  We present a novel calculation of the four-momentum that is radiated into
gravitational waves during the scattering of two arbitrarily spinning bodies.
Our result, which is accurate to leading order in $G$, to quadratic order in
the spins, and to all orders in the velocity, is derived by using a
Routhian-based worldline effective field theory formalism in concert with a
battery of analytic techniques for evaluating loop integrals. While nonspinning
binaries radiate momentum only along the direction of their relative velocity,
we show that the inclusion of spins generically allows for momentum loss in all
three spatial directions. We also verify that our expression for the radiated
energy agrees with the overlapping terms from state-of-the-art calculations in
post-Newtonian theory.
