Solving the Wrong Hierarchy Problem

TL;DR

This paper introduces a novel approach to the hierarchy problem using parity- or $ ext{Z}_2$-symmetric theories with multiple Higgs vacua, linking scalar masses to dimensional transmutation and making specific predictions for particle masses.

Contribution

It proposes a new solution to the hierarchy problem by connecting scalar masses to matter content via discrete symmetries, reducing fine-tuning and predicting new particles.

Findings

Predicts scalar color octets with masses 9-200 TeV.

Postdicts the top Yukawa within 1 sigma of current measurements.

Provides a solution to the strong CP problem with testable predictions.

Abstract

Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and $\mathbb{Z}_2$-symmetric theories where the Standard Model Higgs potential has two vacua. The parity or $\mathbb{Z}_2$ copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs mass by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. We show this mechanism postdicts the top Yukawa to be within $1 \sigma$ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV.