Spontaneous CP-violation in the Simplest Little Higgs Model

We proposed how spontaneous CP-violation can be generated in the simplest little Higgs model in this talk. Comparing with the original paper, both formalism and phenomenology are updated. The model is still alive facing the collider and electric dipole moment (EDM) measurements. Strictest constraint comes from LHC $Z'$ direct search, which leads to $f\gtrsim8~\textrm{TeV}$. Higgs measurements also set strict constraint on the scalar mixing angle, if the Higgs rare decay channel is open. EDM measurements still set weak constraints for this model, even after the recent ACME updated measurement on electron's EDM. In this talk, we also discussed the test of CP-violation in the scalar sector, through the interactions between scalars and gauge bosons.