This Master's Thesis is composed of two contextually different parts, both related to the Vector Boson Scattering (VBS). The first, larger part, deals with measurement of polarized VBS. We used Phantom and MadGraph Monte-Carlo generators for this purpose. We performed comparison of predictions of those Monte-Carlo generators and validated Phantom, which is used as a leading Monte-Carlo generator throughout the work. The main part of the study aims at a development of the algorithm for the neutrino momentum reconstruction. We studied semi-leptonic channel ($pp\rightarrow WW\rightarrow\ell\nu jjjj$) and fully-leptonic channel ($pp\rightarrow WW\rightarrow\ell\nu\ell\nu jj$). We present the use of the MAOS algorithm for reconstruction of neutrino momenta in the fully-leptonic channel. We introduce two new discriminating variables, $p_{\text{T}}^{WW}$ in $\Delta\varphi_{\ell\ell}$, for the phase space discrimination in the fully-leptonic channel with longitudinal $W$ boson content. We performed a comparison of the predictions from the Delphes fast simulation to the full ATLAS simulation. The second part of the Master's Thesis deals with the uncertainty of the parton distribution function (PDF) in the VBS predictions. We present the calculations of the PDF uncertainty in the same sign fully-leptonic channel.
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