The presented project explores the current theoretical and experimental tools available within the study group for the Future Circular Collider (FCC) with focus on the electron-positron collider. The aim of the study is to evaluate the current frameworks used for simulation, and investigate the possibility of simulating long-lived particles, that could be dark matter candidates, through them. Pythia cards were run through the framework of Delphes and several different software packages were studied on the journey through the work. It was found that the current framework reconstructs the masses of a Z bosons and Higgs bosons accurately from the ZH signal, which is central for the analysis at the FCC-ee. When the same analysis was applied for the new physics case of a dark matter particle included in the new card for study, a ROOT file was produced indicating that the framework was able to handle the new case. When this card was run through the analysis software however, difficulties arose and a final output could not be achieved. Conclusively, it can be said that the current framework has the possibilities of handling new physics cases but further study is required to be able to run certain software packages on these cases.

Heavy Neutral Leptons (HNLs) are the heavier counterparts of the light neutrinos of the Standard Model of particle physics. HNLs can simultaneously solve several of the problems the Standard Model cannot yet resolve, one example being that they provide a candidate for Dark Matter. This thesis work aims to shed light on the nature of HNLs and study the displaced signature the particle gives rise to at colliders. The collider of interest is the Future Circular Collider that will be colliding electrons and positrons and the signal studied is the production of an HNL and a light neutrino from an intermediate Z boson, produced from the collision of an electron and a positron. The event generation was set up through MadGraph and PYTHIA and for the detector simulations DELPHES was used. Validation of three HNL samples were carried out in a standalone framework and in the FCC framework. The samples were validated by comparing theoretically calculated lifetimes with the lifetimes attained by simulation. Kinematic studies of the transverse momentum of the HNL and its decay particles showed correlation to the mass of the HNL. Reconstruction of the number of tracks created by the HNL decay was possible and the results of two track dominance were found to correlate with theory. For the vertexing study, the reconstruction of the production vertex of the decay particles was possible where displaced vertices were observed, hence proving the possibility of implementing displaced signatures in the FCC framework for the very first time. The next step in this trajectory of the study would be to investigate vertex fitting of the reconstructed vertices in order to carry out tracking studies of the HNL. This work hence sets the foundation for further exploration of HNLs and provides stepping stones for the possibility of discovery of HNLs in the FCC-ee.