On the Construction of Scattering Amplitudes for Spinning Massless Particles

Abstract In this paper the general form of scattering amplitudes for massless particles with equal spins s ( ss → ss ) or unequal spins ( s a s b → s a s b 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.