T Parity and the Littlest Higgs

We construct T-parity invariant extensions of the littlest Higgs model, inwhich 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 symmetrybreaking pattern SU(5)_l x H_r / SO(5), where H_r can be SO(5) or other largersymmetry groups. The structure of the models in the SU(5)_l sector is identicalto the littlest Higgs model based on SU(5)/SO(5). Since the full symmetry groupis realized linearly, these models can be thought of as possible UV extensionsof the T-invariant model using non-linear representations via CCWZ, with whomthey share similar low energy phenomenology. We also comment on how to avoidconstraints from four-fermion operators on T-invariant models with or withoutCCWZ construction. The electroweak data therefore place a very weak bound onthe symmetry breaking scale, f > 450 GeV.Comment: 13 pages, no figure; v2: typos corrected. comments added to clarify eqs. (9) and (32