On the Construction of Scattering Amplitudes for Spinning Massless Particles

TL;DR

This paper derives the general form of scattering amplitudes for massless particles with arbitrary spins, revealing that higher-spin interactions require more momenta than previously thought, challenging existing 3-vertex models.

Contribution

It introduces a new derivation of gauge-invariant scattering amplitudes for massless particles with arbitrary spins, highlighting limitations of existing 3-vertex approaches for spins greater than 2.

Findings

Higher spins require more momenta in amplitudes than existing 3-vertex models suggest.

Existing 3-vertices imply smaller coupling constants than derived from gauge invariance.

Standard QCD, QED, and gravity amplitudes are recovered when spins greater than 2 are absent.

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.