Searches for Dark Matter production in events with top quarks in the final state with the ATLAS detector at the LHC

Many cosmological observations give convincing evidence for the existence of dark matter (DM), estimated to constitute around 26% of the Universe by measurements of the cosmic microwave background. While the existence of DM thus seems well established, very little is known about its nature. Numerous models of DM have been proposed, and a possible strategy to test them is to use particle accelerators. This thesis focuses in particular on the detection of DM produced in the ATLAS experiment at the Large Hadron Collider, studying signatures with top quarks in the final state in the framework of a two-Higgs-doublet model with an additional pseudoscalar mediator, called 2HDMa. The first part of the work consisted in the study of the production of DM in association with a pair of top quarks, trying to assess the sensitivity in the parameters space of 2HDMa of already existing ATLAS analyses. These analyses were performed in the framework of a different model, similar to the 2HDMa model since it included a pseudoscalar mediator. The production of DM in association with a pair of top quarks was chosen because it is directly sensitive to the nature of the mediator through the polarization of the two top quarks, which can be reconstructed from their decays products. The model employed in the existing analyses and the 2HDMa model were thus compared in detail, and after that a recasting strategy to translate the existing results in the parameter space of 2HDMa was developed and validated. The second part of the present study focused instead on a new search channel for the 2HDMa model, never explored before, including the production of dark matter associated with a single top quark. This signature was identified as the only one sensitive to the production of charged Higgs bosons, and thus holds a key role in the ATLAS research program dedicated to the 2HDMa model. Being a new and challenging signature, dedicated strategies were developed to maximise the sensitivity of the analyses focusing on the different final states.