Phenomenology of the littlest Higgs model withT-parity

Little Higgs models offer an interesting approach to weakly coupled electroweak symmetry breaking without fine-tuning. The original little Higgs models were plagued by strong constraints from electroweak precision data which required a fine-tuning to be reintroduced. An economical solution to this problem is to introduce a discrete symmetry (analogous to $R$-parity of SUSY) called $T$-parity. $T$-parity not only eliminates most constraints from electroweak precision data, but it also leads to a promising dark matter candidate. In this paper we investigate the dark matter candidate in the littlest Higgs model with $T$-parity. An upper bound on the symmetry breaking scale $f\lesssim 1.8\mathrm{T}\mathrm{e}\mathrm{V}$ naturally arises from calculating the relic density. We begin the study of the LHC phenomenology of the littlest Higgs model with $T$-parity. We find that the model offers an interesting collider signature that has a generic missing energy signal which could “fake” SUSY at the LHC. We also investigate the properties of the heavy partner of the top quark which is common to all littlest Higgs models, and how its properties are modified with the introduction of $T$-parity. We include an appendix with a list of Feynman rules specific to the littlest Higgs with $T$-parity to facilitate further study.