The same-charged W± boson scattering is the first possibility to study the polarization in vector boson scattering (VBS). The Run 2 data recorded by the ATLAS collaboration at the LHC from 2015 to 2018 are examined for the polarization states of the scattered W± bosons.
In this thesis, the first experimental application of approximate polarized next-to-leading-order corrections on same-charged W± bosons scattering is achieved. These corrections employ state-of-the-art calculations of the polarized cross-sections and significantly improve the Standard Model prediction.
Based on the Standard Model prediction, deep neural networks (DNNs) are trained to study the W± boson polarization in the measured data. The DNNs are optimized for the polarization discrimination and validated against data in a control region. The decision-making of the DNNs is investigated to achieve a better understanding of the kinematic information learned by the networks. The DNN output for the measured data and the Standard Model prediction is analyzed by a profile likelihood fit to extract the significance and cross-section of the longitudinal polarization state. The likelihood fit requires the estimation of the theoretical uncertainty of the polarization states which is implemented in this thesis. Furthermore, a new strategy is developed to investigate and constrain the impact of these uncertainties. 
For the final application of the profile likelihood fit, a two-dimensional bin optimization algorithm is designed for the histograms of the DNN output to maximize the expected significance. The contribution of the W±W± scattering with at least one longitudinally polarized W± boson is measured with a significance of 3.4 σ and a fiducial cross-section of 1.04 ± 0.35 fb. Thus, this ATLAS analysis provides the first evidence for the longitudinal polarization in VBS. The measured fiducial cross-section is in agreement with the Standard Model prediction of 1.35 fb.
For the scattering of two longitudinally polarized W± bosons, a significance of 0.082 σ is observed. The corresponding fiducial cross-section is found to be smaller than 0.50 fb at 95% confidence level. This upper limit covers the Standard Model prediction of 0.33 fb and constraints the fiducial cross-sections predicted by alternative theories.