Gleaning gravitational amplitudes -- a double copy for canceling dilatons

TL;DR

This paper develops a novel double-copy method to automatically cancel unwanted dilaton contributions in gravitational scattering amplitudes by treating certain gauge-theory fields as ghosts, verified up to six external scalars and at one-loop level.

Contribution

It introduces an asymmetric double-copy prescription that effectively removes dilatons from gravitational amplitudes, extending the double-copy framework to handle unwanted scalar states.

Findings

Successfully reproduces dilaton graphs up to six scalars in general dimensions.

Requires subtraction of bubble graphs at one-loop to cancel residual dilaton and axion contributions.

Provides a systematic approach to eliminate dilaton contamination in gravitational amplitude calculations.

Abstract

Scattering amplitudes in general relativity can be conveniently computed using the double copy, which relates them to Yang-Mills amplitudes. However, unwanted dilatons are sourced by massive scalar matter, which must be removed from the double copy in order to match the long range gravitational interactions. In this paper, we study how to automatically cancel out the dilatons by finding a suitable double-copy prescription in terms of gauge-theory fields, effectively treating the new contributions as ghosts that subtract out the unwanted states. At tree level, we find that an asymmetric double copy can reproduce the dilaton graphs in general dimension, which we explicitly verify up to six external massive scalars. Considering a one-loop four-point example, the same asymmetric double copy needs to be supplemented by the subtraction of bubble graphs that originate both from the axion and a residual dilaton term.