Obtaining One-loop Gravity Amplitudes Using Spurious Singularities

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.

Minor corrections. Appendix added

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Cited by in corpus (7)

• An R^4 non-renormalisation theorem in N=4 supergravity
• On the associativity of 1-loop corrections to the celestial operator product in gravity
• One-loop four-graviton amplitudes in N=4 supergravity models
• Complex Factorisation and Recursion for One-Loop Amplitudes
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• Two-Loop Gravity amplitudes from four dimensional Unitarity
• The $\mathcal{N}=4$ Supergravity NMHV six-point one-loop amplitude