  We consider a procedure for directly constructing general tree-level
four-particle scattering amplitudes of massive spinning particles that are
consistent with the usual requirements of Lorentz invariance, unitarity,
crossing symmetry, and locality. There are infinitely many such amplitudes, but
we can isolate interesting theories by bounding the high-energy growth of the
tree amplitudes within the effective field theory. This allows us to set
model-independent lower bounds on the growth of tree-level amplitudes in any
effective field theory with a given particle content and any interaction terms
with an arbitrary but finite number of derivatives. In certain common cases
this corresponds to finding the highest possible strong coupling scale. When
applied to spin 2, we show that the only amplitudes that saturate this bound
are generated by the known ghost-free theories of a massive spin-2 particle,
namely dRGT massive gravity and the pseudolinear theory. We also make a
conjecture for the allowed growth of tree amplitudes in a theory with a single
massive particle of any integer spin.
