Obtaining One-loop Gravity Amplitudes Using Spurious Singularities

TL;DR

This paper investigates how one-loop gravity amplitudes can be reconstructed from spurious singularity cancellations, showing that certain amplitudes can be fully determined from initial scalar integral coefficients, with ambiguities resolved by physical singularities.

Contribution

It demonstrates a method to determine one-loop gravity amplitudes from a small set of initial data, highlighting the role of spurious singularities and physical constraints in the process.

Findings

Some four-point and five-point supergravity amplitudes are fully determined from box coefficients.

Ambiguities in higher-leg amplitudes can be resolved using physical singularity structures.

The approach simplifies the calculation of complex one-loop gravity amplitudes.

Abstract

The decomposition of a one-loop scattering amplitude into elementary functions with rational coefficients introduces spurious singularities which afflict individual coefficients but cancel in the complete amplitude. These cancellations create a web of interactions between the various terms. We explore the extent to which entire one-loop amplitudes can be determined from these relationships starting with a relatively small input of initial information, typically the coefficients of the scalar integral functions as these are readily determined. In the context of one-loop gravity amplitudes, of which relatively little is known, we find that some amplitudes with a small number of legs can be completely determined from their box coefficients. For increasing numbers of legs, ambiguities appear which can be determined from the physical singularity structure of the amplitude. We illustrate this with the four-point and N=1,4 five-point (super)gravity one-loop amplitudes.