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# Title: Little Hierarchy, Little Higgses, and a Little Symmetry

Authors: Hsin-Chia Cheng, Ian Low (Harvard University)
Abstract: 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 measurements showing no evidence for new physics up to 5-10 TeV. In little Higgs theories, the Higgs mass-squareds are protected to the one-loop order from the quadratic divergence. This allows the cutoff to be raised up to \~10 TeV, beyond the scales probed by the precision data. However, strong constraints can still arise from the contributions of the new TeV scale particles 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 a 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 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.
 Comments: 20 pages, 2 figures, RevTeX; v2: Yukawa sector in the SU(5)/SO(5) model slightly modified. Also added comments on the Dirac mass term for the fermionic doublet partner; v3: clarifying comments on the modified Yukawa sector. version to appear on JHEP Subjects: High Energy Physics - Phenomenology (hep-ph) Journal reference: JHEP 0408:061,2004 DOI: 10.1088/1126-6708/2004/08/061 Cite as: arXiv:hep-ph/0405243 (or arXiv:hep-ph/0405243v3 for this version)

## Submission history

From: Hsin-Chia Cheng [view email]
[v1] Mon, 24 May 2004 21:44:32 GMT (35kb)
[v2] Tue, 20 Jul 2004 14:53:09 GMT (36kb)
[v3] Mon, 20 Sep 2004 15:50:41 GMT (36kb)
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