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