Simplest little Higgs model revisited: Hidden mass relation, unitarity, and naturalness

Abstract

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 2 η > 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.

Phenomenology of a little Higgs pseudoaxion

“…The parametrization of these Goldstone fields actually has some freedom; we refer the reader to Ref. [19] for an explanation. In the SLH, under the full gauge group SUð3Þ C × SUð3Þ L × Uð1Þ X , Φ 1 and Φ 2 have quantum number ð1; 3Þ − 1 3 .…”

“…We now turn to the scalar potential. Using a CEFT approach and combining tree-level 5 and one-loop contributions, the scalar effective potential in the SLH is calculated to be [19]…”

“…Before starting the phenomenological analysis in the SLH, it is important to notice that there exist certain constraints that we have to take into account [19].…”

“…In particular, the pseudoaxion mass m η is determined from the following hidden mass relation derived in Ref. [19]:…”

“…According to the hidden mass relation derived in Ref. [19], the η mass m η is anticorrelated with the top partner mass m T , which is in turn related to the degree of fine-tuning in the model. The hidden mass relation is derived within an approach consistent with the continuum effective field theory (CEFT) and does not rely on the assumption on the contribution from the physics at the cutoff.…”