Search for physics beyond the Standard Model in di-lepton final state with the ATLAS experiment

The Large Hadron Collider and its experiments are the largest ongoing particle physics research project in the world. In this thesis I present a search accomplished with the LHC and the ATLAS detector to look for new physics beyond that described by the so-called Standard Model of particle and interactions. The data analysis reported here was performed on a sample corresponding to 36.1$~\text{fb}^{-1}$ of integrated luminosity from LHC $pp$ collision at $\sqrt{s}=13~TeV$ recorded by ATLAS. The study focuses on the final state events with two leptons (electrons or muons) of opposite electric charge. In the final event selection, the number of observed events potentially indicating the existence of new physics was found to be consistent with the Standard Model expectation. Limits for different types of models involving the existence of new particles from Dark Matter and Supersymmetry were set. The results on SUSY are interpreted taking into account only the lightest top squark ($\tilde{t}_1$) and the lightest neutralino ($\tilde{\chi}^0_1$). Furthermore, limits are also set on the production cross-section of colour-neutral mediators decaying into Dark Matter particles produced in association with top quark pairs. For a massless neutralino, top squark masses below 720 GeV are excluded at $95\%$ Confidence Level. Neutralino masses below $300$ GeV for $m(\tilde{t}_1)=650$ GeV are excluded as well. Similar limits are also set on a possible phenomenological Minimal Supersymmetric Standard Model. Assuming Dark Matter models, limits are obtained both as a function of the mediator mass and of the Dark Matter particle mass. For $1$ GeV Dark Matter mass particle, scalar mediator masses up to $50$ GeV are excluded. Limits on the spin-independent Dark Matter--nucleon scattering cross-section are set to compare with past fixed target experiments. As a related experimental activity, I also investigated a new pixel silicon sensor technology for the upgrade of the ATLAS inner detector. Using this new technique, both the pixel sensor and the read-out chip are implemented in the same silicon bulk. Sensors of this technology were tested during a beam test at the H8 line at the CERN Super Proton Synchrotron measuring excellent performance and a high 99.6$\%$ efficiency also after irradiation.