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We propose spontaneous CP violation in the simplest little Higgs model. In this model, the pseudoscalar field can acquire a nonzero vacuum expectation value. This leads to a mixing between the two scalars with different CP charge, which means that spontaneous CP violation occurs. It is also a connection between the composite Higgs mechanism and CP violation. Facing the experimental constraints, the model is still viable for both scenarios in which the extra scalar appears below or around the electroweak scale. We also discuss the future collider tests of CP violation in the scalar sector through measuring h₂ZZ and h₁h₂Z^' vertices (see the definitions of the particles in the text), which provide new motivations for future e^+e^- and pp colliders. This also shows the importance of the vector-vector-scalar- and vector-scalar-scalar-type vertices in discovering CP-violation effects in the scalar sector.
Ying-nan Mao (Mon,) studied this question.