Determine the surviving function space and divergence cancellation at 5PM

Determine which functions survive in the offset parameter shift at 5PM order, given that the dissipative part of the 1SF impulse already involves Calabi–Yau periods, and determine whether divergences in the 5PM dissipative sector cancel against conservative terms.

Background

The paper computes the mechanical angular-momentum loss for gravitational two-body scattering through 4PM order using worldline quantum field theory. At 5PM order, the authors identify two unresolved issues associated with extending the offset-parameter-shift calculation: the dissipative part of the first self-force impulse already involves Calabi–Yau periods, but it is not known which subset or combination of functions will remain in the corresponding offset shift; moreover, the 4PM calculation exhibits cancellation of divergences between dissipative and conservative contributions, and it remains unresolved whether an analogous cancellation persists at 5PM order.