Abstract
The Higgs boson sector of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) is considered with explicit and spontaneous CP violation. With the mixing between CP-even and CP-odd Higgs states caused by the non-zero CP phase, the Higgs spectrum and coupling to weak gauge boson are calculated. Full one loop contribution from third generation quark and squark are taken into account by using effective potential method. Logarithmic enhanced two loop contribution is considered by using renormalization group method. Acceptable region in parameter space is considered with three conditions, the LEP limit, global minimum and positivity of Higgs mass square. Numerical results are presented with three scenarios, which focus on the comparison between acceptable region with and without the inclusion of RG improvement and acceptable region with and without non-zero CP phase. It shows that the RG improvement and CP non-conserving effect can provide substantial modification to the acceptable region in parameter space depending on the scenarios.