Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions

TL;DR

This paper develops new four-dimensional formulas for tree-level scattering amplitudes across multiple theories, clarifies relations between different mathematical forms, and explores double-soft theorems in supersymmetric contexts.

Contribution

It introduces novel formulas for amplitudes in non-linear sigma, Galileon, and super-DBI theories, and analyzes double-soft limits in these frameworks.

Findings

New formulas for tree amplitudes in several theories.

Clarification of relations between polynomial and rational scattering equations.

Analysis of double-soft theorems for various particle emissions.

Abstract

We study scattering equations and formulas for tree amplitudes of various theories in four dimensions, in terms of spinor helicity variables and on-shell superspace for supersymmetric theories. As originally obtained in Witten's twistor string theory and other twistor-string models, the equations can take either polynomial or rational forms, and we clarify the simple relation between them. We present new, four-dimensional formulas for all tree amplitudes in the non-linear sigma model, a special Galileon theory and the maximally supersymmetric completion of the Dirac-Born-Infeld theory. Furthermore, we apply the formulas to study various double-soft theorems in these theories, including the emissions of a pair of soft photons, fermions and scalars for super-amplitudes in super-DBI theory.