Top-forms of Leading Singularities in Nonplanar Multi-loop Amplitudes
Abstract
Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW)-decomposable on-shell diagram process a rational top-form if and only if the algebraic ideal comprised of the geometrical constraints is shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top-form integration contours can thus be obtained, and understood, in a straightforward way. All rational top-form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW-decomposable.
Cite
@article{arxiv.1506.02880,
title = {Top-forms of Leading Singularities in Nonplanar Multi-loop Amplitudes},
author = {Baoyi Chen and Gang Chen and Yeuk-Kwan E. Cheung and Ruofei Xie and Yuan Xin},
journal= {arXiv preprint arXiv:1506.02880},
year = {2018}
}
Comments
This article has been merged with arXiv:1411.3889 and published in Eur.Phys.J. C. Thanks for the citations! and please cite "Eur.Phys.J. C77 (2017) no.2, 80" from now on