Electroweak hierarchy from conformal and custodial symmetry

TL;DR

This paper introduces 'Custodial Naturalness', a new approach explaining the electroweak scale's stability via conformal and custodial symmetries, predicting new particles like a heavy Z' and a light dilaton.

Contribution

It proposes a novel mechanism combining classical scale invariance and SO(6) custodial symmetry to address the hierarchy problem without extending the scalar sector beyond a single new scalar.

Findings

Predicts a heavy Z' boson with mass 4-100 TeV.

Identifies a light dilaton around 75 GeV.

Provides a minimal parameter set matching the Standard Model.

Abstract

We present "Custodial Naturalness" as a new mechanism to explain the separation between the electroweak (EW) scale and the scale of potential ultraviolet completions of the Standard Model (SM). We assume classical scale invariance as well as an extension of the SM scalar sector custodial symmetry to $\mathrm{SO}(6)$. This requires a single new complex scalar field charged under a new $\mathrm{U}(1)_\mathrm{X}$ gauge symmetry which partially overlaps with $B-L$. Classical scale invariance and the high-scale scalar sector $\mathrm{SO}(6)$ custodial symmetry are radiatively broken by quantum effects that generate a new intermediate scale by dimensional transmutation. The little hierarchy problem is solved because the Higgs boson arises as an elementary (i.e. non-composite) pseudo-Nambu-Goldstone boson (pNGB) of the spontaneously broken $\mathrm{SO}(6)$ custodial symmetry. The minimal setting has the same number of parameters as the SM and predicts new physics in the form of a heavy $Z'$ with fixed couplings to the SM and a mass of $m_{Z'}\approx4-100\,\mathrm{TeV}$, as well as a light but close-to invisible dilaton with a mass $m_{h_\Phi}\approx75\,\mathrm{GeV}$.