  Advanced methods for computing perturbative, quantum-gravitational scattering
amplitudes show great promise for improving our knowledge of classical
gravitational dynamics. This is especially true in the weak-field and
arbitrary-speed (post-Minkowskian, PM) regime, where the conservative dynamics
at 3PM order has been recently determined for the first time, via an amplitude
calculation. Such PM results are most relevantly applicable to relativistic
scattering (unbound orbits), while bound/inspiraling binary systems, the most
frequent sources of gravitational waves for the LIGO and Virgo detectors, are
most suitably modeled by the weak-field and slow-motion (post-Newtonian, PN)
approximation. Nonetheless, it has been suggested that PM results can
independently lead to improved modeling of bound binary dynamics, especially
when taken as inputs for effective-one-body (EOB) models of inspiraling
binaries. Here, we initiate a quantitative study of this possibility, by
comparing PM, EOB and PN predictions for the binding energy of a two-body
system on a quasi-circular inspiraling orbit against results of numerical
relativity (NR) simulations. The binding energy is one of the two central
ingredients (the other being the gravitational-wave energy flux) that enters
the computation of gravitational waveforms employed by LIGO and Virgo
detectors, and for (quasi-)circular orbits it provides an accurate diagnostic
of the conservative sector of a model. We find that, whereas 3PM results do
improve the agreement with NR with respect to 2PM (especially when used in the
EOB framework), it is crucial to push PM calculations at higher orders if one
wants to achieve better performances than current waveform models used for
LIGO/Virgo data analysis.
