Measurement of the top quark coupling to the $Z$ boson, and applications to searches for physics Beyond the Standard Model

This thesis presents results using data collected by the ATLAS experiment in the 2015-2016 and 2015-2018 periods, corresponding to integrated luminosities at a centre-of-mass energy $\sqrt{s}=13\,\text{TeV}$ of $36.1\,\text{fb}^{-1}$ and $139\,\text{fb}^{-1}$respectively. It explores a connection between the top quark sector of the Standard Model and searches for supersymmetry in the all-hadronic final state. In Part II, a measurement of the inclusive cross section of the $t\bar{t}Z$ process in multi-lepton events results in $\sigma_{t\bar{t}Z}= 0.95\pm 0.13\,\text{pb}$ with $36.1\,\text{fb}^{-1}$ of data, and $\sigma_{t\bar{t}Z}= 1.09\pm 0.10\,\text{pb}$ with the full LHC Run 2 dataset. Both results are compatible with the Standard Model prediction of $\sigma_{t\bar{t}Z}^\text{theory}= 0.863^{+0.09}_{-0.10}\text{(scale)}\pm 0.03(\text{PDF}+\alpha_s)\,\text{pb}$. In the former analysis, exclusion limits are set on relevant dimension-6 effective field theory operators, while in the latter, the very first measurement of the differential $t\bar{t}Z$ cross section at ATLAS is presented. In Part III, a search for the supersymmetric partner to the top quark in the all-hadronic final state, characterised by six or more jets and large $E_\mathrm{T}^\text{miss}$, is described. No significant excess over the expected Standard Model background is observed, using $36.1\,\text{fb}^{-1}$ of ATLAS data. Assuming a $100\%$ branching ratio of $\tilde{t}_1\to t+\tilde{\chi}^0_1$, stop masses are excluded up to $1\,$TeV for neutralino masses smaller than $350\,$GeV. The estimation of the irreducible $t\bar{t}Z(\to\nu\bar{\nu})$ through a boson replacement technique is described in detail. Following the results obtained in Part II, the use of a multi-lepton $t\bar{t}Z$ control sample is instead proposed and shown to significantly improve modelling uncertainties in a subsequent analysis using the full LHC Run 2 dataset.