On the Construction of Scattering Amplitudes for Spinning Massless Particles

In this paper the general form of scattering amplitudes for massless particles with equal spins s (ss → ss) or unequal spins (sasb → sasb) are derived. The imposed conditions are that the amplitudes should have the lowest possible dimension, have propagators of dimension m−2, and obey gauge invariance. It is shown that the number of momenta required for amplitudes involving particles with s > 2 is higher than the number implied by 3-vertices for higher spin particles derived in the literature. Therefore, the dimension of the coupling constants following from the latter 3-vertices has a smaller power of an inverse mass than our results imply. Consequently, the 3-vertices in the literature cannot be the first interaction terms of a gauge-invariant theory. When no spins s > 2 are present in the process the known QCD, QED or (super) gravity amplitudes are obtained from the above general amplitudes. FERMILAB-Pub-97/056-T CERN-TH/97-33 March 1997