Spontaneous violation of theCPsymmetry in the Higgs sector of the next-to-minimal supersymmetric model

Abstract

The spontaneous violation of $\mathrm{CP}$ symmetry in the next-to-minimal supersymmetric standard model (NMSSM) is investigated. It is found that the spontaneous violation of $\mathrm{CP}$ symmetry can occur in the Higgs sector of the NMSSM for a wide region of the parameter space of the model, at the 1-loop level where radiative corrections due to top quark and scalar-top quark loops are found to generate scalar-pseudoscalar mixings between the two Higgs doublets of the NMSSM. In our model, we assume that the masses of the left-handed and the right-handed scalar-top quarks are not degenerate. And we investigate our model anaytically: We derive analytical formulas of the 1-loop mass matrix for neutral Higgs bosons. We calculate the upper bound on the lightest neutral Higgs boson mass under the assumption. It is found to be about 140 GeV for our choice of parameter values in the presence of the spontaneous violation of $\mathrm{CP}$ symmetry in the NMSSM. Thus, the possibility of spontaneous violation of $\mathrm{CP}$ symmetry is not completely ruled out in the Higgs sector of the NMSSM if the masses of the left-handed and the right-handed scalar-top quarks are not degenerate. Further, the phenomenology of $K\ensuremath{-}\overline{K}$ mixing within the context of our model is studied. The lower bound on the $\mathrm{CP}$ violating phase in $K\ensuremath{-}\overline{K}$ mixing is found to increase if either $\mathrm{tan}\ensuremath{\beta}$ decreases or ${A}_{t}$ increases.