  We study the gravitational radiation emitted during the scattering of two
spinless bodies in the post-Minkowskian Effective Field Theory approach. We
derive the conserved stress-energy tensor linearly coupled to gravity and the
classical probability amplitude of graviton emission at leading and
next-to-leading order in the Newton's constant $G$. The amplitude can be
expressed in compact form as one-dimensional integrals over a Feynman parameter
involving Bessel functions. We use it to recover the leading-order radiated
angular momentum expression. Upon expanding it in the relative velocity between
the two bodies $v$, we compute the total four-momentum radiated into
gravitational waves at leading-order in $G$ and up to an order $v^8$, finding
agreement with what was recently computed using scattering amplitude methods.
Our results also allow us to investigate the zero frequency limit of the
emitted energy spectrum.
