# Spontaneous CP-violation in the Simplest Little Higgs Model and its Future Collider Tests: the Scalar Sector

## TL;DR

This paper explores spontaneous CP-violation in the Simplest Little Higgs model, highlighting how scalar mixing occurs and proposing future collider experiments to detect CP-violation effects in the scalar sector.

## Contribution

It introduces a novel mechanism for spontaneous CP-violation within the Simplest Little Higgs model and discusses potential collider signatures for future experiments.

## Key findings

- Spontaneous CP-violation occurs via pseudoscalar vacuum expectation value.
- The model remains viable under current experimental constraints.
- Future collider measurements can probe CP-violation through specific scalar vertices.

## Abstract

We proposed the spontaneous CP-violation in the Simplest Little Higgs model. In this model, the pseudoscalar field can acquire a nonzero vacuum expected value. It leads to a mixing between the two scalars with different CP-charge, which means spontaneous CP-violation happens. It is also a connection between composite Higgs mechanism and CP-violation. Facing the experimental constraints, the model is still alive for both scenarios in which the extra scalar appears below or around the electro-weak scale. We also discussed the future collider tests on CP-violation in the scalar sector through measuring $h_2ZZ$ and $h_1h_2Z'$ vertices (see the definitions of the particles in the text) which provides new motivations on future $e^+e^-$ and $pp$ colliders. It also shows the importance of the vector-vector-scalar- and vector-scalar-scalar-type vertices to discover CP-violation effects in the scalar sector.