On the solutions of the scattering equations

Abstract

This paper addresses the question, whether the solutions of the scattering equations in four space-time dimensions can be expressed as rational functions of the momentum twistor variables. This is the case for $n\le 5$ external particles. For general $n$ there are always two solutions, which are rational functions of the momentum twistor variables. However, the remaining solutions are in general not rational. In the case $n=6$ the remaining four solutions can be expressed as algebraic functions. These four solutions are constructed explicitly in this paper.

16 pages, version to be published, additional file with explicit expressions for eq.56 and eq.61 provided

Cited by in corpus (12)

• Black Hole Formation and Classicalization in Ultra-Planckian 2 -> N Scattering
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• Ambitwistor formulations of $R^2$ gravity and $(DF{)}^2$ gauge theories
• Scattering equations, generating functions and all massless five point tree amplitudes
• CHY-Graphs on a Torus
• Permutation Symmetry of the Scattering Equations
• The Scattering Variety
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• Characterizing the solutions to scattering equations that support tree-level ${\text{N}}^k\text{MHV}$ gauge/gravity amplitudes
• Sudakov Representation of the Cachazo-He-Yuan Scattering Equations Formalism