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We proposed the spontaneous CP-violation in the Simplest Little Higgs model.In this model, the pseudoscalar field can acquire a nonzero vacuum expectedvalue. It leads to a mixing between the two scalars with different CP-charge,which means spontaneous CP-violation happens. It is also a connection betweencomposite Higgs mechanism and CP-violation. Facing the experimentalconstraints, the model is still alive for both scenarios in which the extrascalar appears below or around the electro-weak scale. We also discussed thefuture 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 thetext) which provides new motivations on future $e^+e^-$ and $pp$ colliders. Italso shows the importance of the vector-vector-scalar- andvector-scalar-scalar-type vertices to discover CP-violation effects in thescalar sector.

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