Tree-Level Unitarity Constraints on the Gravitational Couplings of Higher-Spin Massive Fields

We analyse the high-energy behavior of tree-level graviton Compton amplitudes for particles of mass m and arbitrary spin, concentrating on a combination of forward amplitudes that will be unaffected by eventual cross- couplings to other, higher spins. We first show that for any spin larger than 2, tree-level unitarity is already violated at energies well below the Planck scale M, if m << M. We then restore unitarity to this amplitude up to M by adding non-minimal couplings that depend on the curvature and its derivatives, and modify the minimal description - including particle gravitational quadrupole moments - at scales O(1/m).