Total and Differential Cross-Section Measurement and Interpretation of $W^\pm W^\pm$ Scattering in Effective Field Theories with the Run 2 Data of the ATLAS Experiment

Vector boson scattering (VBS) is an essential process to probe the details of electroweak symmetry breaking in the Standard Model of Particle Physics. It is sensitive to the for now last extension of this very successful model: the Higgs boson and its underlying mechanism which plays a crucial role in the quartic gauge boson scattering. For this purpose, the $W^\pm W^\pm$jj final state is analysed with full Run~2 data of $139\,\text{fb}^{-1}$ from the ATLAS experiment at a centre-of-mass energy $\sqrt{s} = 13$\,TeV at the LHC. Two different signal definitions are investigated: electroweak (EW) $W^\pm W^\pm$jj with the focus on VBS and the inclusive $W^\pm W^\pm$jj signal definition which is gauge invariant separable from other processes also at NLO. After the observation of the EW $W^\pm W^\pm$jj process by both the ATLAS and CMS experiments the details of electroweak symmetry breaking are studied now in more detail. It is the first detailed study of the $W^\pm W^\pm$jj final state with the ATLAS experiment.\\ The cross-section for EW $W^\pm W^\pm$jj is measured to be $2.88 \pm ^{0.22} _{0.21} \text{(stat.)} \pm ^{0.20} _{0.18} \text{(syst.) fb}$ and for inclusive $W^\pm W^\pm$jj a cross-section of $3.35 \pm ^{0.22} _{0.22} \text{(stat.)} \pm ^{0.21} _{0.19} \text{(syst.) fb}$ is found. They are both compatible with the Standard Model prediction.\\ Differential cross-sections in variables sensitive to the characteristics of VBS and effective field theories (EFT) are derived with the likelihood-based unfolding approach for the number of gap jets $N_{\text{gapJets}}$, the Zeppenfeld variable of the third jet $\xi_{\mathrm{j}_3}$, the invariant mass of the tagging jets $m_{\mathrm{jj}}$, the invariant mass of the two charged leptons $m_{\ell\ell}$ and the transverse mass $m_{\mathrm{T}}$. In general, good agreement with the theory predictions is found. The largest discrepancy is found for $310 \leq m_{\mathrm{T}} <410$\,GeV for inclusive $W^\pm W^\pm$jj where more events are observed than expected with a local (global) significance of 3.1\,$\sigma$ (2.5\,$\sigma$).\\ Limits on EFT parameters, modelling anomalous quartic gauge boson couplings with dimension-eight operators, are set for unclipped and clipped EFT predictions also near the unitarization bound. Overall, the limited number of collision events is the dominant source of uncertainty, followed by modelling uncertainties of the signal and the $\text{W}^\pm$Zjj background.