Nonplanar On-shell Diagrams and Leading Singularities of Scattering 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.
Keywords
Cite
@article{arxiv.1411.3889,
title = {Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes},
author = {Baoyi Chen and Gang Chen and Yeuk-Kwan E. Cheung and Yunxuan Li and Ruofei Xie and Yuan Xin},
journal= {arXiv preprint arXiv:1411.3889},
year = {2019}
}
Comments
13 pages with 12 figures; final version appeared in Eur.Phys.J. C77 (2017) no.2, 80