High-energy scatterings of many electroweak gauge bosons

We present an application of the equivalence theorem and the multispinor representation of gauge fields to the standard model of electroweak interactions at very high energies. The equivalence theorem allows us to efficiently treat the longitudinal vector bosons while the multispinor formalism makes the transverse vector bosons easy to handle. We generalize the work of Berends and Giele to derive a recursion relation for a current consisting of a pair of longitudinal vector bosons plus any number of transverse vector bosons. It is shown that for certain helicity configurations this current is related to a corresponding current involving only transverse vector bosons. Consideration of a U(N), rather than an SU(N), gauge theory enables us to incorporate the mixing in the SU(2) × U(1) electroweak theory and to derive certain sum rules for the currents for transverse gauge bosons. We also give explicit expressions for four-particle and five-particle scattering amplitudes involving a pair of longitudinal vector bosons.