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.
Highlights
The perturbative treatment of the Higgs boson is highly successful in order to describe high-energy processes at the LHC
The definition of electroweak observables, e.g., the mass and decay width of the Higgs, as well as the computation of cross sections are commonly derived in terms of properties of the elementary fields of the standard model Lagrangian
Viewing the right-hand side of Eq (2) as an expansion in the fluctuations over the characteristic scale of electroweak physics and ignoring the unimportant constant term, we find that at nontrivial leading order in the expansion parameter φ=v the properties of the gauge-invariant operator jφj2 are described by the gauge-dependent elementary Higgs field h
Summary
Both groups are broken to a global diagonal subgroup SUð2Þgauge × SUð2Þglobal → SUð2Þdiag The fact that these groups coincide allows a one-to-one mapping of gauge-invariant bound state operators and elementary fields within the electroweak standard model at leading order in the FMS formalism.. In particular the results of the gauge-variant n-point functions of the elementary fields computed in common gauges will be of central importance in the FMS approach Taking all such terms appearing on the right-hand side of the FMS expansion into account will allow us to enhance usual perturbative calculations to a gauge-independent framework operating on in principle nonperturbative bound states. We test as to whether the perturbative treatment of the right-hand side of the FMS expansion is able to capture all relevant information of the bound state operator or under which circumstances nonperturbative effects might spoil the perturbative treatment
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