Partially Natural Two Higgs Doublet Models

TL;DR

This paper explores models where a second light scalar doublet is naturally light due to a discrete symmetry, despite the general expectation that additional scalars imply worse fine-tuning, involving new vectorlike fermions and complex vacuum structures.

Contribution

It introduces partially natural Two Higgs Doublet Models with discrete symmetries that relate the second scalar's mass to the Standard Model Higgs, challenging conventional fine-tuning expectations.

Findings

Models require new vectorlike fermions at the electroweak scale.

The models feature a rich electroweak vacuum structure.

The mechanism does not protect small CP-odd Higgs mass in certain supersymmetry scenarios.

Abstract

It is possible that the electroweak scale is low due to the fine-tuning of microscopic parameters, which can result from selection effects. The experimental discovery of new light fundamental scalars other than the Standard Model Higgs boson would seem to disfavor this possibility, since generically such states imply parametrically worse fine-tuning with no compelling connection to selection effects. We discuss counterexamples where the Higgs boson is light because of fine-tuning, and a second scalar doublet is light because a discrete symmetry relates its mass to the mass of the Standard Model Higgs boson. Our examples require new vectorlike fermions at the electroweak scale, and the models possess a rich electroweak vacuum structure. The mechanism that we discuss does not protect a small CP-odd Higgs mass in split or high-scale supersymmetry-breaking scenarios of the MSSM due to an incompatibility between the discrete symmetries and holomorphy.