Top-forms of Leading Singularities in Nonplanar Multi-loop Amplitudes
arXiv:1507.03214 · doi:10.1140/epjc/s10052-018-5629-z
Abstract
The on-shell diagram is a very important tool in studying scattering amplitudes. In this paper we discuss the on-shell diagrams without external BCFW-bridges. We introduce an extra step of adding an auxiliary external momentum line. Then we can decompose the on-shell diagrams by removing external BCFW-bridges to a planar diagram whose top-form is well-known to all now. The top-form of the on-shell diagram with the auxiliary line can be obtained by adding the BCFW-bridges in an inverse order as discussed in our former paper \cite{Chen:2014ara}. To get the top-form of the original diagram, the soft limit of the auxiliary line is needed. We obtain the evolution rule for the Grassmannian integral and the geometry constraint under the soft limit. This completes the top-form description of leading singularities in nonplanar scattering amplitudes of Super Yang-Mills (SYM), which is valid for arbitrary higher-loops and beyond the Maximally-Helicity-Violation (MHV) amplitudes.
Revised and to appear in Eur.Phys.J. C. arXiv admin note: text overlap with arXiv:1411.3889
References in corpus (12)
- Total positivity, Grassmannians, and networks
- On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
- Hunt for new phenomena using large jet multiplicities and missing transverse momentum with ATLAS in 4.7 fb^-1 of sqrt(s) = 7 TeV proton-proton collisions
- One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
- The Amplituhedron from Momentum Twistor Diagrams
- N=4 Scattering Amplitudes and the Deformed Grassmannian
- Grassmannians for scattering amplitudes in 4d SYM and 3d ABJM
- Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory
- Inverse Soft Factors and Grassmannian Residues
- Cross-Order Integral Relations from Maximal Cuts
- Cluster Algebras and the Positive Grassmannian
- Non-Planar On-Shell Diagrams