We provide a systematic method to compute tree-level scattering amplitudes with spinning external states from amplitudes with scalar external states in arbitrary spacetime dimensions. We write down analytic answers for various scattering amplitudes, including the four graviton amplitude due to the massive spin J exchange. We verify the results by computing angular distributions in 3 + 1 dimensions using various identities involving Jacobi polynomials.

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 $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 4 Supersymmetry in 3+1 dimensions.