Simplest Little Higgs Revisited: Hidden Mass Relation, Unitarity and Naturalness

TL;DR

This paper revisits the Simplest Little Higgs model, deriving a key mass relation, analyzing unitarity bounds, and proposing a fine-tuning assessment method consistent with effective field theory, providing new tests and constraints for the model.

Contribution

It derives a mass relation between pseudo-axion and heavy top, establishes unitarity bounds, and introduces a fine-tuning analysis strategy applicable to Little Higgs models.

Findings

Derived a relation between $m_\eta$ and $m_T$ for EWSB consistency.

Established upper bounds on $m_T$, $m_\eta$, and $f$ from unitarity.

Mapped the allowed parameter space considering EWSB and unitarity constraints.

Abstract

We analyze the scalar potential of the Simplest Little Higgs (SLH) model in an approach consistent with the spirit of continuum effective field theory (CEFT). By requiring correct electroweak symmetry breaking (EWSB) with the $125\,\text{GeV}$ Higgs boson, we are able to derive a relation between the pseudo-axion mass $m_\eta$ and the heavy top mass $m_T$, which serves as a crucial test of the SLH mechanism. By requiring $m_\eta^2>0$ an upper bound on $m_T$ can be obtained for any fixed SLH global symmetry breaking scale $f$. We also point out that an absolute upper bound on $f$ can be obtained by imposing partial wave unitarity constraint, which in turn leads to absolute upper bounds of $m_T\lesssim 19\,\text{TeV}, m_\eta\lesssim 1.5\,\text{TeV}$ and $m_{Z'}\lesssim 48\,\text{TeV}$. We present the allowed region in the three-dimensional parameter space characterized by $f,t_\beta,m_T$, taking into account the requirement of valid EWSB and the constraint from perturbative unitarity. We also propose a strategy of analyzing the fine-tuning problem consistent with the spirit of CEFT and apply it to the SLH. We suggest that the scalar potential and fine-tuning analysis strategies adopted here should also be applicable to a wide class of Little Higgs and Twin Higgs models, which may reveal interesting relations as crucial tests of the related EWSB mechanism and provide a new perspective on assessing their degree of fine-tuning.