Gauge-invariant description of the Higgs resonance and its phenomenological implications

TL;DR

This paper develops a gauge-invariant framework for describing the Higgs particle as a bound state, revealing subtle deviations from the conventional elementary Higgs description and providing a consistent, physically meaningful spectral function.

Contribution

It introduces a perturbative, gauge-invariant bound state approach to the Higgs, connecting it to the elementary Higgs and analyzing deviations in scattering amplitudes.

Findings

Bound state Higgs properties match elementary Higgs at leading order.

Deviations in off-shell Higgs scattering amplitudes are quantified.

Gauge-invariant spectral function avoids unphysical artifacts.

Abstract

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.