  We formulate an effective field theory describing large mass scalars and
fermions minimally coupled to gravity. The operators of this effective field
theory are organized in powers of the transfer momentum divided by the mass of
the matter field, an expansion which lends itself to the efficient extraction
of classical contributions from loop amplitudes in both the post-Newtonian and
post-Minkowskian regimes. We use this effective field theory to calculate the
classical and leading quantum gravitational scattering amplitude of two heavy
spin-1/2 particles at the second post-Minkowskian order.
