The Minimal Composite Higgs Model and Electroweak Precision Tests

TL;DR

This work tests the viability of the Minimal Composite Higgs Model (MCHM) against electroweak precision data by a complete holographic calculation of $Z\to b\bar{b}$ and $\Delta\rho$ in a 5D warped setup with $SO(5)/SO(4)$. The authors classify the relevant $3$-point form factors and map the results to the $\varepsilon_i$ formalism (including $\varepsilon_b$) to compare with LEP1/SLD data, finding that oblique corrections can be satisfied with modest tuning while the $Z\to b\bar{b}$ constraint is more significant. Consequently some fermionic resonances must lie near $\sim 4$ TeV (implying a few percent EW fine tuning), although other states such as a $Z'$ can be lighter in parts of parameter space. The work provides a fully calculable EWPT analysis within a UV-complete composite-Higgs framework and highlights avenues for extending beyond the minimal model to relax the $Zbb$ constraint.

Abstract

A complete analysis of the electroweak precision observables is performed within a recently proposed minimal composite Higgs model, realized as a 5-dimensional warped compactification. In particular, we compute Z->bb and the one-loop correction to the rho parameter. We find that oblique data can be easily reproduced without a significant amount of tuning in the parameters of the model, while Z->bb imposes a stronger constraint. As a consequence of the latter, some of the new fermionic resonances must have mass around 4 TeV, which corresponds to an electroweak fine tuning of a few percent. Other resonances, such as Z', can be lighter in sizeable portions of the parameter space. We discuss in detail the origin of the Z->bb constraint and we suggest several possible avenues beyond the minimal model for weakening it.

Figures (2)

• Figure 1: Diagrams in the 4D holographic theory that generate the correction to $Z\to b_L \bar{b}_L$ (a), and $\Delta\rho$ (b). A grey blob represents the 4D CFT dynamics or, equivalently, the 5D bulk.
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