Higgs Boson Decays in the Minimal Supersymmetric Standard Model with Radiative Higgs Sector CP Violation

We re-evaluate the decays of the Higgs bosons in the minimal supersymmetric standard model (MSSM) where the tree-level CP invariance of the Higgs potential is explicitly broken by the loop effects of the third-generation squarks with CP-violating soft-breaking Yukawa interactions. This study is based on the mass matrix of the neutral Higgs bosons that is valid for arbitrary values of all the relevant MSSM parameters. It extends the previous work considerably by including neutral Higgs-boson decays into virtual gauge bosons and those into top-squark pairs, by implementing squark-loop contributions to the two-gluon decay channel, and by incorporating the decays of the charged Higgs boson. The constraints from the electron electric dipole moment on the CP phases are also discussed. We find that the branching fractions of both the neutral and charged Higgs-boson decays and their total decay widths depend strongly on the CP phases of the top (and bottom) squark sectors through the loop-induced neutral Higgs boson mixing as well as the direct couplings of the neutral Higgs bosons to top squark pairs.