  We propose a formula relating scattering S-matrix amplitudes to correlators
of a conformal field theory. The proposal implements a flat limit of the field
theory, providing an indirect microscopic description of gravitational theories
with asymptotically flat boundary conditions. The formula is valid for both
massive and massless external particles, and reduces to existing expressions in
the literature when all particles are either simultaneously massless or
massive. We test the result in various (2+1)-dimensional examples such as
simple BMS3 invariant correlators and blocks. We also study two-point
correlators in conformal field theory deficit states to obtain known
expressions for non-trivial scattering in asymptotically flat conical
geometries.

High Energy Physics - Theory;General Relativity and Quantum Cosmology