Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
Abstract
We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and gravity. The integrand basis we construct is diagonalized on a spanning set of non-vanishing leading singularities that ensures the manifest matching of all soft-collinear singularities in both theories. As a consequence, this integrand basis naturally splits into infrared-finite and infrared-divergent parts, with hints toward an integrand-level exponentiation of infrared divergences. Importantly, we use the same basis of integrands for both theories, so that the presence or absence of residues at infinite loop momentum becomes a feature detectable by inspecting the cuts of the theory. Complete details of our results are provided as ancillary files. This work has been updated to take into account the results of [arXiv:1911.09106], which leads to a simpler and more uniform representation of these amplitudes.
Cite
@article{arxiv.1909.09131,
title = {Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops},
author = {Jacob L. Bourjaily and Enrico Herrmann and Cameron Langer and Andrew J. McLeod and Jaroslav Trnka},
journal= {arXiv preprint arXiv:1909.09131},
year = {2021}
}
Comments
Fixed pentabox numerators in v3 (v2 inherited a typographical mistake in 1911.09106). Major update in v2/3: This work has been significantly updated to reflect the results of [arXiv:1911.09106] which allow for a more uniform representation of these amplitudes. 53 pages, 156 figures. Full details available in updated ancillary files