Simultaneous production of two bosons in the ATLAS experiment at the LHC

This thesis explores diboson and vector boson scattering (VBS) processes, focusing on the simultaneous production of a $W^{\pm}$ and a $Z$ gauge boson from proton-proton collisions at the Large Hadron Collider (LHC) at CERN. For this study, data, which were collected from 2015 to 2018 by the ATLAS experiment and correspond to an integrated luminosity of $140\:fb^{-1}$ at a center-of-mass $13\:TeV$, are used. These two processes provide the ideal ground for searches for physics beyond the Standard Model (SM) through deviations from the predicted vector boson self-couplings. These deviations could result in additional contributions to triple and quartic gauge couplings. The way to study such deviations is through an Effective Field Theory (EFT). The use of an EFT allows for systematic exploration of higher-dimensional operators. The relevant operators to our processes are the dimension-6 and dimension-8 operators. The potential effect of various dimension-6 and dimension-8 operators on the $W^{\pm}Z$ diboson and VBS productions are studied. Finally, the $95\%$ Confidence Level (CL) expected and observed limits for the dimension-8 operators that affect the $WZjj$ VBS process, are extracted.