Study of Different Unfolding Methods of Kinematic Distributions of the WZ$\,\to\,$WZ Scattering with Data and Simulations of the ATLAS Detector at the LHC

It is analyzed in this work which unfolding methods are suited for the P-value calculation in statistical tests. It is analyzed for distributions of Vector Boson Scattering in the channel WZ$\,\to\,$WZ for fully leptonic final states. WZ$\,\to\,$WZ scattering is predicted by the most successful model of particle physics, the Standard Model of Particle Physics - but was not measured yet. It is scheduled to record $100~\mathrm{fb}^{-1}$ with the ATLAS detector in Run$~$2 at LHC. With that integrated luminosity an observation of that process, via a cross section measurement, is expected. The distributions of the transverse mass of the WZ system $M_T(WZ)$ and the transverse momentum of the Z boson $p_T^Z$ which are sensitive to deviations of the WZ$\,\to\,$WZ scattering from the Standard Model are analyzed in this work. For comparisons between data and theory predictions detector effect have to be considered, for which the theory has to be folded or the data has to be unfolded. In this study, no significant advantages of using the unfolding approach instead of the folding approach have been found for computer based statistical tests. If data and theory distributions should be compared independently from detector effects then unfolding is necessary. For visual comparisons regularization, like in 'Bayesian Iterative Unfolding', can be useful, for computerized calculations the unfolding method 'Matrix Inversion' has the most advantages.