Abstract
All-loop planar scattering amplitudes in maximally supersymmetric Yang-Mills theory can be formulated geometrically in terms of the “amplituhedron”. We study the mathematical structures of the one-loop amplituhedron, and present a new formula for its canonical measure, or the one-loop Grassmannian measure formula. Using the recently proposed momentum-twistor diagrams, we show that there is a correspondence between the cells of one-loop amplituhedron, BCFW terms or equivalently on-shell diagrams, and residues of the one-loop Grassmannian formula. In particular, for the first non-trivial case of one-loop NMHV, these structures are naturally associated with a nice geometric picture as polygons in projective space, as we discuss in various illustrative examples.
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ArXiv ePrint: 1510.03553
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Bai, Y., He, S. & Lam, T. The amplituhedron and the one-loop Grassmannian measure. J. High Energ. Phys. 2016, 112 (2016). https://doi.org/10.1007/JHEP01(2016)112
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DOI: https://doi.org/10.1007/JHEP01(2016)112