Tree-level graviton exchange yields Newtonian potentials plus spin-dependent corrections at O(G) for massive spin-2 scattering off scalars, vectors, and fermions, plus the leading spin-independent O(G^2) term for spin-2 plus scalar.
Pagels,Energy-Momentum Structure Form Factors of Particles, Phys
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Scattering of massive spin-2 field via graviton exchanges with different spin fields and the long range gravitational potential
Tree-level graviton exchange yields Newtonian potentials plus spin-dependent corrections at O(G) for massive spin-2 scattering off scalars, vectors, and fermions, plus the leading spin-independent O(G^2) term for spin-2 plus scalar.