Polarization amplitudes forW-boson and photon production

We study the polarization amplitudes for the production of a weak boson ($W$) and a photon from quark-antiquark annihilation in the standard model minimally extended by giving the $W$ an arbitrary anomalous magnetic moment $\kappa$. We find that in the c.m. frame the amplitude where the polarization of the $W$ is longitudinal and that of the photon is transverse to the scattering plane shows a unique behavior: When we neglect the $W$-boson width this amplitude vanishes identically for all scattering angles if $\kappa$ is put equal to its gauge-theory value, $\kappa =1\mathrm{}$, but is nonzero otherwise.