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Any extension of the standard model that aims to describe TeV-scale physicswithout fine-tuning must have a radiatively-stable Higgs potential. In littleHiggs theories, radiative stability is achieved through so-called collectivesymmetry breaking. In this letter, we focus on the necessary conditions for alittle Higgs to have a collective Higgs quartic coupling. In one-Higgs doubletmodels, a collective quartic requires an electroweak triplet scalar. Intwo-Higgs doublet models, a collective quartic requires a triplet or singletscalar. As a corollary of this study, we show that some little Higgs theorieshave dangerous singlets, a pathology where collective symmetry breaking doesnot suppress quadratically-divergent corrections to the Higgs mass.

Collective Quartics and Dangerous Singlets in Little Higgs