Evidence for Scattering of Electroweak Gauge Bosons in the $W^\pm Z$ Channel with the ATLAS Detector at the Large Hadron Collider

The Standard Model (SM) is the fundamental theory describing elementary particles and their main interactions at typical energy scales at collider experiments, the electromagnetic, the weak, and the strong interactions. The more complex underlying structure describing the weak and the strong interactions in the SM compared to the electromagnetic interaction necessitates direct three-point and four-point interactions among the mediators of the weak and strong interactions, called gauge bosons. Such self-interactions do not exist for the gauge boson of the electromagnetic interaction, the photon. While the three-point interaction was studied in detail in earlier collider experiments, the four-point interaction is a fundamental prediction of the SM, which was not observed for the weak interaction when starting this study. One process, where both the three-point as well as the four-point interactions contribute is the scattering of electroweak gauge bosons $W^\pm, Z, \gamma$ also referred to as vector boson scattering (VBS). In the SM, this scattering is mediated by gauge boson self-interactions, or via the exchange of a Higgs boson. The scattering contributions mediated by a Higgs boson are sensitive to the properties of the Higgs boson and the details of the mechanism in which the $W^\pm$ and $Z$ bosons acquire their masses, called electroweak symmetry breaking. At hadron colliders such as the Large Hadron Collider (LHC), VBS is observable in a final state with the decay products of two gauge bosons in combination with two jets. These jets have a distinct signature allowing for good suppression of backgrounds and consequently for studies of the complex final state despite the low cross-sections. The first evidence for a VBS process was presented based on the Run 1 dataset alone by the ATLAS collaboration in the $W^\pm W^\pm \to W^\pm W^\pm$ channel in the fully leptonic final state. The CMS collaboration published the first observation of VBS in the same channel using data from 2015 and 2016 of Run 2, which was later confirmed by the ATLAS collaboration with contributions by the author, e.g. in the modelling of $W^\pm Z$ background processes and associated uncertainties. The second boson channel for which VBS was observed was the $W^\pm Z/\gamma \to W^\pm Z$ boson channel in the fully leptonic final state. This observation was published by the ATLAS collaboration with significant contributions by the author. The studied dataset was collected with the ATLAS detector at a centre-of-mass energy $\sqrt{s}=13\,\mathrm{TeV}$ during 2015 and 2016 of Run 2 of the LHC and amounts to an integrated luminosity of $36.1\,\mathrm{fb}^{-1}$. In this study, the dataset was re-analysed following the same overall approach but with improvements in several key aspects. A comprehensive overview of available setups for reliable simulations of the signal process is presented. In a modelling study of the available setups, modelling issues in the parton shower simulation of SHERPA and earlier versions of PYTHIA observed in earlier studies are confirmed. The best matrix-element accuracies in available setups are leading-order for the full VBS signal process and next-to-leading-order in the VBF approximation. For upcoming analyses, a leading-order calculation of the full process including an additional QCD emission merged with parton shower simulations is found to be most promising, before full next-to-leading order calculations become available for all boson channels in VBS. Additional emphasis is set on the modelling of backgrounds, mainly $W^\pm Z$ diboson production in association with additional QCD emissions as well as the experimental background due to misidentified leptons. A data-driven approach is applied and studied in detail for a reliable estimate of the latter background. Significant improvements to the estimate, e.g. in the form of additional corrections, are found via dedicated tests of the self-consistency of the approach using simulations. Machine-learning algorithms in the form of Boosted-Decision-Trees (BDT) are trained and optimized for improved separation of the background and signal processes. Evidence for the signal process is found with a significance of $3.44\,\sigma$ using the profile likelihood method in a binned maximum-likelihood fit. The fiducial cross-section is measured to be $\sigma_\text{obs} = 1.41 \pm {} ^{0.46} _{0.40}\, \text{(stat)} \pm {} ^{0.38} _{0.28}\, \text{(theo)} \pm {}^{0.13} _{0.13} \,\text{(sys)} \, \mathrm{fb}$, which is in good agreement with the leading-order SM prediction of $ \sigma_\text{pred} = 1.33 \pm {}^{0.15} _{0.14} \,\mathrm{fb}$.