Precise predictions for polarised vector-boson scattering at the LHC

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The first two runs of the Large Hadron Collider (LHC) have confirmed the validity of the Standard Model (SM) of elementary particle physics as an impressively accurate description of fundamental interactions. The discovery of the Higgs boson in 2012 and the subsequent measurement of many of its couplings have established the Higgs mechanism as an appropriate description of electroweak symmetry breaking (EWSB) at the accessible energies. Nonetheless, the dynamics underlying the EWSB, including the nature of the Higgs boson itself, are still unknown. Understanding the origin of EWSB is one of the most important problems in fundamental physics and may be deeply intertwined with other big open questions, such as the origin of the matter-antimatter asymmetry in the universe and the pattern of fermion masses and mixings.In order to investigate the EWSB mechanism, it is necessary to scrutinise the dynamics of the scalar sector of the SM. A particular role in this respect is played by the longitudinal degrees of freedom of the vector bosons, which are generated from the scalar sector via EWSB. A class of processes that is exceptionally sensitive to deviations from the SM is the scattering of longitudinal vector bosons. These processes respect unitarity only owing to the gauge structure of the SM and the presence of the Higgs boson. As a consequence, even small deviations from the SM, i.e. anomalous couplings, will lead to measurable effects.During run 2 of the LHC the scattering of unpolarised vector bosons has been measured in various channels with leptonically decaying vector bosons, and limits on anomalous couplings have been set. In addition first measurements of VBS with semileptonic final states have been attempted. Run 3 of the LHC, which shall start in 2022, will allow for polarisation measurements in vector-boson scattering, and at the high-luminosity LHC the scattering of longitudinal vector bosons is expected to be measured with an accuracy of 2-3 standard deviations. For a proper analysis and interpretation of these upcoming measurements adequate theoretical predictions are required.The electroweak corrections to the scattering of unpolarised vector bosons in the leptonic channels turned out to be surprisingly large, at the level of 15% for cross sections and more than 40% in distributions. The corrections to polarised VBS are expected to be of similar size, but could differ substantially in detail.The central goal of this research proposal is the computation of precise theoretical predictions for the scattering of polarised vector bosons at the LHC. This shall be done for the scattering of W and Z bosons and the scattering of like-sign W bosons including their leptonic decays. In addition we aim at predictions for VBS in the semileptonic channel, where a W or Z boson decays hadronically and a W boson leptonically.