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Little Hierarchy, Little Higgses, and a Little Symmetry

Hsin-Chia Cheng, Ian Low

TL;DR

This work introduces a discrete symmetry, $T$-parity, within little Higgs frameworks to eliminate tree-level electroweak constraints and preserve naturalness. By implementing $T$-parity through CCWZ-based constructions in both the minimal $SU(3)$ moose and the $SU(5)/SO(5)$ littlest Higgs models, the authors show how heavy gauge bosons and scalar triplets become $T$-odd while Standard Model fields stay $T$-even, thereby suppressing precision-weak corrections. To maintain naturalness, the fermion sectors are completed into complete multiplets, or embedded via CCWZ, which cancels dangerous two-loop quadratic divergences and yields consistent top-quark Yukawa couplings with heavy partners. Phenomenologically, $T$-parity implies pair production of $T$-odd states and a stable LTP (often a neutral $B'$), leading to missing-energy signatures and potential dark matter candidates, with collider signals resembling those of SUSY or UED. The framework thus broadens the viable parameter space of little Higgs theories and provides a systematic path to natural electroweak breaking in symmetric coset spaces.

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.

Little Hierarchy, Little Higgses, and a Little Symmetry

TL;DR

This work introduces a discrete symmetry, -parity, within little Higgs frameworks to eliminate tree-level electroweak constraints and preserve naturalness. By implementing -parity through CCWZ-based constructions in both the minimal moose and the littlest Higgs models, the authors show how heavy gauge bosons and scalar triplets become -odd while Standard Model fields stay -even, thereby suppressing precision-weak corrections. To maintain naturalness, the fermion sectors are completed into complete multiplets, or embedded via CCWZ, which cancels dangerous two-loop quadratic divergences and yields consistent top-quark Yukawa couplings with heavy partners. Phenomenologically, -parity implies pair production of -odd states and a stable LTP (often a neutral ), leading to missing-energy signatures and potential dark matter candidates, with collider signals resembling those of SUSY or UED. The framework thus broadens the viable parameter space of little Higgs theories and provides a systematic path to natural electroweak breaking in symmetric coset spaces.

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 -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.

Paper Structure

This paper contains 5 sections, 45 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. An $SU(3)$ minimal moose model with $T$ parity
  3. An $SU(5)/SO(5)$ model with $T$ parity
  4. Little Higgs phenomenology with $T$-parity
  5. Conclusions

Figures (2)

  • Figure 1: The two-loop diagram with the quartic divergence.
  • Figure 2: The diagrams responsible for cancelling the quartic divergence. Diagram $(a)$ is there only for the $U(1)_Y$ gauge boson since $\chi$ is an $SU(2)_W$ singlet and doesn't couple to $W$ and $Z$ bosons directly.