T Parity and the Littlest Higgs

TL;DR

This work constructs $T$-parity invariant extensions of the littlest Higgs model using linear representations, organized as cosets $SU(5)_l\times SO(5)_r/SO(5)_v$ and $SU(5)_l\times SU(5)_r/SO(5)_v$, to provide UV-complete-like frameworks that replicate the littlest Higgs phenomenology at low energy. By treating the full symmetry linearly, the authors present UV-amenable variants with heavy scalar and gauge sectors decoupled near $\sim 10$ TeV while keeping a single light Higgs doublet and TeV-scale top-sector dynamics, all within a $T$-parity context that avoids large EW corrections. They analyze fermion embeddings, mirror fermions, and top Yukawas to maintain naturalness and cancel quadratic divergences, and discuss constraints from four-fermion operators, ultimately finding $f>450$ GeV from electroweak data. The paper also compares CCWZ-based constructions with the linear-extension approach, arguing for similar low-energy spectra and dark matter prospects through the lightest $T$-odd particle.

Abstract

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 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)_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.