Tree-level unitarity constraints on the gravitational couplings of higher-spin massive fields

We analyze 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 >2, tree-level unitarity is already violated at energies ∼ mMPl, rather than at the Planck scale MPl, even for mMPl. We then restore unitarity to this amplitude up to MPl by adding nonminimal couplings that depend on the curvature and its derivatives, and modify the minimal description, including particle gravitational quadrupole moments, at ∼m-1 scales.