Infrared Divergences and the Eikonal Exponentiation

Abstract

The aim of this note is to explore the interplay between the eikonal resummation in impact-parameter space and the exponentiation of infrared divergences in momentum space for gravity amplitudes describing collisions of massive objects. The eikonal governs the classical dynamics relevant to the two-body problem, and its infrared properties are directly linked to the zero-frequency limit of the gravitational wave emission spectrum and to radiation-reaction effects. Combining eikonal and infrared exponentiations it is possible to derive these properties at a given loop order starting from lower-loop data. This is illustrated explicitly in $\mathcal{N}=8$ supergravity and in general relativity by deriving the divergent part of the two-loop eikonal from tree-level and one-loop elastic amplitudes.

arXiv comment22 pages, 3 figures. v2: References updated, published in Phys. Rev. D

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• Exposing the threshold structure of loop integrals
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• Yang-Mills observables: from KMOC to eikonal through EFT