Search for flavour-changing neutral-current top quark decays to c-quark and Z boson using the ATLAS detector at the LHC

The main focus of this thesis is the search for the $t\rightarrow Z c$ process in the proton–proton collisions data collected by the ATLAS detector at the Large Hadron Collider located at CERN.\\ The flavour-changing neutral-current (FCNC) processes are forbidden at tree-level and highly suppressed at loop-level which is why they are very rare phenomena in the Standard Model of particle physics. However, these processes have a higher probability to occur in several theories beyond the Standard Model where the suppression could be relaxed and the loop diagrams mediated by new bosons could contribute.\\ The FCNC top-quark decays $\mathrm{t\rightarrow Z c}$ are searched in \ttbar pair events with one top quark decaying through the $\mathrm{t\rightarrow Z c}$ channel and the other through the dominant Standard Model mode $\mathrm{t\rightarrow W b}$. The analyzed data were recorded at a center-of-mass energy of \SI{13}{\TeV} and correspond to the full Run-2 dataset with an integrated luminosity of \SI{139}{\ifb}.\\ The data are consistent with Standard Model background contributions, and, at 95\% confidence level, the search sets observed (expected) upper limits of $\mathrm{11.8\times 10^{-5}}$ ($\mathrm{9.5\times 10^{-5}}$) on the $\mathrm{t\rightarrow c Z}$ branching ratio, constituting the most stringent limit to date and improving the previous ATLAS results by a factor of 2 (2.5).