# Precision Tests and Fine Tuning in Twin Higgs Models

## TL;DR

This paper evaluates the fine-tuning and electroweak precision compatibility of Twin Higgs models, especially composite realizations, showing they can achieve moderate tuning with new particles potentially detectable at future colliders.

## Contribution

It provides a detailed analysis of fine-tuning in Twin Higgs models and assesses their electroweak precision fit, highlighting the role of infrared effects and the viability of composite realizations.

## Key findings

- Moderate tuning (~5-10%) is sufficient for compatibility with electroweak data.
- Colored states with masses 3-5 TeV are consistent with current bounds and out of LHC reach.
- Future 100 TeV colliders could discover these states, testing the models' validity.

## Abstract

We analyze the parametric structure of Twin Higgs (TH) theories and assess the gain in fine tuning which they enable compared to extensions of the Standard Model with colored top partners. Estimates show that, at least in the simplest realizations of the TH idea, the separation between the mass of new colored particles and the electroweak scale is controlled by the coupling strength of the underlying UV theory, and that a parametric gain is achieved only for strongly-coupled dynamics. Motivated by this consideration we focus on one of these simple realizations, namely composite TH theories, and study how well such constructions can reproduce electroweak precision data. The most important effect of the Twin states is found to be the infrared contribution to the Higgs quartic coupling, while direct corrections to electroweak observables are sub-leading and negligible. We perform a careful fit to the electroweak data including the leading-logarithmic corrections to the Higgs quartic up to three loops. Our analysis shows that agreement with electroweak precision tests can be achieved with only a moderate amount of tuning, in the range 5-10\%, in theories where colored states have mass of order 3-5 TeV and are thus out of reach of the LHC. For these levels of tuning, larger masses are excluded by a perturbativity bound, which makes these theories possibly discoverable, hence falsifiable, only at a future 100 TeV collider.