On massive higher spins and gravity. IV. Arbitrary spin

In this paper, we investigate gravitational interactions of massive fields with arbitrary integer and half-integer spin, trying to construct a vertex that contains both standard minimal and non-minimal interaction terms necessary to make the vertex gauge invariant. We propose an ansatz for these non-minimal terms and show that it leads to a unique solution that correctly reproduces our previous results for spins 5/2, 3 and 7/2, including all possible partially massless limits.