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We propose a mechanism in which the lightness of Higgs boson and thesmallness of CP-violation are correlated based on the Lee model, namely thespontaneous CP-violation two-Higgs-doublet-model. In this model, the mass ofthe lightest Higgs boson $m_h$ as well as the quantities $K$ and $J$ are$\propto t_{\beta}s_{\xi}$ in the limit $t_{\beta}s_{\xi}\rightarrow0$ (seetext for definitions of $t_\beta$ and $\xi$), namely the CP conservation limit.Here $K$ and $J$ are the measures for CP-violation effects in scalar and Yukawasectors respectively. It is a new way to understand why the Higgs bosondiscovered at the LHC is light. We investigated the important constraints fromboth high energy LHC data and numerous low energy experiments, especially themeasurements of EDMs of electron and neutron as well as the quantities ofB-meson and kaon. Confronting all data, we found that this model is stillviable. It should be emphasized that there is no standard-model limit for thisscenario, thus it is always testable for future experiments. In order to pindown Lee model, it is important to discover the extra neutral and charged Higgsbosons and measure their CP properties and the flavor-changing decays. At theLHC with $\sqrt{s}=14\textrm{TeV}$, this scenario is favored if there issignificant suppression in the $b\bar{b}$ decay channel or any vector bosonfusion (VBF), V+H production channels. On the contrary, it will be disfavoredif the signal strengths are standard-model-like more and more. It can be easilyexcluded at $(3\sim5)\sigma$ level with several $\textrm{fb}^{-1}$ at future$e^+e^-$ colliders, via the accurately measuring the Higgs boson productioncross sections.

Lightness of Higgs Boson and Spontaneous CP Violation in Lee Model