Electroweak Vector Boson Scattering at the LHC after the Higgs Discovery

The Large Hadron Collider (LHC) has greatly enlarged our understanding of electroweak symmetry breaking by the discovery of a Higgs boson compatiblewith the Standard Model (SM) of Particle Physics. The LHC was guaranteed tocontribute to this understanding before it was switched on because the processof scattering of the longitudinal modes of the electroweak gauge bosons would have entered a strong interaction regime in the LHC energy reach without thepresence of a light Higgs particle. There was for the first time evidence of this scattering process in the 2012 LHC data. Delicate cancellations in its otherwise rising cross section makes this process an ideal telescope for searches of physics beyond the SM (BSM). Some prime examples will be shown as well as methods to theoretically consistently describe these searches in a model-independent way