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Institute
In this thesis we examine the vector boson scattering (VBS) process \(\mathrm p \mathrm p \to \mathrm e^+ \nu_\mathrm e\mu^-\bar\nu_\mu\mathrm j\mathrm j +X\) (short: \(\mathrm W^+\mathrm W^-\) scattering) at NLO accuracy in two experimental setups by performing a Monte Carlo analysis of a \(13\,\mathrm{TeV}\) LHC run. \(\mathrm W^+\mathrm W^-\) scattering shows similarities and differences compared to the scattering of other vector bosons. We present a detailed description of the types of appearing subprocesses and background processes. We give insight into our code which solves the problems we are faced within \(\mathrm W^+\mathrm W^-\) scattering. This is especially the presence of the Higgs-boson resonance in the fiducial phase-space region. Particular attention is dedicated to the permutation of resonances. The integrated signal cross section at LO \(\mathcal O(\alpha^6)\) amounts to \(2.6988(3)\,\mathrm{fb}\) and \(1.5322(2)\,\mathrm{fb}\), respectively, in the two experimental setups. The LO QCD-induced background of \(\mathcal O(\alpha_\mathrm s^2\alpha^4)\) amounts to \(6.9115(9)\,\mathrm{fb}\) and \(1.6923(3)\,\mathrm{fb}\). The EW corrections to the signal are \(-11.4\%\) and \(-6.7\%\), the QCD corrections amount to \(-5.2\%\) and \(-23.0\%\). The EW corrections to the background are \(-8.3\%\) and \(-5.3\%\), the QCD corrections amount to \(-30.3\%\) and \(-77.6\%\). Our results for the QCD corrections and the QCD-induced background include a large uncertainty from varying the renormalisation and factorisation scale, and we discuss improvements for future calculations. We show the differential cross sections with unique features of \(\mathrm W^+\mathrm W^-\) scattering compared to other VBS processes and investigate in particular the subprocess of Higgs-boson production by using a modified version of our setups.