Study of Polarization Fractions in the Scattering of Massive Gauge Bosons $W^\pm Z \to W^\pm Z$ with the ATLAS Detector at the Large Hadron Collider

The scattering of massive electroweak gauge bosons is an essential process for the study of the mechanism of electroweak symmetry breaking. Especially the scattering of longitudinally polarized bosons is sensitive to the way in which electroweak symmetry is broken and extensions of the Standard Model, since it would violate unitarity without e.$\,$g. a Standard Model Higgs boson canceling the divergences. At the Large Hadron Collider this process is measureable in the final states with decay products of two massive gauge bosons and two additional jets $VVjj$. To extract longitudinal polarization modes in leptonic final states originating from a $W^\pm Z$ boson pair, different methods to obtain simulated events of known boson polarization are studied and validated in different phase spaces. The approach of factorizing the decay of the bosons and the production with defined helicity utilizing the narrow-width approximation is favored over the commonly used reweighting procedure due to methodical deficiencies after applying selection criteria. For the former the production process of bosons is simulated using WHIZARD and MadGraph5_aMC@NLO. The tool WZdecay is developed to simulate the leptonic decay according to the helicity of the boson and the validity of the applied approximation is tested. The sensitivity of different observables to the polarization of the bosons are studied in the $W^+ Zjj$ final state at a center-of-mass energy of $13\,$TeV. The highest sensitivity of different to the polarization of the $W^+$ boson is found in the pseudorapidity as well as the transverse momentum of the charged lepton assigned to the $W^+$ boson and the scalar sum of this transverse momentum and the missing transverse momentum. For the $Z$ boson the cosine of its decay angle and the scalar sum of the transverse momenta of the lepton pair assigned to the $Z$ boson are most sensitive.