Classical Gravitational Scattering from the Ultraviolet and the Absence of Calabi-Yau Integrals in the Conservative Sector at $O(G^5)$

TL;DR

This paper demonstrates why certain complex integrals do not influence conservative gravitational observables at fifth post-Minkowskian order, clarifying the role of ultraviolet singularities and proposing new analysis strategies for multiloop integrals.

Contribution

It reveals the absence of Calabi-Yau and elliptic integrals in the classical limit at fifth post-Minkowskian order and offers alternative methods for multiloop integral analysis.

Findings

Calabi-Yau and elliptic integrals do not contribute at this order

Conservative contributions relate to logarithmic terms from UV singularities

Proposes new strategies for analyzing multiloop integrals in the classical limit

Abstract

We explain why Calabi-Yau and complete elliptic integrals do not contribute to conservative observables at fifth post-Minkowskian order, despite appearing in intermediate steps. At even loop orders, conservative contributions are tied to terms proportional to the logarithm of the momentum transfer, which in dimensional regularization arise from singular regions. We show that in the classical limit, the integral classes responsible for Calabi-Yau and complete elliptic behavior are absent from the ultraviolet singular structures that generate the required logarithm. This perspective also suggests alternative strategies for analyzing the classical limit of multiloop integrals in the conservative sector at even loop orders.