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On the Construction of Scattering Amplitudes for Spinning Massless Particles

F. A. Berends·W. T. Giele
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Abstract

In this paper the general form of scattering amplitudes for massless particles with equal spins s ($s s \to s s$) or unequal spins ($s_a s_b \to s_a s_b$) 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.

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F. A. Berends, W. T. Giele. 1997-04-01. On the Construction of Scattering Amplitudes for Spinning Massless Particles. https://doi.org/10.1016/s0550-3213(97)00560-9

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