Testing the operation and response with cosmics of the Micromegas detector for the NSW upgrade of the ATLAS experiment and study of the Higgs boson production in the $WW^*\rightarrow\ell\nu\ell\nu$ decay channel through VBF mechanism

This thesis is divided into two main parts with the focus on the ATLAS experiment at the Large Hadron Collider at CERN. The first part is subject of the most important upgrade for the Run-3 data taking period, the New Small Wheel, and the one of its two constituents, the resistive-strip Micromegas detectors. The detector geometry and its implementation in the software being a key component for the reconstruction of both simulated and real data is presented. Subsequently, the tools that were developed, and are currently in use, for the offline data quality assessment are discussed too. After the installation of the two wheels in ATLAS, series of tests using muons in combination with a radioactive source were carried out for New Small Wheel Micromegas detectors with the final electronics integrated on them. The performance, in terms of efficiency and spatial resolution, of one of the Micromegas detectors was studied with the main results concluding this first part. The second part concerns the measurement of fiducial cross sections of the Higgs boson produc- tion via the vector-boson-fusion in the $H \rightarrow WW^∗$ decay channel studying the fully leptonically final states. The analysis uses the full Run-2 proton collision data at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector, corresponding to an integrated luminosity of 139 fb$^{−1}$. Particular detail is given to the data-driven estimation of the background originating from jets that are misidentified as prompt leptons. Studies conducted with the aim to insert systematic uncertain- ties to the data-driven method are presented. These include the investigation of dependence on the pileup contamination and on properties characterizing the production mode, such as the presence of jets. Finally, a closure test was performed in order to demonstrate the robustness of the data-driven technique.