Note on solutions of scattering equations

2021/05/31 by Bo Feng, Chang Hu, Yaobo Zhang
Computer Science · Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Algorithm #Classical mechanics #Factorization #Gravitational singularity #Kinematics #Limit (mathematics) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Optics #Physics #Polynomial and algebraic computation #Scattering #Scattering amplitude #Singularity #hep-th

paper · pdf · doi:10.1103/physrevd.105.036015

52 pages, 4 figures

arxiv created 2021/10/18 · openalex publication_date 2022/02/24 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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→ 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.

Citations

• Evidence for a New Soft Graviton Theorem
• New recursion relations for tree amplitudes of gluons
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Role of Möbius constants and scattering functions in Cachazo-He-Yuan scalar amplitudes
• CHY loop integrands from holomorphic forms
• Quadratic Feynman loop integrands from massless scattering equations
• Gluons and gravitons at one loop from ambitwistor strings