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

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 $h_{2}ZZ$ and $h_1{h}_2{Z}^{\prime }$ 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.

31 pages, 3 figures, almost everywhere refined: abstract, introduction, and conclusions updated; the improved formalism added; details on quantum corrections added; experimental constaints on f and EDM added; more discussions about future tests updated in which the conclusions changed comparing with the previous version; references updated; more typos and errors corrected