CHY loop integrands from holomorphic forms
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Date
2017-03-01
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Publisher
Springer Verlag
Abstract
Recently, the Cachazo-He-Yuan (CHY) approach for calculating scattering amplitudes has been extended beyond tree level. In this paper, we introduce a way of constructing CHY integrands for Φ3 theory up to two loops from holomorphic forms on Riemann surfaces. We give simple rules for translating Feynman diagrams into the corresponding CHY integrands. As a complementary result, we extend the Λ-algorithm, originally introduced in arXiv:1604.05373, to two loops. Using this approach, we are able to analytically verify our prescription for the CHY integrands up to seven external particles at two loops. In addition, it gives a natural way of extending to higher-loop orders. © 2017, The Author(s).
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Keywords
Differential and Algebraic Geometry, Scattering Amplitudes, Superstrings and Heterotic Strings