Variations of little Higgs models and their electroweak constraints

We calculate the tree-level electroweak precision constraints on a wide class of little Higgs models including variations of the littlest Higgs SU(5)/SO(5), SU(6)/Sp(6), and $\mathrm{SU}{(4)}^{4}/\mathrm{SU}{(3)}^{4}$ models. By performing a global fit to the precision data we find that for generic regions of the parameter space the bound on the symmetry breaking scale f is several TeV, where we have kept the normalization of f constant in the different models. For example, the ``minimal'' implementation of SU(6)/Sp(6) is bounded by $fg3.0\mathrm{TeV}$ throughout most of the parameter space, and $\mathrm{SU}{(4)}^{4}/\mathrm{SU}{(3)}^{4}$ is bounded by ${f}^{2}\ensuremath{\equiv}{f}_{1}^{2}{+f}_{2}^{2}g(4.2\mathrm{TeV}{)}^{2}.$ In certain models, such as $\mathrm{SU}{(4)}^{4}/\mathrm{SU}{(3)}^{4},$ a large f does not directly imply a large amount of fine-tuning since the heavy-fermion masses that contribute to the Higgs boson mass can be lowered below f for a carefully chosen set of parameters. We also find that for certain models (or variations) there exist regions of parameter space in which the bound on f can be lowered into the range 1\char21{}2 TeV. These regions are typically characterized by a small mixing between heavy and standard model gauge bosons and a small (or vanishing) coupling between heavy U(1) gauge bosons and light fermions. Whether such a region of parameter space is natural or not is ultimately contingent on the UV completion.