# A symmetry for $\epsilon_K$

## TL;DR

This paper proposes a symmetry-based mechanism within a composite Higgs framework to suppress CP violation in kaon mixing, predicts a new light scalar, and explores the model's phenomenological viability.

## Contribution

It introduces a novel symmetry in composite Higgs models that naturally suppresses $ ext{CP}$ violation in $K-ar K$ mixing and predicts a new light scalar state.

## Key findings

- $ ext{CP}$ violation in kaon mixing can be suppressed by the proposed symmetry.
- The model predicts a new singlet scalar lighter than the Higgs.
- Parameter space allows for correct top mass and symmetry breaking conditions.

## Abstract

We show a symmetry that, in the context of a composite Higgs with anarchic flavor, can suppress the dominant CP violating contributions to $K-\bar K$ mixing. Based on previous extensions of SU(3)$_c$, we consider the case in which the composite sector has a global SU(6) symmetry, spontaneously broken to a subgroup containing SU(3)$\times$SU(3). We show that the interactions with the Standard Model can spontaneously break the remaining symmetry to the diagonal subgroup, identified with the group of color interactions, and naturally suppress $\epsilon_K$. We consider this scenario in the context of the Minimal Composite Higgs Model based on SO(5)/SO(4) for the electroweak sector. By working in the framework of 2-site models, we compute the scalar potential, determine the conditions for a successful breaking of the symmetries and calculate the spectrum of lightest states. We find that $\epsilon_K$ can be suppressed and the top mass reproduced for a large region of the parameter space where the symmetries are dynamically broken. Besides other new resonances, the model predicts the presence of a new singlet scalar state, generally lighter than the Higgs, that could have evaded detection at colliders.