Massive Spin-5/2 Fields Coupled to Gravity: Tree-Level Unitarity vs. the Equivalence Principle

I show that the gravitational scattering amplitudes of a spin-5/2 field with mass $m\ll M_{Pl}$ violate tree-level unitarity at energies $\sqrt{s}\approx \sqrt{m{M}_{Pl}}$ if the coupling to gravity is minimal. Unitarity up to energies $\sqrt{s}\approx M_{Pl}$ is restored by adding a suitable non-minimal term, which gives rise to interactions violating the (strong) equivalence principle. These interactions are only relevant at distances $d\text{lequiv}1\mathrm{/}m$.