  We investigate the phenomenological consequences of a strict gauge-invariant
formulation of the Higgs particle. This requires a description of the
observable scalar particle in terms of a bound state structure. Although this
seems to be at odds with the common treatment of electroweak particle physics
at first glance, the properties of the bound state can be described in a
perturbative fashion due to the Fr\"ohlich-Morchio-Strocchi (FMS) framework. In
particular a relation between the bound-state Higgs and the elementary Higgs
field is obtained within $R_{\xi}$ gauges such that the main quantitative
properties of the conventional description reappear in leading order of the FMS
expansion. Going beyond leading order, we show that the pole structure of the
elementary and the bound-state propagator coincide to all orders in a
perturbative expansion. However, slight deviations of scattering amplitudes
containing off-shell Higgs contributions can be caused by the internal bound
state structure. We perform a consistent perturbative treatment to all orders
in the FMS expansion to quantify such deviations and demonstrate how
gauge-invariant expressions arrange in a natural way at the one-loop level.
This also provides a gauge-invariant Higgs spectral function which is not
plagued by positivity violations or unphysical thresholds. Furthermore, the
mass extracted from the gauge-invariant bound state is only logarithmically
sensitive to the scale of new physics at one-loop order in contrast to its
elementary counterpart.
