Little Higgs and Custodial SU(2)

TL;DR

The paper constructs a little Higgs model with custodial SU(2) as an approximate symmetry by gauging SU(2)$_r$ in an SO(5)–based Minimal Moose. Through collective symmetry breaking and TeV-scale vector bosons and top partners, it stabilizes the weak scale with a breaking scale $f \approx 700$ GeV while remaining consistent with precision electroweak constraints, thanks to custodial protection and a two-Higgs-doublet low-energy sector. It predicts a spectrum featuring $W'$, $B'$, $t'$ around a few TeV and a light Higgs typically below $250$ GeV, with collider-accessible signs at the LHC. The analysis highlights the interplay between oblique and non-oblique effects, the role of the Higgs sector in $T$–parameter constraints, and mechanisms (e.g., Ω plaquettes) to manage triplet vevs, illustrating the viability of natural TeV-scale completions within precision bounds.

Abstract

In this note we present a little Higgs model that has custodial SU(2) as an approximate symmetry. This theory is a simple modification of the ``Minimal Moose'' with SO(5) global symmetries protecting the Higgs mass. This allows for a simple limit where TeV physics makes small contributions to precision electroweak observables. The spectrum of particles and their couplings to Standard Model fields are studied in detail. At low energies this model has two Higgs doublets and it favours a light Higgs from precision electroweak bounds, though for different reasons than in the Standard Model. The limit on the breaking scale, f, is roughly 700 GeV, with a top partner of 2 TeV, W' and B' of 2.5 TeV, and heavy Higgs partners of 2 TeV. These particles are easily accessible at hadron colliders.