Lightness of a Higgs Boson and Spontaneous CP-violation in the Lee Model: An Alternative Scenario

Based on the weakly-coupled two-Higgs-doublet model with spontaneous CP-violation (named Lee model) and the mechanism to generate the correlation between smallness of CP-violation and lightness of scalar mass, as we proposed earlier, we predicted a light CP-mixing scalar $\eta$ in which pseudoscalar component is dominant. It is a natural scenario in which $m_{\eta}\sim\mathcal{O}(10\textrm{GeV})\ll v$. Masses of all other scalars ($h$, $H$, $H^\pm$) should be around the electro-weak scale $v$. Among them, the 125 GeV Higgs ($h$) couplings are standard-model like, and the charged Higgs ($H^\pm$) mass should be around the heaviest neutral scalar ($H$) mass. We discussed all experimental constraints and showed that this scenario is still allowed by data. The strictest constraints come from the experiments of the flavor-changing processes and the EDM of lepton and neutron. We also discussed the future tests for this scenario. It is possible to discover the extra scalars or exclude this scenario at future colliders, especially at the LHC and $e^+e^-$ colliders with $\mathcal{O}(\textrm{ab}^{-1})$ luminosity. We also pointed out that the $Z$-mediated Higgs pair production via $e^+e^-\rightarrow h_ih_j$ ($h_i, h_j$ stand for two of the $\eta, h, H$) would be the key observable to confirm or exclude CP-violation in Higgs sector. The sensitivity to test this scenario is worth further studying in greater detail.