Exploring Fine-tuning of the Next-to-Minimal Composite Higgs Model

TL;DR

This paper analyzes the fine-tuning in the Next-to-Minimal Composite Higgs Model, comparing it to the minimal version, and assesses the impact of future collider measurements on the model's naturalness and dark matter potential.

Contribution

It provides a detailed quantification of fine-tuning in the NMCHM using a new measure, and compares it with the minimal model under future experimental scenarios.

Findings

Little difference in fine-tuning between NMCHM and minimal model.

Future collider measurements have limited impact on fine-tuning.

The scalar as a dark matter candidate is naturally stabilized by a Z2 symmetry.

Abstract

We perform a detailed study of the fine-tuning of the two-site, 4D, Next-to-Minimal Composite Higgs Model (NMCHM), based on the global symmetry breaking pattern $SO(6)\rightarrow SO(5)$. Using our previously-defined fine-tuning measure that correctly combines the effect of multiple sources of fine-tuning, we quantify the fine-tuning that is expected to result from future collider measurements of the Standard Model-like Higgs branching ratios, in addition to null searches for the new resonances in the model. We also perform a detailed comparison with the Minimal Composite Higgs Model, finding that there is in general little difference between the fine-tuning expected in the two scenarios, even after measurements at a high-luminosity, 1 TeV linear collider. Finally, we briefly consider the relationship between fine-tuning and the ability of the extra scalar in the NMCHM model to act as a dark matter candidate, finding that the realisation of a $Z_2$ symmetry that stabilises the scalar is amongst the most natural regions in the parameter space, regardless of future collider measurements.