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 ∼ √mM_(P1), rather than at the Planck scale M_(P1), even for m≪ M_(P1). We then restore unitarity to this amplitude up to M_(P1) 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