Implications of strict gauge invariance for particle spectra and precision observables

The discovery of the Higgs together with the excellent performance of the LHC allow to make precision tests of Brout-Englert-Higgs Physics, and especially its underlying field-theory. In this field theory strict gauge-invariance requires observable states to have a more involved structure than assumed in standard perturbation theory. This can lead to, likely rather very small, deviations in precision tests of the standard model. Here, the mechanism behind these deviations will be elucidated, and, as an example, its possible implications for the $R$ ratio at future linear colliders will be estimated.