One-loopP- andT-oddW±electromagnetic moments

We compute the $P$- and $T$-violating electromagnetic moments (electric dipole and magnetic quadrupole) generated at one loop for the $W$ boson. We argue that only models in which the physical $W$ has both left- and right-handed fermion couplings at the tree level can generate these moments at one loop. The resulting magnetic quadrupole moment is quite generally related to the electric dipole moment (EDM) by the following one-loop relation: ${2d}_W+M_W{\tilde{Q}}_W=0\mathrm{}$. On fairly general grounds ${\mathrm{SU}}_L\mathrm{}\left(2\right)\mathrm{}\times {\mathrm{U}}_{\gamma }\mathrm{}\left(1\right)\mathrm{}$ invariance relates the nonvanishing $\mathrm{CP}$- and $P$-odd $\mathrm{WWZ}$ form factor to its electromagnetic counterpart: $f_Z\mathrm{}\left(0\right)={-f}_{\gamma }\mathrm{}\left(0\right)\mathrm{}{sin}^2{\theta }_W$. A reasonable estimate of the resulting $W$ EDM is ${10}^{-22\mathrm{}}$ ${-10\mathrm{}}^{-23\mathrm{}}$ e cm depending on values chosen for unknown parameters. Such a dipole moment would induce an EDM for electrons and neutrons of order ${10}^{-30\mathrm{}}$ ${-10\mathrm{}}^{-31\mathrm{}}$ e cm and ${10}^{-29\mathrm{}}$ ${-10\mathrm{}}^{-27\mathrm{}}$ e cm, respectively. For some corners of parameter space the fermion EDM's can be observable in current searches. The effects of $\mathrm{CP}$ violation from a heavy fourth generation can be typically ten times as large.