  After a rediscussion of the vanishing theorems for helicity amplitudes in
unbroken gauge theories, we study the case of spontaneously broken gauge
theories at high energy. The vanishing theorems generalize to a definite
pattern of m/E-suppression of the amplitudes that vanish in the massless case,
where E is the energy scale of the process and m is the mass of the gauge
vectors. We use only elementary arguments, and as an application we show how
these methods can be employed to understand some aspects of the effective W
approximation in the polarized case.
