  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 of Damour [arXiv:2010.01641]. 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 order $v^8$, finding agreement with Herrmann et al. [arXiv:2101.07255]. Our
results also allow to investigate the zero frequency limit of the emitted
energy spectrum.
