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 ∼ √${\mathit{mM}}_{\mathrm{Pl}}$ , rather than at the Planck scale ${\mathit{M}}_{\mathrm{Pl}}$, even for m≪${\mathit{M}}_{\mathrm{Pl}}$. We then restore unitarity to this amplitude up to ${\mathit{M}}_{\mathrm{Pl}}$ by adding nonminimal couplings that depend on the curvature and its derivatives, and modify the minimal description, including particle gravitational quadrupole moments, at ∼${\mathit{m}}^{\mathrm{-}1}$ scales.