T parity and the littlest Higgs

We construct T-parity invariant extensions of the littlest Higgs model, in which only linear representations of the full symmetry group are employed, without recourse to the non-linear representations introduced by Coleman, Callan, Wess, and Zumino (CCWZ). These models are based on the symmetry breaking pattern SU(5)l x Hr/SO(5), where Hr can be SO(5) or other larger symmetry groups. The structure of the models in the SU(5)l sector is identical to the littlest Higgs model based on SU(5)/SO(5). Since the full symmetry group is realized linearly, these models can be thought of as possible UV extensions of the T-invariant model using non-linear representations via CCWZ, with whom they share similar low energy phenomenology. We also comment on how to avoid constraints from four-fermion operators on T-invariant models with or without CCWZ construction. The electroweak data therefore place a very weak bound on the symmetry breaking scale, f ≥ 450 GeV. (author)