Measurement of the production cross section of a top-antitop quark pair in association with a $Z$ boson at $\sqrt{s}=13\,\text{TeV}$ with the ATLAS detector

The coupling of the top quark to the $Z$ boson is precisely predicted within the Standard model of particle physics via the electroweak interaction. However, experimentally it is not yet well constrained and its value can vary significantly in many models featuring physics beyond the Standard Model. A process that is particularly sensitive to this coupling is the associated production of a top-antitop quark pair with a $Z$ boson. The large centre-of-mass energy of the LHC and the tremendous amount of data collected in recent years have opened up the possibility to study this rare process which was previously inaccessible due to its small production cross section. The production cross section of the $t\bar{t}Z$ process is measured, using $139\,\text{fb}^{-1}$ of proton-proton collision data at a centre-of-mass energy of $13\,\text{TeV}$, recorded by the ATLAS detector at the LHC in the years from $2015$ to $2018$. In order to estimate the expected number of events for both signal and the associated Standard Model background, Monte Carlo simulations are employed. The $Z$ boson is identified by targeting events featuring a pair of electrons or muons with opposite electric charge and an invariant mass consistent with the parent particle. The final targeted signature is then characterised by the number of leptons from the decay of the associated $t\bar{t}Z$ system. The first part of this thesis presents several studies conducted in the context of a $t\bar{t}Z$ cross-section measurement that targets the most sensitive decay modes of the $t\bar{t}Z$ process with three or four isolated leptons with high transverse momentum in the final state and reports measurements of both the inclusive and differential cross sections. A series of validation studies are performed for sets of simulated Monte Carlo samples used in the analysis to describe the signal process as well as one of the dominant backgrounds featuring the associated production of single top quarks with both a $W$ and a $Z$ boson. Furthermore, an attempt to reduce the contributions from the dominant background processes in these $t\bar{t}Z$ decay channels - the production of pairs of vector bosons and single top quarks in association with vector bosons - is shown by exploiting the discrimination provided by an algorithm based on a partial reconstruction of the $t\bar{t}$ system. In the second part of this thesis, a new approach for a measurement of the $t\bar{t}Z$ production cross section in the dilepton channel, labelled $2\ell\text{OS}$, is introduced. In contrast to the $t\bar{t}Z$ decay modes with three or four isolated leptons in the final state, the $2\ell\text{OS}$ channel suffers from significantly larger background rates. In order to isolate the signal from the two dominant background processes - dileptonically decaying $t\bar{t}$ events and the associated production of a single $Z$ boson with jets - two Boosted Decision Trees are independently trained, with each dedicated to a unique one of the two major background contributions. The output of the two classifiers is then combined in order to select phase space regions highly enriched in events from either signal or either one of the two dominant background processes. A profile-likelihood fit of the Monte Carlo prediction to the data within those regions is employed to determine the inclusive $t\bar{t}Z$ production cross section, which is measured to be \begin{equation*} \sigma_{t\bar{t}Z}=0.91\pm0.08\,\text{(stat.)}\,\pm0.14\,\text{(syst.)}\,\text{pb} \end{equation*} with an observed statistical significance of $5.9\,\sigma$. The result is found to be in agreement with the most precise theoretical prediction.