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 $\mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}^4/\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}^4$ 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 $f>\mathrm{}3.0\mathrm{}\mathrm{TeV}$ throughout most of the parameter space, and $\mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}^4/\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}^4$ is bounded by $f^2\equiv f_1^2{+f}_2^2>(4.2\mathrm{}\mathrm{TeV}{)}^2.$ In certain models, such as $\mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}^4/\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}^4,$ 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 1–2 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.