Gauge theories of microweakCPviolation

Abstract

We investigate systematically the condition that $\mathrm{CP}$ violation in $|\ensuremath{\Delta}S|=1$ processes is "microweak" [i.e., of order of ${G}_{F}\ensuremath{\epsilon}{(\frac{m}{{m}_{W}})}^{2}$ where $m$ is a typical hadronic mass] naturally (i.e., for all values of complex parameters of the theory) in SU(2) \ifmmode\times\else\texttimes\fi{} U(1) gauge theories of weak and electromagnetic interactions. We consider only those models in which $\mathrm{CP}$ violation occurs in the quark mass terms. The conditions for microweak $\mathrm{CP}$ violation in $|\ensuremath{\Delta}S|=1$ processes are that (1) quarks of charge $\ensuremath{-}\frac{1}{3}$ and of a given chirality have the same weak isospin $I$ and ${I}_{3}$, and (2) quarks of charge $\frac{2}{3}$ ($\ensuremath{-}\frac{4}{3}$, if they exist) and quarks of charge $\ensuremath{-}\frac{1}{3}$ 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 ${I}_{3}$, 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 ${10}^{\ensuremath{-}30}$ cm. Several examples of this class of models are given, one of which is the six-quark model of Kobayashi and Maskawa.