Collective Quartics and Dangerous Singlets in Little Higgs

TL;DR

This paper investigates the conditions under which little Higgs models can generate a collective Higgs quartic coupling, highlighting the necessity of certain scalar fields and identifying potential issues with dangerous singlets that undermine stability.

Contribution

It establishes the necessary scalar field conditions for collective quartic couplings in little Higgs models and reveals the problem of dangerous singlets that can reintroduce fine-tuning.

Findings

A collective quartic in one-Higgs models requires an electroweak triplet.

In two-Higgs models, a triplet or singlet scalar is needed for a collective quartic.

Some little Higgs theories contain dangerous singlets that undermine radiative stability.

Abstract

Any extension of the standard model that aims to describe TeV-scale physics without fine-tuning must have a radiatively-stable Higgs potential. In little Higgs theories, radiative stability is achieved through so-called collective symmetry breaking. In this letter, we focus on the necessary conditions for a little Higgs to have a collective Higgs quartic coupling. In one-Higgs doublet models, a collective quartic requires an electroweak triplet scalar. In two-Higgs doublet models, a collective quartic requires a triplet or singlet scalar. As a corollary of this study, we show that some little Higgs theories have dangerous singlets, a pathology where collective symmetry breaking does not suppress quadratically-divergent corrections to the Higgs mass.