Comments on the evaluation of massless scattering

Abstract

The goal of this work is threefold. First, we give an expression of the most general five point integral on M_{0,n} in terms of Chebyshev polynomials. Second, we choose a special kinematics that transforms the polynomial form of the scattering equations to a linear system of symmetric polynomials. We then explain how this can be used to explicitly evaluate arbitrary point integrals on M_{0,n}. Third, we comment on the recently presented method of companion matrices and we show its equivalence to the elimination theory and an algorithm previously developed by one of the authors.

14 pages; v2 minor changes, published version

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Cited by in corpus (34)

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• Elliptic scattering equations
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• General Solution of the Scattering Equations
• CHY Loop Integrands from Holomorphic Forms
• Scattering Equations: Real Solutions and Particles on a Line
• CHY-Graphs on a Torus
• The Polynomial Form of the Scattering Equations is an H-Basis
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Feynman Rules of Higher-order Poles in CHY Construction
• The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes
• Mellin-(Schwinger) representation of One-loop Witten diagrams in AdS
• A Combinatoric Shortcut to Evaluate CHY-forms
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• One-loop CHY-Integrand of Bi-adjoint Scalar Theory
• CHY formula and MHV amplitudes
• A differential operator for integrating one-loop scattering equations
• Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
• Derivation of Feynman Rules for Higher Order Poles Using Cross-ratio Identities in CHY Construction
• Pushforwards via Scattering Equations with Applications to Positive Geometries
• Note on the Labelled tree graphs
• Note on solutions of scattering equations
• CHY Theory for Several Fields
• Analytic expressions of amplitudes by the cross-ratio identity method
• CHY-construction of Planar Loop Integrands of Cubic Scalar Theory