Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order

TL;DR

This paper advances the theoretical understanding of black hole scattering by calculating the conservative scattering angle at fifth post-Minkowskian order, including second self-force contributions, using complex four-loop quantum field theory techniques.

Contribution

It provides the first complete 5PM conservative scattering calculation with 2SF effects, introducing new computational methods and a propagator prescription to ensure physical consistency.

Findings

Successfully computed 5PM conservative scattering angle with 2SF contributions.

Identified and resolved a spurious velocity divergence in the potential region.

Validated results against existing post-Newtonian literature.

Abstract

Using the worldline quantum field theory formalism, we compute the conservative scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian (5PM) order by providing the second self-force (2SF) contributions. This four-loop calculation involves non-planar Feynman integrals and requires advanced integration-by-parts reduction, novel differential-equation strategies, and efficient boundary-integral algorithms to solve a system of hundreds of master integrals in four integral families on high-performance computing systems. The resulting function space includes multiple polylogarithms as well as iterated integrals with a K3 period, which generate a spurious velocity divergence at $v/c=\sqrt{8}/3$. This divergence is present in the potential region and must be canceled by contributions from the radiative memory region, while its dimensional-regularisation pole should cancel against the radiative tail region. We find that the standard use of Feynman propagators to access the conservative sector fails to ensure this cancellation. We propose a conservative propagator prescription which realises both cancellations leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied.