Observation and Measurement of the Electroweak $W^{\pm}W^{\pm}jj$ Process in Proton-Proton Collisions at $\sqrt{s}$ = 13 TeV with the ATLAS Detector

Measurements of the production of $W$ boson pairs through vector boson scattering are a vital test for the electroweak sector of the Standard Model (SM) and the mechanism of the electroweak symmetry breaking. They could detect small deviations from the predictions through which new physics could manifest itself. In the SM the couplings of the gauge bosons among themselves and with the Higgs boson are precisely balanced such that divergences in the $WW$ scattering amplitude are avoided, and small deviations from the predictions could lead to significant effects. This thesis presents the first measurement with the ATLAS detector at the LHC of the electroweak production of two $W$ bosons with the same electric charge, in the signature with two charged leptons, missing transverse energy and two jets. The process is observed for the first time at ATLAS with a significance of 6.5$\sigma$ using data recorded in proton-proton collisions at $\sqrt{s}$ = 13 TeV corresponding to an integrated luminosity of 36.1 fb$^{-1}$, and its cross section in a defined fiducial phase space is measured to be $\sigma^{\text{fid}}_{\text{meas}}$ = $\text{2.89}^{+\text{0.51}}_{-\text{0.48}} \text{(stat)} \, \, ^{+\text{0.29}}_{-\text{0.28}} \text{(syst)} \, \, \text{fb}$. The requirement of two same-charge $W$ bosons leads on one hand to a better suppression of background processes, among them the $WW$ production induced by the strong interaction. On the other hand it is experimentally more challenging due to the contributions from opposite-charge dilepton production, where the charge of one electron is wrongly reconstructed. This thesis details the estimation of this background, whose contribution in the signal region kinematic phase space is determined with a relative uncertainty of 15%. A precise estimation of this background requires a good knowledge of the probability of reconstructing an electron with the wrong charge sign. A measurement of this quantity is presented in this thesis, and the probabilities vary from less than 1% to about 10% for increasing transverse momentum and pseudorapidity of the electrons. Correction factors are provided for the modelling of this effect in simulation, which deviate from unity by up to 30% for wrongly reconstructed electrons, and are determined with relative systematic uncertainties between 2% and 20%. The contained amount of data limits the precision and sensitivity of the measurement. However, vector boson scattering is one of the most favourable ways to assess clues on the theoretical extension of the SM in a model independent way, and larger datasets at higher energies will make the inner mechanism of the electroweak symmetry breaking and possible new physics more accessible.