The Higgs boson from an extended symmetry

TL;DR

The paper investigates whether a naturally light Higgs can emerge from an extended symmetry, focusing on a minimal SO(5)/SO(4) description of the Higgs–top sector. It analyzes the EWSB sector, electroweak precision tests, naturalness, and the implications of extending the third generation, finding significant tension for the minimal realizations with EWPT and B‑physics. It then evaluates non‑minimal constructions (Little Higgs, holographic 5D) and a perturbative variant, concluding that these options offer limited relief and that the fundamental question of whether the Higgs is elementary or composite remains to be decided experimentally. The work highlights how precision data constrain symmetry‑based Higgs sectors and outlines avenues for future model building and LHC tests.

Abstract

The variety of ideas put forward in the context of a "composite" picture for the Higgs boson calls for a simple and effective description of the related phenomenology. Such a description is given here by means of a "minimal" model and is explicitly applied to the example of a Higgs-top sector from an SO(5) symmetry. We discuss the spectrum, the ElectroWeak Precision Tests, B-physics and naturalness. We show the difficulty to comply with the different constraints. The extended gauge sector relative to the standard SU(2)xU(1), if there is any, has little or no impact on these considerations. We also discuss the relation of the "minimal" model with its "little Higgs" or "holographic" extensions based on the same symmetry.

Figures (4)

• Figure 1: Quadratically divergent gauge-boson contributions to the renormalization of $A$. If the Higgs boson is composite, the scalar form factor cuts off the divergence in the first diagram. The second diagram is related to the first one by gauge invariance, and hence will be cut off at a comparable scale.
• Figure 2: The minimal model in the ST plane, including the contributions (\ref{['meff']}) ('from scalars') and (\ref{['Scutoff']}) ('from cutoff'). The dashed arrow shows an extra positive contribution to $T$ needed to make the model consistent with the data. In Section \ref{['one-loop']} we discuss if such $\delta T>0$ may come from an extended 3rd generation. Experimental contours taken from the LEPEWWG ST plot EWWG.
• Figure 3: ($f=500$ GeV) The masses of the light and heavy scalars in the perturbative minimal model, Eq. (\ref{['masses']}). The region above the dashed line corresponds to $z>1/2$ and is relatively disfavored by Naturalness, see Eq. (\ref{['ftAA']}).
• Figure 4: ($f=500$ GeV) The mixing angle $\alpha$ between the heavy and light scalars, see Eq. (\ref{['scalars']}), and the effective EWPT mass as defined by (\ref{['meff']}) with $\Lambda$ replaced by $m_{\sigma}$. The region above the dashed line has the same meaning as in Fig. \ref{['mass-plot']}.