The Advantages of Four Dimensions for Composite Higgs Models

TL;DR

This paper explores the relationship between 4d little Higgs models and 5d composite models, showing their equivalence through deconstruction, and analyzes their compatibility with experimental data, highlighting the viability of certain models.

Contribution

It demonstrates the equivalence of 4d and 5d composite Higgs models via deconstruction and compares their experimental viability, emphasizing the robustness of the Minimal Moose model.

Findings

Finiteness of the Higgs potential in 5d is due to collective symmetry breaking.

The Minimal Moose with custodial symmetry is viable without tuning.

The data constrains the Minimal Composite Higgs model more strongly.

Abstract

We examine the relationship between little Higgs and 5d composite models with identical symmetry structures. By performing an "extreme" deconstruction, one can reduce any warped composite model to a little Higgs theory on a handful of sites. This allows us to use 4d intuition and the powerful constraints of nonlinear sigma models to elucidate obscure points in the original setup. We find that the finiteness of the Higgs potential in 5d is due to the same collective symmetry breaking as in the little Higgs. We compare a 4d and a 5d model with the same symmetry to the data. Reviewing the constraints on models related to the Minimal Composite Higgs (hep-ph/0412089), we see that it has difficulty in producing acceptable values for S, T, and m_{top} simultaneously. By contrast, in a global analysis, the Minimal Moose with custodial symmetry is viable in a large region of its parameter space and suffers from no numeric tunings. We conjecture that this result is generic for 4d and 5d models with identical symmetries. The data will less strongly constrain the little theory.