Explicit $CP$ Violation of the Higgs Sector in the Next-to-Minimal Supersymmetric Standard Model

We study the explicit $CP$ violation of the Higgs sector in the minimal supersymmetric standard model with a gauge singlet Higgs field. The magnitude of $CP$ violation is discussed in the limiting cases of $x\gg v_1,\ v_2$ and $x\ll v_1,\ v_2$, where $x$ and $v_{1,2}$ denote VEV of singlet and doublet Higgs scalars, respectively. Our numerical predictions of the electric dipole moments of electron and neutron lie around the present experimental upper limits. It is found that the large $CP$ violation effect reduces the magnitude of the lightest Higgs boson mass in the order of a few ten GeV.