Amplitude Zeros in \(W^\pm Z\) Production

Abstract

We demonstrate that the Standard Model amplitude for \(f_1 \bar f_2 \rightarrow W^\pm Z \) at the Born-level exhibits an approximate zero located at \(\cos\theta = (g^{f_1}_{-} + g^{f_2}_{-}) / (g^{f_1}_{-} - g^{f_2}_{-})\) at high energies, where the \(g^{f_i}_{-}\) (\(i=1,2\)) are the left-handed couplings of the \(Z\)-boson to fermions and \(\theta\) is the center of mass scattering angle of the \(W\)-boson. The approximate zero is the combined result of an exact zero in the dominant helicity amplitudes \({\cal M}(\pm,\mp)\) and strong gauge cancelations in the remaining amplitudes. For non-standard \(WWZ\) couplings these cancelations no longer occur and the approximate amplitude zero is eliminated.