https://doi.org/10.1140/epjc/s10052-017-4659-2
Regular Article - Theoretical Physics
Nonplanar on-shell diagrams and leading singularities of scattering amplitudes
1
Department of Physics, Zhejiang Normal University, Jinhua, Zhejiang, People’s Republic of China
2
Department of Physics, Nanjing University, 22 Hankou Road, Nanjing, 210093, People’s Republic of China
* e-mail: gang.chern@gmail.com
Received:
30
September
2016
Accepted:
31
January
2017
Published online:
8
February
2017
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 the geometrical constraints are 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.
© The Author(s), 2017
