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

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 GeV Higgs boson, we are able to derive a relation between the pseudo-axion mass m_η and the heavy top mass m_T, which serves as a crucial test of the SLH mechanism. By requiring m_η^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≲ 19 TeV, m_η≲ 1.5 TeV and m_Z'≲ 48 TeV. We present the allowed region in the three-dimensional parameter space characterized by f,t_β,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.