T parity and the littlest Higgs -: art. no. 067

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)(t) x H-r/SO(5), where H-r can be SO(5) or other larger symmetry groups. The structure of the models in the SU(5)1 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 greater than or equal to 450 GeV.