Feynman Rules of Higher-order Poles in CHY Construction

Abstract

In this paper, we generalize the integration rules for scattering equations to situations where higher-order poles are present. We describe the strategy to deduce the Feynman rules of higher-order poles from known analytic results of simple CHY-integrands, and propose the Feynman rules for single double pole and triple pole as well as duplex-double pole and triplex-double pole structures. We demonstrate the validation and strength of these rules by ample non-trivial examples.

arXiv comment52 pages, 37 figures

References in corpus (21)

• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Scattering Equations and KLT Orthogonality
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• The Polynomial Form of the Scattering Equations
• Integration Rules for Loop Scattering Equations
• Scattering Equations and Feynman Diagrams
• Integration Rules for Scattering Equations
• Computation of Contour Integrals on ${\mathcal{M}}_{0,n}$
• An Algebraic Approach to the Scattering Equations
• Scattering Equations and Global Duality of Residues
• Evaluation of the CHY Gauge Amplitude
• Elimination and recursions in the scattering equations
• On the solutions of the scattering equations
• General Solution of the Scattering Equations
• Scattering equations, generating functions and all massless five point tree amplitudes
• Comments on the evaluation of massless scattering
• The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes
• CHY formula and MHV amplitudes
• CHY-construction of Planar Loop Integrands of Cubic Scalar Theory

Cited by in corpus (18)

• Cross-ratio Identities and Higher-order Poles of CHY-integrand
• Elliptic scattering equations
• Analytic Representations of Yang-Mills Amplitudes
• CHY Loop Integrands from Holomorphic Forms
• 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
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• A Combinatoric Shortcut to Evaluate CHY-forms
• Derivation of Feynman Rules for Higher Order Poles Using Cross-ratio Identities in CHY Construction
• Note on the Labelled tree graphs
• Permutation in the CHY-Formulation
• Analytic expressions of amplitudes by the cross-ratio identity method
• CHY Theory for Several Fields