Spontaneous $CP$-violation in the simplest little Higgs model and its future collider tests: The scalar sector

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

Figure 1

The $h_1\to 2h_2$ decay branching ratio distribution in the $s_{\theta }-m_2$ plane with $f=8\mathrm{TeV}$. From left to right, we choose $t_{\beta }=1$, 3, 6, respectively.

Figure 2

Dominant Feynman diagrams contributing to the EDM of electron and quarks and the CEDM of quarks. $F$ running in the loop includes $t$, $T$, $D$, $S$.

Figure 3

Additional Feynman diagrams contributing to the neutron EDM.