Observation of Electroweak Same-Charge $W^{\pm} W^{\pm} jj$ Production at $\sqrt{s}=13$ TeV with the ATLAS Detector at the LHC

The Standard Model of particle physics provides a gauge invariant description of the electroweak and strong interactions between elementary particles. Particle masses are generated through spontaneous breaking of the $SU(2)_L\times U(1)_Y$ gauge symmetry, which also results in an additional boson, the Higgs-boson. In the Higgs-less Standard Model, the scattering of longitudinally polarized $W^{\pm}$-bosons violates unitarity at energies of approximately 1 TeV. For energies beyond that threshold, the $WW$ production rate would exceed the collision rate, which is unphysical. Contributions of the Higgs-boson are expected to unitarize the vector boson scattering (VBS) cross section. Thus, VBS measurements provide a powerful means to investigate Standard Model predictions and the electroweak symmetry breaking mechanism. Across all VBS channels, electroweak same-charge $W^{\pm} W^{\pm}$ production promises the highest ratio of signal to irreducible backgrounds. All diagrams that, at leading order, involve purely electroweak couplings, $\alpha_{\text{ew}}$, and are of the order $\mathcal{O}(\alpha_{\text{ew}}^6)$ are considered as electroweak production. Due to the small production cross sections, high center-of mass energies and luminosities are necessary to observe VBS processes; these measurements have only become accessible at the LHC. At the LHC, electroweak $W^{\pm} W^{\pm}$ production can be studied in proton-proton collisions at a center-of-mass energy of 13 TeV. This thesis is based on 36.1 $\text{fb}^{-1}$ of data recorded in 2015 and 2016 by the ATLAS detector. VBS events show a special topology with two final state quarks with large rapidity and two centrally decaying gauge bosons. In this analysis, fully leptonic production is considered, where the $W^{\pm}$-bosons decay into lepton-neutrino pairs. The quarks appear as particle jets in the detector. Neutrinos escape the detector without interaction, however the reconstruction of the total transverse neutrino momentum is possible using momentum conservation. The selected final state consists of at least two jets, high missing transverse momentum due to the neutrinos, and two same-charge electrons or muons. Leptonically decaying $\tau$-leptons are not included. Signal event candidates are selected in a VBS-like phase space requiring a high invariant mass $m_\text{jj}$ of the leading and subleading jets and a large angular separation between them. A profile likelihood method is implemented to measure the electroweak $W^{\pm} W^{\pm}$ fiducial cross section and determine the statistical significance of the observed data with respect to the background-only expectation using the differential $m_\text{jj}$ distribution. The highest background contributions originate in $W^{\pm}Z^0$ production as well as events with mis-reconstructed or mis-identified leptons caused by detector inefficiencies. A total of 122 signal candidate events are observed, where 118 events are expected. The highest signal-to-background ratio is reached in the high-$m_\text{jj}$ region above 1500 GeV. Electroweak, leptonic $W^{\pm} W^{\pm}$ production is significantly observed with a significance of 6.7 $\sigma$. An expected significance of 4.6 $\sigma$ is derived. The measured fiducial cross section amounts to $\left(2.94~ \pm~ ^{0.62} _{0.56}\right)$ fb. At leading order, the SHERPA generator predicts a fiducial cross section of $\left(2.01~ \pm~ ^{0.34} _{0.24}\right)$ fb. The measured and predicted cross sections agree within their uncertainties.