CP VIOLATION IN MULTI-HIGGS SUPERSYMMETRIC MODELS

We consider supersymmetric extensions of the standard model with two p airs of Higgs doublets. We study the possibility of spontaneous CP vio lation in these scenarios and present a model where the origin of CP v iolation is soft, with all the complex phases in the Lagrangian derive d from complex masses and vacuum expectation values (VEVs) of the Higg s fields. The main ingredient of the model is an approximate global sy mmetry, which determines the order of magnitude of Yukawa couplings an d scalar VEVs. We assume that the terms violating this symmetry are su ppressed by powers of the small parameter epsilon(PQ) = O(m(b)/m(t)). The tree-level flavor-changing interactions are small due to a combina tion of this global symmetry and a flavor symmetry, but they can be th e dominant source of CP violation. All CP-violating effects occur at o rder epsilon(PQ)(2) as the result of exchange of almost decoupled extr a Higgs bosons and/or through the usual mechanisms with an almost real CKM matrix. On dimensional grounds, the model gives epsilon(K) approx imate to epsilon(PQ)(2) and predicts for the neutron electric dipole m oment (and possibly also for epsilon'(K)) a suppression of order; epsi lon(PQ)(2) with respect to the values obtained in standard and minimal supersymmetric scenarios. The predicted CP asymmetries in B decays ar e generically too small to be seen in the near future. The mass of the lightest neutral scalar, the strong CP problem, and possible contribu tions to the Z decay into b quarks (the R(b) puzzle) are also briefly addressed in the framework of this model.