CHY Loop Integrands from Holomorphic Forms

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 ${\Phi }^3$ 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 $\Lambda$-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.

arXiv comment30+12 pages, notation modified and references added

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• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Gluons and gravitons at one loop from ambitwistor strings
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• One-loop Correlators and BCJ Numerators from Forward Limits
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
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• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
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• A String Deformation of the Parke-Taylor Factor
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
• New Factorization Relations for Non-Linear Sigma Model Amplitudes
• New Factorization Relations for Yang Mills Amplitudes
• Scattering Equations and Factorization of Amplitudes II: Effective Field Theories
• Note on solutions of scattering equations
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands