The $W^{\pm}W^{\pm}$ Scattering Process $-$ Theoretical Studies, Observation, Cross-section Measurement, and EFT Reinterpretation at $\sqrt{s}=13$ TeV with the ATLAS Detector

Vector Boson Scattering (VBS) processes involving massive, electroweak gauge bosons include the fundamental interactions of the triple and quartic electroweak self-couplings, and the exchange of the Higgs boson. Hence, the interplay of the gauge structure and the Electroweak Symmetry Breaking mechanism of the Standard Model (SM) shape this class of processes. Containing VBS contributions, the \ew production of two like-charge $W^\pm$ bosons in association with two jets ($W^\pm W^\pm jj$-EW6), can be employed to simultaneously probe these two fundamental components in the SM and beyond. This thesis presents comprehensive investigations of the electroweak $W^\pm W^\pm$ scattering process in the fully leptonic final state in proton-proton collisions at a centre-of-mass energy of $13$ TeV. An amount of $36.1$ fb$^{-1}$ of data, taken with the ATLAS detector, is utilised. The theoretical predictions of the $W^\pm W^\pm jj$ and, in particular, the $W^\pm W^\pm jj$-EW6 process are studied. Three different Monte-Carlo (MC) event generation programmes are employed: the PowhegBox programme at NLO QCD accuracy with the VBS approximation, the Sherpa programme in a LO multi-jet merged setup with up to three jets in the matrix-element, and the MadGraph5_aMC@NLO programme at LO accuracy. The predictions of the three nominal setups in the fiducial region are found to disagree beyond their uncertainty envelopes. Subsequently, their individual settings, such as the nominal renormalisation and factorisation scales in the matrix-element calculations and the parton shower configurations, are investigated. The first observation of the $W^\pm W^\pm jj$-EW6 process with data from the ATLAS experiment is established and published in Ref. [1] by rejecting the background-only hypothesis with a significance in experimental data of $6.5\sigma$. The expected significance, employing the prediction from Sherpa for the $W^\pm W^\pm jj$-EW6 process, is $4.4\sigma$. The fiducial cross-section of the $W^\pm W^\pm jj$-EW6 process as predicted by the SM is measured as $\left(2.89^{+0.59}_{-0.56}\right)$ fb, which, per construction of the analysis, includes the contribution of the interference with $W^\pm W^\pm jj$-EW4 process. This measurement is dominated by the statistical uncertainty of the data sample. All three studied theoretical predictions agree with the measured fiducial cross-section within the total uncertainty envelopes. The components of the analysis of the SM $W^\pm W^\pm jj$-EW6 process are reutilised for a reinterpretation of the experimental data in terms of an Effective Field Theory (EFT) model describing beyond SM extensions which generate anomalous quartic gauge couplings in the electroweak sector through operators of mass dimension eight [2,3]. For the first time, one-dimensional exclusion bounds on the coefficients of these operators are determined in the fully leptonic $W^\pm W^\pm jj$ final state with data from the ATLAS experiment, at the same time presenting the first overall dimension-eight EFT parameter exclusion bounds derived with $\sqrt{s}=13$ TeV data from the ATLAS experiment. Comparisons with existing results of all final states show that the obtained results are less stringent. The thesis' focus for this part lies in the investigation of the fundamental ingredients for the analysis of dimension-eight EFT models. The novel technique of amplitude decomposition is employed for the MC generation of the EFT signal contributions. It considerably improves the signal predictions and accuracy, as well as the simulation efficiency in the sensitive regions of the EFT contribution at high invariant masses. Moreover, along the profound validation of this new approach, it is found that the conventional simulation technique is insufficient in terms of phase space integration accuracy in the MC event generation. The application of the clipping unitarisation on the EFT signal contributions is thoroughly investigated, and exclusion limits obtained with this approach are derived, alongside the ununitarised exclusion bounds. For the first time in the $W^\pm W^\pm jj$ final state, exclusion bounds scanning multiple values of the clipping energy are shown in this thesis. Comparisons with unitarity bounds calculated from Ref. [4] shown that the obtained results do not yet reach physically reasonable regions in terms of unitarity. Moreover, exclusion bounds are studied, including the impact of dimension-six EFT operators on the \wz-EW4 background process. The results of this study constitute the first of their kind across final states and experiments. The inclusion of effects of dimension-six EFT operators with coefficients at their current best limit values yields no sizable effect on the exclusion bounds of the dimension-eight coefficients in the tested configuration.