Constraints on Little Higgs with Fully-Radiative Electroweak Symmetry Breaking

In a recent paper, we introduced a new Little Higgs model, which contains the gauge structure $SU(2)^3\times U(1)$, embedded in an approximate global $SO(5)\times SO(5)$ symmetry. After breaking to the standard model, $SU(2)_L \times U(1)_Y$, this produces two heavy $Z^\prime$ bosons and two heavy $W^{\prime\pm}$ bosons, along with a single Standard Model-like Higgs scalar. The unique feature of the model was that it was possible to obtain electroweak symmetry breaking and a light Higgs mass entirely from perturbative loop contributions to the Higgs effective potential. In this paper we consider the electroweak constraints on this model, including tree and loop contributions to the universal oblique and non-oblique parameters, tree-level corrections to the $ZWW$ vertex, and tree and loop level corrections to $Zb\bar{b}$. The most significant corrections are positive tree-level corrections to $\hat{S}$ and negative fermion-loop corrections to $\hat{T}$, which require that the scale for the global symmetry breaking be $\gtrsim2$ TeV, depending on the top-quark mixing parameter and the extra gauge couplings. In addition, the loop corrections to $Zb\bar{b}$ contain a divergence that must be absorbed into the coefficient of a new operator in the theory. The finite part of this $Zb\bar{b}$ correction, however, is negligible.