Spontaneous CP violation in the triplet extended supersymmetric standard model

We find that, at the one-loop level, the spontaneous CP violation is possible in a supersymmetric standard model that has an extra chiral Higgs triplet with hypercharge Y=0. At the tree level, this triplet-extended supersymmetric standard model (TESSM) cannot have any reasonable parameter spaces for the spontaneous CP violation, because the experimental constraints on the coupling coefficient of the neutral Higgs boson to a pair of $Z$ bosons exclude them. By contrast, at the one-loop level, we find that there are experimentally allowed parameter regions, where the spontaneous CP violation may take place. The mass of the lightest neutral Higgs boson in the TESSM in this case may be as large as about 100 GeV, by considering the one-loop contribution due to the top quark and squark loops.