Analysis of top-quark production processes for the search of new physics and correlated tracking studies in the ATLAS experiment at the LHC

Since the top-quark is the heaviest elementary particle in the Standard Model (SM), with a mass close to the scale of electroweak symmetry breaking, it plays an essential role in many models (SM and beyond SM (BSM)), and it might answer several questions still unanswered in the SM. For this reason, I tackled this topic in different ways. This thesis presents a study of the tracking-efficiency performance of the Inner Detector of the ATLAS experiment to reconstruct pion tracks in data and simulated events. Also, it presents analyses of different processes involving top quarks. The first one is the study of four-top-quark production in the single-lepton and opposite-sign dilepton final states, where a new method has been developed to reject backgrounds in the signal region for both channels. The second search looks for the existence of new particles as predicted by several theoretical BSM models, which are the Topcolor Assisted Technicolor model (TC2), and the Randall-Sundrum model. No evidence for resonant productions of top-quark pairs is found. As a result, expected limits are set on the production cross-section times branching ratio of these models at $95\%$ confidence level. Both these analyses are based on data from proton-proton collisions at a centre-of-mass energy $\sqrt{s}=13$ TeV collected by the ATLAS experiment at the Large Hadron Collider (LHC) at CERN and simulated Monte Carlo (MC) events as predicted from the SM and BSM models.