Collective Quartics and Dangerous Singlets in Little Higgs
  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. 
Martin Schmaltz, Jesse Thaler