On-shell Supersymmetry and higher-spin amplitudes

Abstract: We use on-shell Supersymmetry to constrain the three-point function of two massless particles and one massive particle in 3+1 dimensions. We use this information to write down the tree-level four-point function of massless particles for $\mathcal{N}=1$, $2$ and $4$ theories. In particular, we derive the expressions for four-photon/gluon amplitudes with massive higher spin exchange in theories with $\mathcal{N}=4$ Supersymmetry in 3+1 dimensions.