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 SU(4)/SU(3). 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 > 3.0 TeV throughout most of the parameter space, and SU(4)/SU(3) is bounded by f ≡ f 1 + f 2 > (4.2 TeV). In certain models, such as SU(4)/SU(3), a large f does not directly imply a large amount of fine tuning since the heavy fermion masses that contribute to the Higgs 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 the light fermions. Whether such a region of parameter space is natural or not is ultimately contingent on the UV completion.