Renormalization-Group-Improved Effective Potential for the MSSM Higgs Sector with Explicit CP Violation

We perform a systematic study of the one-loop renormalization-group-improved effective potential of the minimal supersymmetric extension of the Standard Model (MSSM), including CP violation induced radiatively by soft trilinear interactions related to squarks of the third generation. We calculate the charged and neutral Higgs-boson masses and couplings, including the two-loop logarithmic corrections that arise from QCD effects, as well as those associated with the top- and bottom-quark Yukawa couplings. We also include the potentially large two-loop non-logarithmic corrections induced by one-loop threshold effects on the top- and bottom-quark Yukawa couplings, due to the decoupling of the third-generation squarks. Within this minimal CP-violating framework, the charged and neutral Higgs sectors become intimately related to one another and therefore require a unified treatment. In the limit of a large charged Higgs-boson mass, $M_{H^{\pm}} \gg M_Z$, the lightest neutral Higgs boson resembles that in the Standard Model (SM), and CP violation occurs only in the heavy Higgs sector. Our analysis shows that sizeable radiative effects of CP violation in the Higgs sector of the MSSM may lead to significant modifications of previous studies for Higgs-boson searches at LEP~2, the Tevatron and the LHC. In particular, CP violation could enable a relatively light Higgs boson to escape detection at LEP~2.