Radiation-reaction and angular momentum loss at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:

We point out that the odd-in-velocity contribution to the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">O</a:mi><a:mo stretchy="false">(</a:mo><a:msup><a:mi>G</a:mi><a:mn>4</a:mn></a:msup><a:mo stretchy="false">)</a:mo></a:math> radiated angular momentum for two-body scattering is determined by the radiation-reaction (RR) term in the one-loop waveform. This RR term is actually proportional to the tree-level waveform, and this reduces the calculation of the odd-in-velocity contribution to the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="script">O</f:mi><f:mo stretchy="false">(</f:mo><f:msup><f:mi>G</f:mi><f:mn>4</f:mn></f:msup><f:mo stretchy="false">)</f:mo></f:math> angular momentum loss, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:msub><k:mrow><k:mi>J</k:mi></k:mrow><k:mrow><k:mn>2</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>rad</k:mi></k:mrow></k:msub></k:mrow></k:math>, to two loops, instead of three loops as one would expect by power counting. We exploit this simplification, which follows from unitarity, to obtain a closed-form expression for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>J</m:mi></m:mrow><m:mrow><m:mn>2</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>rad</m:mi></m:mrow></m:msub></m:mrow></m:math> for generic velocities, which resums all fractional post-Newtonian (PN) corrections to the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="script">O</o:mi><o:mo stretchy="false">(</o:mo><o:msup><o:mi>G</o:mi><o:mn>4</o:mn></o:msup><o:mo stretchy="false">)</o:mo></o:math> angular momentum loss starting at 1.5PN.