B_s mixing and electric dipole moments in the framework of minimal flavor violation

We analyze the general structure of four-fermion operators capable of introducing CP violation preferentially in B_s mixing within the framework of minimal flavor violation. The effect requires a minimum of O(Yu4Yd4) Yukawa insertions, and at this order we find a total of six operators with different Lorentz, color, and flavor contractions that lead to enhanced B_s mixing. We then estimate the impact of these operators and of their close relatives on the possible sizes of electric dipole moments (EDMs) of neutrons and heavy atoms. We identify two broad classes of such operators: those that give EDMs in the limit of vanishing Cabibbo-Kobayashi-Maskawa angles, and those that require quark mixing for the existence of nonzero EDMs. The natural value for EDMs from the operators in the first category is up to an order of magnitude above the experimental upper bounds, while the second group predicts EDMs well below the current sensitivity level. Finally, we discuss plausible UV completions for each type of operator.