Extracting Einstein from the Loop-Level Double-Copy

TL;DR

This paper introduces a graph-based method combining maximal cuts and double-copy techniques to isolate pure Einstein-Hilbert gravitational contributions at loop level, enabling the computation of classical observables in black-hole scattering.

Contribution

A systematic framework to extract pure Einstein-Hilbert gravity amplitudes from double-copy constructions involving massive matter at loop level.

Findings

Successfully isolated pure Einstein-Hilbert contributions at one-loop level.

Constructed the five-point integrand relevant for black-hole scattering.

Demonstrated the method's applicability to classical gravitational observables.

Abstract

The naive double-copy of (multi) loop amplitudes involving massive matter coupled to gauge theories will generically produce amplitudes in a gravitational theory that contains additional contributions from propagating antisymmetric tensor and dilaton states even at tree-level. We present a graph-based approach that combines the method of maximal cuts with double-copy construction to offer a systematic framework to isolate the pure Einstein-Hilbert gravitational contributions through loop level. Indeed this allows for a bootstrap of pure-gravitational results from the double-copy of massive scalar-QCD. We apply this to construct the novel result of the D-dimensional one-loop five-point QFT integrand relevant in the classical limit to generating observables associated with the radiative effects of massive black-hole scattering via pure Einstein-Hilbert gravity.