Origin of the MPM–EFT center-of-mass worldline discrepancy

Determine the physical origin of the difference between the definitions of the center-of-mass worldline used in the Multipolar Post-Minkowskian and Effective Field Theory gravitational-wave formalisms, and establish whether the discrepancy is caused by including the full Veneziano–Vilkovisky supertranslation in the EFT waveform rather than only its multipoles with l ≥ 2.

Background

The paper compares its two-loop-level, 3.5PN-accurate octupolar waveform computed in the Multipolar Post-Minkowskian formalism with the corresponding one-loop Effective Field Theory waveform. The apparent discrepancy is shown to be fully accounted for by the same 2.5PN-level shift in the spatial center-of-mass origin identified in the authors’ earlier quadrupolar comparison, so it is not a disagreement in the waveform after the origins are aligned.

Although the required center-of-mass shift is known and is compatible with a contribution from the time-odd incoming MPM center-of-mass position, the physical reason why the MPM and EFT formalisms define the center-of-mass worldline differently remains unresolved. The paper records the authors’ conjecture that the EFT waveform may include the full Veneziano–Vilkovisky supertranslation, whereas the relevant comparison may require its projection onto multipoles with l ≥ 2, but does not establish this explanation.