Parting gravity's tail: quadrupole tails at fifth order and beyond via integer partitions

TL;DR

This paper develops a systematic method to organize higher-order gravitational quadrupole tail effects using integer partitions, enabling efficient computation of complex tail contributions to gravitational wave energy loss.

Contribution

It introduces a constructive algorithm linking tail effective actions to integer partitions, reducing the number of unitarity cuts needed at each order.

Findings

Computed fifth-order tail contributions to gravitational wave energy loss.

Validated the effective action through counterterm extraction and renormalization.

Established a link between loop integral basis and integer partitions.

Abstract

This work studies the systematic organization of higher-order gravitational quadrupole tails using generalized unitarity methods imported from the study of scattering amplitudes. The first major result is a constructive algorithm for generic arbitrary-order tail effective actions which links the structure of their loop integral basis expansion with integer partitions, and predicts that only a single new unitarity cut needs to be evaluated at each tail order with all other contributions given in terms of lower-loop data. The algorithm is employed to compute the tail-of-tail-of-tail-of-tail-of-tail (T$^5$) contributions to the effective action and associated energy loss to gravitational waves. Validation of the new effective action and radiated energy is done through counterterm extraction and renormalization analysis, leading to complete agreement with known counterterms and renormalization flow equations.