The one-loop contribution of the two $CP$-violating components of the $WW\gamma$ vertex, ${\tilde{\kappa }}_{\gamma }{W}_{\mu }^{+}{W}_{\nu }^{-}{\tilde{F}}^{\mu \nu }$ and $({\tilde{\lambda }}_{\gamma }/m_W^2)W_{\mu \nu }^{+}{W}_{\rho }^{-\nu }{\tilde{F}}^{\rho \mu }$, on the electric dipole moment (EDM) of fermions is calculated using dimensional regularization and its impact at low energies reexamined in the light of the decoupling theorem. The Ward identities satisfied by these couplings are derived by adopting a $S{U}_L(2)\times U_Y(1)$-invariant approach and their implications in radiative corrections discussed. Previous results on ${\tilde{\kappa }}_{\gamma }$, whose bound is updated to $|{\tilde{\kappa }}_{\gamma }|<5.2\times {10}^{-5}$, are reproduced, but disagreement with those existing for ${\tilde{\lambda }}_{\gamma }$ is found. In particular, the upper bound $|{\tilde{\lambda }}_{\gamma }|<1.9\times {10}^{-2}$ is found from the limit on the neutron EDM, which is more than 2 orders of magnitude less stringent than that of previous results. It is argued that this difference between the ${\tilde{\kappa }}_{\gamma }$ and ${\tilde{\lambda }}_{\gamma }$ bounds is the one that might be expected in accordance with the decoupling theorem. This argument is reinforced by analyzing carefully the low-energy behavior of the loop functions. The upper bounds on the $W$ EDM, $|d_W|<6.2\times {10}^{-21}\mathrm{e}·\mathrm{cm}$, and the magnetic quadrupole moment, $|{\tilde{Q}}_W|<3\times {10}^{-36}\mathrm{e}·{\mathrm{cm}}^2$, are derived. The EDM of the second and third families of quarks and charged leptons are estimated. In particular, EDM as large as ${10}^{-20}\mathrm{e}·\mathrm{cm}$ and ${10}^{-21}\mathrm{e}·\mathrm{cm}$ are found for the $t$ and $b$ quarks, respectively.

• Received 4 September 2007

DOI:https://doi.org/10.1103/PhysRevD.77.015011