Higgs-Mediated Electric Dipole Moments in the MSSM: An Application to Baryogenesis and Higgs Searches

We perform a comprehensive study of the dominant two- and higher-loop contributions to the $^{205}$Tl, neutron and muon electric dipole moments induced by Higgs bosons, third-generation quarks and squarks, charginos and gluinos in the Minimal Supersymmetric Standard Model (MSSM). We find that strong correlations exist among the contributing CP-violating operators, for large stop, gluino and chargino phases, and for a wide range of values of $\tan\beta$ and charged Higgs-boson masses, giving rise to large suppressions of the $^{205}$Tl and neutron electric dipole moments below their present experimental limits. Based on this observation, we discuss the constraints that the non-observation of electric dipole moments imposes on the radiatively-generated CP-violating Higgs sector and on the mechanism of electroweak baryogenesis in the MSSM. We improve previously suggested benchmark scenarios of maximal CP violation for analyzing direct searches of CP-violating MSSM Higgs bosons at high-energy colliders, and stress the important complementary r\^ole that a possible high-sensitivity measurement of the muon electric dipole moment to the level of $10^{-24}$ $e$ cm can play in such analyses.