Search for direct production of charginos and sleptons in LHC Run 2 $pp$ collision data collected by the ATLAS experiment, and discovery prospects for top-squark pair production at High-Luminosity LHC with the ATLAS detector

Among the several beyond the Standard Model (BSM) theories, one of the most accredited is Supersymmetry (SUSY), foreseeing the existence of a new set of particles that could be observed at the Large Hadron Collider (LHC). In this thesis two searches for SUSY at LHC are described. The first deals with the electroweak direct production of either slepton or chargino pairs, decaying into two-lepton final states and missing transverse energy, by using $\sqrt{s}=13$ TeV proton-proton collision data collected by the ATLAS detector during Run 2 of LHC, corresponding to 139 fb$^{-1}$. Two R-parity-conserving simplified SUSY models are considered: the direct production of sleptons ($\tilde{\ell}\tilde{\ell}$), each decaying into a charged lepton and a lightest neutralino ($\tilde{\chi}_1^0$), and the direct production of charginos ($\tilde\chi_1^\pm\tilde\chi_1^\mp$), each decaying into a $W$-boson, which decays in turn leptonically, and a $\tilde{\chi}_1^0$. The lightest neutralino is assumed to be the lightest supersymmetric particle (LSP). The analysis was optimized to target the experimentally challenging regions of the phase-space, called ``moderately compressed'', where $m(\tilde\ell)-m(\tilde\chi_1^0)$ and $m(\tilde\chi_1^\pm)-m(\tilde\chi_1^0)$ are of the order of the $W$-boson mass. No significant excess over the SM expectation was observed and exclusion limits on the masses of the searched particles were set. Slepton masses up to 150 GeV were excluded at 95% CL in the case of 50 GeV of difference between the slepton and the LSP masses, while chargino masses were excluded at 95% CL up to 140 GeV for 100 GeV of difference between the chargino and the LSP masses. The second search consists in a discovery prospect study of top-squark pair production ($\tilde t_1 \tilde t_1$), decaying in final states with two opposite-charge leptons, jets and missing transverse energy, in the ATLAS experiment during the High-Luminosity LHC. In this search $\sqrt{s}=14$ TeV and a total integrated luminosity of 3000 fb$^{-1}$ are considered. The study focuses on optimizing the analysis strategy already developed by a previous Run 2 search on the same channel, accounting for the expected increased statistics. Results show an improvement of the expected exclusion and discovery limits with respect to Run 2.