Note on solutions of scattering equations

Abstract

In the CHY-frame for the amplitudes, there are two kinds of singularities we need to deal with. The first one is the pole singularities when the kinematics is not general, such that some of $S_A\to 0$. The second one is the collapse of locations of points after solving scattering equations (i.e., the singular solutions). These two types of singularities are tightly related to each other, but the exact mapping is not well understood. In this paper, we have initiated the systematic study of the mapping. We have demonstrated the different mapping patterns using three typical situations, i.e., the factorization limit, the soft limit and the forward limit.

arXiv comment52 pages, 4 figures

References in corpus (54)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• 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
• Evidence for a New Soft Graviton Theorem
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Ambitwistor strings and the scattering equations at one loop
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• One-loop amplitudes on the Riemann sphere
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• One-loop Scattering Equations and Amplitudes from Forward Limit
• The Polynomial Form of the Scattering Equations
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Integration Rules for Loop Scattering Equations
• Gluons and gravitons at one loop from ambitwistor strings
• Scattering Equations and Feynman Diagrams
• Integration Rules for Scattering Equations
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Cross-ratio Identities and Higher-order Poles of CHY-integrand
• Computation of Contour Integrals on ${\mathcal{M}}_{0,n}$
• An Algebraic Approach to the Scattering Equations
• Massless scattering at special kinematics as Jacobi polynomials
• Scattering Equations and Global Duality of Residues
• Elimination and recursions in the scattering equations
• On the solutions of the scattering equations
• One-loop Correlators and BCJ Numerators from Forward Limits
• General Solution of the Scattering Equations
• Comments on the evaluation of massless scattering
• Scattering equations, generating functions and all massless five point tree amplitudes
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• 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
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
• 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
• Permutation Symmetry of the Scattering Equations
• One-Loop Yang-Mills Integrands from Scattering Equations
• The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes
• A Combinatoric Shortcut to Evaluate CHY-forms
• One-loop CHY-Integrand of Bi-adjoint Scalar Theory
• A differential operator for integrating one-loop scattering equations
• Bootstrapping solutions of scattering equations
• Analytical amplitudes from numerical solutions of the scattering equations
• Note on the Labelled tree graphs

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