Abstract
The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in \( \mathcal{N} \) = 4 super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum amplituhedron ℳn, k and explain how these boundaries are related to the expected factorization channels, and soft and collinear limits of tree amplitudes. Conversely, all physical singularities of tree amplitudes are encoded in this boundary stratification. Finally, we find that the momentum amplituhedron ℳn, k has Euler characteristic equal to one, which provides a first step towards proving that it is homeomorphic to a ball.
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ArXiv ePrint: 2003.13704
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Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
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Ferro, L., Łukowski, T. & Moerman, R. From momentum amplituhedron boundaries to amplitude singularities and back. J. High Energ. Phys. 2020, 201 (2020). https://doi.org/10.1007/JHEP07(2020)201
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DOI: https://doi.org/10.1007/JHEP07(2020)201