  For a low energy effective theory to admit a standard local, unitary,
analytic and Lorentz-invariant UV completion, its scattering amplitudes must
satisfy certain inequalities. While these bounds are known in the forward limit
for real polarizations, any extension beyond this for particles with nonzero
spin is subtle due to their non-trivial crossing relations. Using the
transversity formalism (i.e. spin projections orthogonal to the scattering
plane), in which the crossing relations become diagonal, these inequalities can
be derived for 2-to-2 scattering between any pair of massive particles, for a
complete set of polarizations at and away from the forward scattering limit.
This provides a set of powerful criteria which can be used to restrict the
parameter space of any effective field theory, often considerably more so than
its forward limit subset alone.
