A "Littlest Higgs" Model with Custodial SU(2) Symmetry

TL;DR

The work introduces a custodial SU(2)–symmetric littlest Higgs model built on the coset SO(9)/(SO(5)×SO(4)), yielding a single light Higgs doublet alongside TeV-scale singlets and triplets. Through an extended top sector and a near-oblique electroweak analysis, the authors show that one-loop quadratic divergences are canceled by symmetry while precision constraints remain mild, allowing a wide range of Higgs masses consistent with naturalness. The model uses a carefully arranged gauge structure and spectrum to suppress custodial SU(2) violation, with heavy vector bosons and fermions contributing modestly to S and T parameters. A stable vacuum can be achieved by augmenting the top sector or introducing operators that correct the singlet/triplet mass structure, making the scenario viable and testable at the LHC. Overall, the paper demonstrates that a custodial-SU(2)–preserving littlest Higgs with a minimal scalar sector can reconcile naturalness with precision data and yield distinctive TeV-scale phenomenology.

Abstract

In this note, a ``littlest higgs'' model is presented which has an approximate custodial SU(2) symmetry. The model is based on the coset space $SO(9)/(SO(5)\times SO(4))$. The light pseudo-goldstone bosons of the theory include a {\it single} higgs doublet below a TeV and a set of three $SU(2)_W$ triplets and an electroweak singlet in the TeV range. All of these scalars obtain approximately custodial SU(2) preserving vacuum expectation values. This model addresses a defect in the earlier $SO(5)\times SU(2)\times U(1)$ moose model, with the only extra complication being an extended top sector. Some of the precision electroweak observables are computed and do not deviate appreciably from Standard Model predictions. In an S-T oblique analysis, the dominant non-Standard Model contributions are the extended top sector and higgs doublet contributions. In conclusion, a wide range of higgs masses is allowed in a large region of parameter space consistent with naturalness, where large higgs masses requires some mild custodial SU(2) violation from the extended top sector.