CPViolation and Electric Dipole Moments in Gauge Theories of Weak Interactions

We present some general considerations on computations of electric dipole moments ($D$) of leptons and of hadrons in gauge theories which incorporate $\mathrm{CP}$ violation. Technical aspects of the isolation of the $\mathrm{CP}$-violating parts of the corresponding graphs are described. We emphasize the distinction (already familiar from $g-2\mathrm{}$ constraints) between "mixed chirality" and "pure chirality" couplings. In the mixed-chirality case, $D\text{'}\mathrm{s}$ can potentially appear to third order in the semiweak-coupling constant; in the pure-chirality case $D$ is at least of fifth order. Estimates are given for prototypes of two classes of gauge models: (1) $\mathrm{CP}$ violation is implemented via the introduction of a small parameter. For the example considered, a model due to Mohapatra, $D_{\mathrm{nucleon}}$ and $D_{\mathrm{lepton}}$ are both of fifth order. (2) The violation is "maximal," as exemplified in the O(4) and O(4)×U(1) models. Here $D_{\mathrm{muon}}$ appears to third order in the (mixed-chirality) O(4) case. All other $D\text{'}\mathrm{s}$ in the "maximal" examples are of fifth order. For the "maximal" model our estimates are below but may not be very far from the present experimental bounds. For the small-parameter model they are quite considerably smaller.