Sudakov Representation of the Cachazo-He-Yuan Scattering Equations Formalism

TL;DR

This paper introduces a Sudakov variable approach to simplify the solutions of scattering equations in the CHY formalism, revealing algebraic simplifications and straightforward puncture functions for four- and five-particle amplitudes.

Contribution

It presents a novel Sudakov variable framework that simplifies solving scattering equations and expressing amplitudes in the CHY formalism.

Findings

Sudakov variables simplify scattering equation solutions.

Punctures are simple functions of Sudakov parameters.

Phase choice reduces algebraic complexity.

Abstract

We show that the use of Sudakov variables greatly simplifies the study of the solutions to the scattering equations in the Cachazo-He-Yuan formalism. We work in the center-of-mass frame for the two incoming particles, which partially fixes the SL(2,C) redundancy in the integrand defining the scattering amplitudes, the remaining freedom translates into a global shift in the azimuthal angle of the outgoing particles. Studying four- and five-particle amplitudes, we see how an appropriate choice of this phase allows for algebraic simplifications when finding solutions to the scattering equations, as well as in the expression of the scattering amplitudes in terms of the locations of the punctures in the sphere. These punctures themselves are remarkably simple functions of the Sudakov parameters.