Scattering equations, twistor-string formulas and double-soft limits in four dimensions

• Published in: The journal of high energy physics Vol. 2016; no. 7; pp. 1 - 24
• Main Authors: He, Song, Liu, Zhengwen, Wu, Jun-Bao
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2016; Springer Nature B.V
• Subjects: Amplitudes; Classical and Quantum Gravitation; Elementary Particles; Formulas (mathematics); Helicity; High energy physics; Mathematical analysis; Mathematical models; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering; String Theory; Supersymmetry; Trees; Scattering Amplitudes; Spontaneous Symmetry Breaking; Effective field theories
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2016)060

A bstract 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.