Gauge theories of microweak CP violation

We investigate systematically the condition that CP violation in abs. value (ΔS) = 1 processes is ''microweak'' [i.e., of order of G/sub F/epsilon (m/m/sub W/)2 where m is a typical hadronic mass] naturally (i.e., for all values of complex parameters of the theory) in SU(2)xU(1) gauge theories of weak and electromagnetic interactions. We consider only those models in which CP violation occurs in the quark mass terms. The conditions for microweak CP violation in abs. value (ΔS) = 1 processes are that (1) quarks of charge -1/3 and of a given chirality have the same weak isospin I and I3, and (2) quarks of charge 2/3 (-4/3, if they exist) and quarks of charge -1/3 do not belong to the same weak isomultiplets for at least one chirality. Special attention is given to a more restricted class of models in which (1) quarks of a given charge and chirality have the same weak isospin I and I3, and (2) quarks of charge q and quarks of charge q + 1 do not belong to the same isomultiplets for at least one chirality. In such models, the electric dipole moment of a quark arises only in second-order weak interactions, and is estimated to be of order of 10-30 cm. Several examples of this class of models are given, one of which is the six-quark model of Kobayashi and Maskawa