Study of vector boson polarisation in the scattering of two W bosons with equal charge with the ATLAS detector at the LHC

One of the core elements of the Standard Model (SM) is the mechanism of Electroweak Sym- metry Breaking (EWSB), which is connected to the Higgs mechanism and the way in which particles gain mass. The study of Vector Boson Scattering (VBS) is is a way to explore this mechanism as the contributions of vertices including the Higgs boson avoid a violation of unitarity. The delicate cancellations required by the SM are more visible in the cross-section of scattering of longitudinally polarised vector bosons, which makes this channel also potentially sensitive to contributions of physics beyond the Standard Model. The model independent approach of Effective Field Theories aims to show the effect at low energies of unknown physics taking place at high energies by systematically extending to the Standard Model Lagrangian. This thesis discusses polarisation in the VBS of two positive W+ bosons in the fully leptonic decay channel. To validate the simulation data used for the study, the differential cross section as a function of the boson decay angle $\Theta$$_{W}^{*}$ is compared to the analytical function. A disagreement is observed and investigated further by considering the influence of different reference frames. The thesis also briefly discusses an EFT that adds one of three dimension eight operators to the Standard Model Lagrangian. It is shown that within the simulation of the model these only affect vertices with specific polarizations as expected.