Sum rules for asymptotic form factors in e+e− → W+W− scattering

At very large energies and in SU(2)L ⊗ U(1)Y gauge theories, the trilinear gauge boson vertices relevant for e+e− → W+W− scattering are related in a simple way to the gauge boson self-energies. We derive these relations, both from the requirement of perturbative unitarity and from the Ward identities of the theory. Our discussion shows that, in general, it is never possible to fully eliminate self-energy dependencies from all the different form factors that parametrize the e+e− → W+W− helicity amplitudes. The exclusion of the self-energy contributions would lead to estimates of the effects wrong by orders of magnitude. We propose a simple way of including the self-energy contributions in an appropriate definition of the form factors.