy cross-section measurements of the $t\bar{t}Z$ production process in the trileptonic final state at $\sqrt{s}=13\,$TeV with the ATLAS detector

After three years of data-taking during the second run of the LHC at CERN, Geneva, Switzerland, the ATLAS detector has recorded its most extensive proton-proton collision data set to date, allowing for a wide range of Standard Model (SM) precision measurements. Through this dataset, a large number of top quark pairs in association with a $Z$ boson ($t\bar{t}Z$) and with it key SM parameters are accessible. Several theories beyond the SM provide possible extensions to the electroweak sector of the SM, leading to deviations of the $t\bar{t}Z$ production cross-section from its SM predictions in the presence of new physics. With the large dataset recorded by ATLAS, a final $t\bar{t}Z$ analysis has gained interest to provide legacy cross-section measurements and interpretations within the SM effective field theory to provide the most cohesive picture of the $t\bar{t}Z$ production process to date. This work mainly presents the results of the inclusive cross-section measurement obtained using the $140\,\text{fb}^{-1}$ large Run2 dataset collected by the ATLAS detector between 2015 and 2018 at $13\,$TeV centre-of-mass energy. It focuses on the measurement of the inclusive cross-section in the trileptonic channel, where exactly three leptons (electrons or muons), two originating from a $Z$ decay and one from a leptonic top quark decay and at least three jets, one of which must be $b$-tagged, are selected. The obtained data is unfolded using the profile-likelihood unfolding approach, and interpretations of the inclusive and differential measurements within the framework of the SM effective field theory are presented. A deeper focus of this thesis lies in developing neural-network-based classifiers for $t\bar{t}Z$ event classification in the trileptonic channel.