Sum rules for asymptotic form factors in $e^+ e^- -> W^+ W^-$ scattering

Abstract

At very large energies and in $SU(2)_L\otimes U(1)_Y$ gauge theories, the trilinear gauge boson vertices relevant for $e^+e^- \to W^+W^-$ 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 neglect vector boson self-energies when computing the form factors which parametrize the $e^+ e^- \to W^+ W^-$ helicity amplitudes. The exclusion of the self-energy contributions would lead to estimates of the effects wrong by orders of magnitudes. We propose a simple way of including the self-energy contributions in an appropriate definition of the form factors.