Little hierarchy, little higgses, and a little symmetry

Little Higgs theories are an attempt to address the "little hierarchy problem," i.e., the tension between the naturalness of the electroweak scale and the precision electroweak measurements showing no evidence for new physics up to 5-10 TeV. In little Higgs theories, the Higgs mass-squareds are protected at one-loop order from the quadratic divergences. This allows the cutoff of the theory to be raised up to similar to10 TeV, beyond the scales probed by the current precision data. However, strong constraints can still arise from the contributions of the new TeV scale particles which cancel the one-loop quadratic divergences from the standard model fields, and hence re-introduces the fine-tuning problem. In this paper we show that a new symmetry, denoted as T-parity, under which all heavy gauge bosons and scalar triplets are odd, can remove all the tree-level contributions to the electroweak observables and therefore makes the little Higgs theories completely natural. The T-parity can be manifestly implemented in a majority of little Higgs models by following the most general construction of the low energy effective theory h la Callan, Coleman, Wess and Zumino. In particular, we discuss in detail how to implement the T-parity in the littlest Higgs model based on SU(5)/SO(5). The symmetry breaking scale f can be even lower than 500 GeV if the contributions from the higher dimensional operators due to the unknown UV physics at the cutoff are somewhat small. The existence of T-parity has drastic impacts on the phenomenology of the little Higgs theories. The T-odd particles need to be pair-produced and will cascade down to the lightest T-odd particle (LTP) which is stable. A neutral LTP gives rise to missing energy signals at the colliders which can mimic supersymmetry. It can also serve as a good dark matter candidate.