Electroweak hierarchy from conformal and custodial symmetry -- "Custodial Naturalness"

TL;DR

This paper proposes 'Custodial Naturalness', a framework combining classical scale invariance and custodial symmetry to naturally explain the electroweak scale hierarchy, predicting new particles like a Z' boson and a dilaton.

Contribution

It introduces a minimal model extending the Standard Model with a new scalar and gauge symmetry, solving the hierarchy problem via radiative symmetry breaking and pNGB Higgs.

Findings

Predicts a heavy Z' boson detectable in future experiments.

Forecasts a light dilaton close to invisible in current searches.

Provides a parameter-efficient model matching SM complexity.

Abstract

I introduce the idea of "Custodial Naturalness" to explain the origin of the electroweak (EW) scale hierarchy. Custodial Naturalness is based on classical scale invariance as well as an extension of the Standard Model (SM) scalar sector custodial symmetry. In a minimal realization, this requires a single new complex scalar field charged under a new U(1) gauge symmetry, which partially overlaps with $B-L$. Classical scale invariance and the high-scale scalar sector 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 pseudo-Nambu-Goldstone boson (pNGB) of the spontaneously broken SO(6) custodial symmetry. The minimal realization of Custodial Naturalness has the same number of parameters as the SM and predicts testable new physics in the form of a heavy $Z'$ as well as a light but close-to invisible dilaton.